Deciding where to go is one of the primary challenges in designing an agent that can explore an unknown environment. Grid-worlds provide a flexible framework for representing different variations of this problem, allowing for various types of goals and constraints. Typically, agents move one cell at a time, gathering new information at each time step. However, recomputing a new action after each step can lead to unintended behaviors, such as indecision and forgetting about previous goals. To mitigate this, we define a set of persistent feature layers that can be used by either a linear weighted policy or a neural network approach to identify potential destination locations. The outputs of these policies are processed using knowledge of the environment to ensure that objectives are met in a timely and effective manner. We demonstrate how to train and evaluate a U-Net model in a custom grid-world environment and provide guidance and suggestions for how to use this approach to build complex agent behaviors.

or respiratory illnesses due to heart-related issues are often misdiagnosed, under-diagnosed or ignored at early stages. Continuous health monitoring using ambient sensors has the potential to ameliorate this problem for older adults at aging-in-place facilities. In this paper, we leverage continuous respiratory health data collected by using ambient hydraulic bed sensors installed in the apartments of older adults in aging-in-place Americare facilities to find data-adaptive indicators related to shortness of breath. We used unlabeled data collected unobtrusively over the span of three years from a COPD-diagnosed individual and used data mining to label the data. These labeled data are then used to train a predictive model to make future predictions in older adults related to shortness of breath abnormality. To pick the continuous changes in respiratory health we make predictions for shorter time windows (60-s). Hence, to summarize each day's predictions we propose an abnormal breathing index (ABI) in this paper. To showcase the trajectory of the shortness of breath abnormality over time (in terms of days), we also propose trend analysis on the ABI quarterly and incrementally. We have evaluated six individual cases retrospectively to highlight the potential and use cases of our approach.

The spatial configuration of objects in a scene is important to many applications. In particular, 3D environments constructed from point cloud observations are often used for navigation and planning with real-time requirements. In these settings, the ability to recognize and distinguish one set of objects from another may depend largely on how they are positioned with respect to each other. In this article, we explore two different approaches for describing the relative spatial relationship between two objects represented as 3D points: the histogram of forces, and a method using bounding boxes and fuzzy numbers. We use 2D axis-aligned projections of the objects to facilitate the computation of force histograms, and compare this approach to the bounding box and fuzzy number method. Our experiments are performed on the NPM3D dataset, consisting of hand-labeled point cloud objects in an outdoor street-level environment. The results highlight the strengths and weaknesses of each approach and we discuss the most appropriate applications for both.

Fuzzy C-means (FCM) has been a prominent clustering algorithm for a long time. It was extended to a type-2 framework by the Linguistic Fuzzy C-means (LFCM) that operates on vectors of fuzzy numbers utilizing the extension principle, the decomposition theorem, and interval analyses. The purpose of this paper is to study the effects of the iterative type-2 fuzzy clustering algorithm. The LFCM incorporates uncertainty through type-2 fuzzy sets, but it is prone to membership spread, i.e., the uncertainty in a membership function can become too large or broad during the iterative alternating optimization procedure. We devise three dampening approaches to mitigate the problem. Vertical cut dampening, linear dampening, and reflection dampening are defined along with the experiments conducted on a synthetic dataset named the butterfly dataset. We also illustrate the updated memberships (fuzzy numbers) and the resulting cluster prototypes (fuzzy vectors) from visual standpoints. Applying any of these dampening approaches will result in thinner membership functions and helps us control the uncertainty not to grow rapidly, and in fact, aid in convergence.

The ability to explain the predictions of machine learning models has become increasingly important, especially in healthcare applications. Streaming clustering is an effective tool to recognize normal baseline patterns and to detect early signs of changes in data streams. However, many streaming clustering algorithms are not designed to explain to the users how predictions are made. In this paper, we extend a streaming clustering algorithm, the sequential possibilistic Gaussian mixture model (SPGMM) for early detection of health change to provide algorithm explainability for the results. Four approaches are discussed to explain either the cluster differences or the reason for the algorithm warnings: (i) linguistic summarization for warnings; (ii) annotation distribution of clusters; (iii) SHapley Additive exPlanations (SHAP); (iv) functional health score. The four approaches are validated on one older adult monitored with a collection of motion, bed, and depth sensors over three years. The results obtained on the older adult show that the four approaches aid understanding of how the clusters and warnings are generated, providing strong support for clinicians to take corresponding actions.

Synthetic aperture sonar (SAS) imagery is crucial for several applications, including target recognition and environmental segmentation. Deep learning models have led to much success in SAS analysis; however, the features extracted by these approaches may not be suitable for capturing certain textural information. To address this problem, we present a novel application of histogram layers on SAS imagery. The addition of histogram layer(s) within the deep learning models improved performance by incorporating statistical texture information on both synthetic and real-world datasets.

Recently, computer vision tasks such as classification and object detection have been dominated by deep neural net-work (DNN) approaches. As DNN methodologies have matured, researchers have found that some of the most common DNN techniques result in models that are highly dependent upon the textures and colors of the imagery, rather than the shape, leading to suboptimal network performance. This problem can be especially problematic in the remote sensing domain, where the discrimination of objects for classification or detection may rely heavily on their shape. To combat this lack of shape bias in DNNs, a network was developed to integrate the Differential Morphological Profile (DMP), an image processing technique for shape extraction, with standard convolutional DNNs for performing computer vision tasks on High Resolution Remote Sensing Imagery (HR-RSI). Previously, this network, known as DMPNet, has been applied to both classification and object detection in HR-RSI with high levels of success. However, the hyper-parametric nature of DMPNet structure required researchers to carefully select the parameters of shape extraction, a choice that could greatly help or hinder DMPNet performance. In this study, we utilize a evolutionary computation algorithm (ECA) to learn the parameters of shape extraction from the data presented to the DMPNet for object detection. Our results show that our DMP-enabled detection models perform better object detection in HR-RSI using an ECA to learn shape extraction parameters than manually selected parameters on the same dataset.

Feature representation is an important aspect of remote-sensing-based image classification. While deep convolutional neural networks (DCNNs) are able to effectively amalgamate information, large numbers of parameters often make learned features inscrutable and difficult to transfer to alternative models. In order to better represent statistical texture information for remote-sensing image classification, in this letter, we investigate performing joint dimensionality reduction (DR) and classification using a novel histogram neural network. Motivated by a popular DR approach, t-distributed stochastic neighbor embedding (t-SNE), our proposed method incorporates a classification loss computed on samples in a low-dimensional embedding space. We compare the learned sample embeddings against coordinates found by t-SNE in terms of classification accuracy and qualitative assessment. We also explore the use of various divergence measures in the t-SNE objective. The proposed method has several advantages such as readily embedding out-of-sample points and reducing feature dimensionality while retaining class discriminability. Our results show that the proposed approach maintains and/or improves classification performance and reveals characteristics of features produced by neural networks that may be helpful for other applications.

Time series analysis has been an active area of research for years, with important applications in forecasting or discovery of hidden information such as patterns or anomalies in observed data. In recent years, the use of time series analysis techniques for the generation of descriptions and summaries in natural language of any variable, such as temperature, heart rate or CO2 emission has received increasing attention. Natural language has been recognized as more effective than traditional graphical representations of numerical data in many cases, in particular in situations where a large amount of data needs to be inspected or when the user lacks the necessary background and skills to interpret it. In this work, we describe a novel mechanism to generate linguistic descriptions of time series using natural language and fuzzy logic techniques. The proposed method generates quality summaries capturing the time series features that are relevant for a user in a particular application, and can be easily customized for different domains. This approach has been successfully applied to the generation of linguistic descriptions of bed restlessness data from residents at TigerPlace (Columbia, Missouri), which is used as a case study to illustrate the modeling process and show the quality of the descriptions obtained.

Three dimensional point cloud data sets are easy to acquire and manipulate, but are often too large to process directly for embedded real-time applications. The spatial information in a point cloud can be represented in a variety of reduced forms, such as voxel grids, Gaussian mixture models, or spatial semantic structures. In this article, we show how a segmented point cloud can be represented as a spatial relationship graph using bounding boxes and triangular fuzzy numbers. This model is a lightweight encoding of the relative distance and direction between objects, and can be used to describe and query for particular spatial configurations using linguistic terms in a multicriteria framework. We show how this approach can be applied on a hand-segmented subset of the NPM3D data set with several illustrative examples. The work herein has useful applications in many applied domains, such as human-robot interaction with unmanned aerial systems.

Synthetic Aperture Sonar (SAS) surveys produce imagery with large regions of transition between seabed types. Due to these regions, it is difficult to label and segment the imagery and, furthermore, challenging to score the image segmentations appropriately. While there are many approaches to quantify performance in standard crisp segmentation schemes, drawing hard boundaries in remote sensing imagery where gradients and regions of uncertainty exist is inappropriate. These cases warrant weak labels and an associated appropriate scoring approach. In this paper, a labeling approach and associated modified version of the Rand index for weakly-labeled data is introduced to address these issues. Results are evaluated with the new index and compared to traditional segmentation evaluation methods. Experimental results on a SAS data set containing must-link and cannot-link labels show that our Weakly-Labeled Rand index scores segmentations appropriately in reference to qualitative performance and is more suitable than traditional quantitative metrics for scoring weakly-labeled data.

In this work, we present an in-depth and systematic analysis using tools such as local interpretable model-agnostic explanations (LIME) [1] and divergence measures to analyze what changes lead to improvement in performance in fine tuned models for synthetic aperture sonar (SAS) data. We examine the sensitivity to factors in the fine tuning process such as class imbalance. Our findings show not only an improvement in seafloor texture classification, but also provide greater insight into what features play critical roles in improving performance as well as a knowledge of the importance of balanced data for fine tuning deep learning models for seafloor classification in SAS imagery.

The rapid aging of the population worldwide requires increased attention from healthcare providers and the entire society. For the elderly to live independently, many health issues related to old age, such as frailty and risk of falling, need increased attention and monitoring. When monitoring daily routines for older adults, it is desirable to detect the early signs of health changes before serious health events, such as hospitalizations, happen so that timely and adequate preventive care may be provided. By deploying multi-sensor systems in homes of the elderly, we can track trajectories of daily behaviors in a feature space defined using the sensor data. In this article, we investigate a methodology for tracking the evolution of the behavior trajectories over long periods (years) using high-dimensional streaming clustering and provide very early indicators of changes in health. If we assume that habitual behaviors correspond to clusters in feature space and diseases produce a change in behavior, albeit not highly specific, tracking trajectory deviations can provide hints of early illness. Retrospectively, we visualize the streaming clustering results and track how the behavior clusters evolve in feature space with the help of two dimension-reduction algorithms: Principal Component Analysis and t-distributed Stochastic Neighbor Embedding. Moreover, our tracking algorithm in the original high-dimensional feature space generates early health warning alerts if a negative trend is detected in the behavior trajectory. We validated our algorithm on synthetic data and tested it on a pilot dataset of four TigerPlace residents monitored with a collection of motion, bed, and depth sensors over 10 years. We used the TigerPlace electronic health records to understand the residents’ behavior patterns and to evaluate the health warnings generated by our algorithm. The results obtained on the TigerPlace dataset show that most of the warnings produced by our algorithm can be linked to health events documented in the electronic health records, providing strong support for a prospective deployment of the approach.

The purpose of this article is twofold. First, and foremost, it fixes an error that somehow made it through all the reviewing, both by the authors and the referees. Second, it provides insights into the meaning and variation of the main PCM parameters in this approach to transfer clustering.

Traditional machine learning and data mining have made tremendous progress in many knowledge-based areas, such as clustering, classification, and regression. However, the primary assumption in all of these areas is that the training and testing data should be in the same domain and have the same distribution. This assumption is difficult to achieve in real-world applications due to the limited availability of labeled data. Associated data in different domains can be used to expand the availability of prior knowledge about future target data. In recent years, transfer learning has been used to address such cross-domain learning problems by using information from data in a related domain and transferring that data to the target task. In this article, a transfer-learning possibilistic c-means (TLPCM) algorithm is proposed to handle the PCM clustering problem in a domain that has insufficient data. Moreover, TLPCM overcomes the problem of differing numbers of clusters between the source and target domains. The proposed algorithm employs the historical cluster centers of the source data as a reference to guide the clustering of the target data. The experimental studies presented here were thoroughly evaluated, and they demonstrate the advantages of TLPCM in both synthetic and real-world transfer datasets.

While most deep learning architectures are built on convolution, alternative foundations such as morphology are being explored for purposes such as interpretability and its connection to the analysis and processing of geometric structures. The morphological hit-or-miss operation has the advantage that it considers both foreground information and background information when evaluating the target shape in an image. In this article, we identify limitations in the existing hit-or-miss neural definitions and formulate an optimization problem to learn the transform relative to deeper architectures. To this end, we model the semantically important condition that the intersection of the hit and miss structuring elements (SEs) should be empty and present a way to express Don't Care (DNC), which is important for denoting regions of an SE that are not relevant to detecting a target pattern. Our analysis shows that convolution, in fact, acts like a hit-to-miss transform through semantic interpretation of its filter differences. On these premises, we introduce an extension that outperforms conventional convolution on benchmark data. Quantitative experiments are provided on synthetic and benchmark data, showing that the direct encoding hit-or-miss transform provides better interpretability on learned shapes consistent with objects, whereas our morphologically inspired generalized convolution yields higher classification accuracy. Finally, qualitative hit and miss filter visualizations are provided relative to single morphological layer.

This article is a position paper about models and algorithms that are generally called “stream clustering.” Semantics and methods used in this field are often co-opted from static clustering, but they do not serve well for streaming data analysis. Most “state-of-the-art” methods, such as sequential k-means, Birch, CluStream, DenStream, etc., acknowledge that the data are seen but once in real streaming analysis (e.g., intrusion detection, voter fraud, etc.). Interpretation of their outputs generally overlooks the fact that when the data cannot be saved, batch clustering ideas, such as preclustering assessment, partitioning, and cluster validity are not relevant. But in the current literature, the data, or some subset of it, are often saved for hindsight evaluation (we call this fake stream clustering). Our position? Useful analysis of real streaming data is in its infancy. We do not argue that current approaches to streaming clustering are wrong: rather, we regard them as transitional methods which will eventually lead to a new and useful paradigm for this type of computation. We think that this class of models and algorithms are actually classifiers, but with a special added component, viz., continuously updated cluster footprints of the instream processing. We need to carefully define the objectives of streaming analysis, and then choose terminology and methods that suit this evolving paradigm.

Fuzzy integrals are useful general purpose aggregation operators, but they can be difficult to understand and visualize in practice. The interaction between an exponentially increasing number of variables-2nfuzzy measure variables for n inputs-makes it hard to understand what exactly is going on in a high dimensional space. We propose a new visualization scheme based on a weighted indicator matrix to better understand the inner workings of an arbitrary fuzzy measure. We provide ways of viewing the Shapley and interaction indices, as well as an optional data coverage histogram. This approach can give insight into which sources are the most relevant in the overall aggregation and decision making process, and it provides a way to visually compare fuzzy measures and subsequently integrals.

In this paper, a new fuzzy granular approach for modeling color categories is proposed. Fuzzy granular colors where introduced by some of the authors as a way to model color categories with non-convex membership functions, particularly those categories that can be defined in terms of the union of a finite collection of sub-categories (which are very commonly found and applied in practice). To build a granular color, an aggregation of fuzzy colors having semantic relationships, the so-called "granules", is performed. In this paper we introduce the use of Voronoi tessellations for modelling the granules, comparing its behavior with respect to a sphere-based approach. We illustrate the advantages of our approach with respect to current state of the art on the basis of some experiments.

To apply clustering algorithms to big data, or to build clustering ensembles, it is a standard process to sample the original data set in a way that hopefully spans the original distribution. There are at least six ways to initialize the Maximin (MM) sampling algorithm. This paper contains experiments to determine whether samples produced by the six methods differ significantly; and whether they are superior to simple random sampling. Empirical evidence supports two conclusions. First, there is not enough difference in MM samples generated by the six initializations to support using any but the least costly method: viz., using the first sample in the data as the first MM point. Second, unless the input data have subsets (clusters) that are compact and separated in a well-defined sense, random sampling is demonstrably superior to MM sampling for even small data sets.

Artificial neural networks are a dominant force in our modern era of data-driven artificial intelligence. The adaptive neuro fuzzy inference system (ANFIS) is a neural network based on fuzzy logic versus a more traditional premise like convolution. Advantages of ANFIS include the ability to encode and potentially understand machine learned neural information in the pursuit of explainable, interpretable, and ultimately trustworthy artificial intelligence. However, real-world data is almost always imperfect, e.g., incomplete or noisy, and ANFIS is not naturally robust. Specifically, ANFIS is susceptible to over inflated uncertainty, poor antecedent (fuzzy set) data alignment, degenerate optimization conditions, and hard to interpret logic, to name a few factors. Herein, we explore the use of possibilistic clustering to identify outliers, specifically typicality degrees, to increase the robustness of ANFIS; or any fuzzy logic neuron/network. Experiments are presented that demonstrate the need and quality of the proposed solutions in the pursuit of robust interpretable machine learned neuro fuzzy logic solutions.

Clustering has long been applied to the problem of image segmentation. Because of spatial connectivity constraints, several approaches have been proposed to incorporate local consistency into image segmentation by clustering. One popular method, the fuzzy local information c-means (FLICM) has been shown to produce good segmentation results. Like the fuzzy cmeans (FCM) from which it is derived, FLICM requires that pixels "share" memberships across clusters, that is, the memberships of a pixel across all clusters need to sum to one. The possibilistic c-means (PCM) clustering was introduced to relax the membership sum-to-one constraint of the FCM, and has found a place in the clustering universe, particularly in those situations where the data contains outliers, is noisy, or highly overlapped. This paper extends the structure of FLICM to possibilistic versions for image segmentation. Two approaches are proposed. The first, called possibilistic local information cmeans (PLICM) inserts the local information term of FLICM into the basic PCM model. PLICM, like PCM, can produce coincident cluster centers. Recently, a sequential application of PCM (with c = 1) has been developed to mitigate negative effects of the co-incident cluster formation. Three algorithms form the family of sequential possibilistic 1-means (SP1M). These algorithms are extended to account for local information in image segmentation (SPLI1M). After development of the approach, experiments are performed on images which show that the SPLI1M family has superior performance in image segmentation over FLICM, PLICM and other clustering algorithms that don't combine local spatial information of the image.

In this paper, we introduce fuzzy granular colors for modeling color categories. Fuzzy granular colors are built by aggregating fuzzy colors having semantic relationships with regard to a certain color category. Our proposal allows us to model color categories which comprise disjoint fuzzy subsets of colors, as well as those having a nonconvex representation in the color space, among other advantages. Such categories are used very often by humans in different real contexts. Fuzzy granular colors are appropriate to provide color models able to deal with ill-defined boundaries, subjectivity, and context-dependence. We illustrate the advantages of our approach with respect to current state of the art with several experiments.

Information fusion is an essential part of numerous engineering systems and biological functions, e.g., human cognition. Fusion occurs at many levels, ranging from the low-level combination of signals to the high-level aggregation of heterogeneous decision-making processes. While the last decade has witnessed an explosion of research in deep learning, fusion in neural networks has not observed the same revolution. Specifically, most neural fusion approaches are ad hoc, are not understood, are distributed versus localized, and/or explainability is low (if present at all). Herein, we prove that the fuzzy Choquet integral (ChI), a powerful nonlinear aggregation function, can be represented as a multilayer network, referred to hereafter as ChIMP. We also put forth an improved ChIMP (iChIMP) that leads to a stochastic-gradient-descent-based optimization in light of the exponential number of ChI inequality constraints. An additional benefit of ChIMP/iChIMP is that it enables explainable artificial intelligence (XAI). Synthetic validation experiments are provided, and iChIMP is applied to the fusion of a set of heterogeneous architecture deep models in remote sensing. We show an improvement in model accuracy, and our previously established XAI indices shed light on the quality of our data, model, and its decisions.

Using non-wearable sensors in eldercare monitoring is a promising solution for improving care and reducing healthcare costs. Abnormal sensor patterns produced by certain resident behaviors can be linked to early signs of illness. We propose an unsupervised framework for detecting abnormal sensor patterns based on clustering activity sensor sequences. We use a 30-day normal window to build a baseline model of an elderly resident by clustering the activity sequences from these days. Each cluster represents different daily activities that are performed in most (normal) days and correspond to normal routines. If a new day contains fewer routine activities, we flag it as abnormal and label the day as one with a possible sign of early illness. A preliminary analysis of the method was conducted on data collected in TigerPlace, an eldercare facility that promotes aging-in-place, with information from our electronic health records (EHR). On a pilot sensor dataset from three residents, with a total of 1902 days, we achieved an average abnormal events prediction of 0.75.

In this paper, we consider the problem of choosing a least-cost path from a graph that is attributed with multiple fuzzy weights. The cost of a path is determined by multiple conflicting objectives that seek to minimize either the total or maximum values of each feature over the length of the path. We present a framework for evaluating paths with various agent preferences. Our method allows the agent to pick any Pareto optimal path and can be used within a larger framework to model decision-making behavior. Our approach is demonstrated on a hand-crafted example problem.

In this paper, we present an incremental version of the Partition Coefficient and Exponential Separation (PCAES) cluster validity index in the context of streaming data analysis. Incremental PCAES (iPCAES) can be used to monitor evolving structures in streaming data. We investigate the use of the proposed index to understand and analyze the performance of the MU Streaming Clustering (MUSC) algorithm. Synthetic and real-life streaming datasets are used to demonstrate the benefits that can be drawn from such indices such as the appearance of a new structure in the data stream, handling of outlier data samples, and the effect of the streaming sample order on the resultant cluster history. We compare the performance of iPCAES index with the incremental Davies-Boudin index (iDB) because iDB was found to be the most stable among other incremental indices that offer comparable approaches.

With the increasing use of intelligent systems to make sense of data, lately, explainable AI systems are gaining a lot of traction. A distance measure that can distinguish data sets in linguistic terms can help AI systems in achieving explainability. We make use of Linguistic Protoform Summaries in tandem with Fuzzy Rules to design a system that can compare datasets numerically, as well as explain the difference in Natural Language. We validate our method with the help of synthetic data and show that it produces high correlation with the well-known Euclidean distance measure. We also employ the proposed method to explain changes in daily pulse rate measurements of an elderly resident living in a sensor equipped smart home. We postulate that the method will help in future endeavors to produce explainable pattern recognition systems.

Herein, a generalization of the ordered weighted average (OWA) is put forth relative to pattern recognition. The resultant linear order statistic neuron (LOSN) is unique in that it bridges fuzzy sets, specifically fuzzy data/information aggregation, with neural networks. This article discusses the gradient descent-based optimization and geometric interpretation of the LOSN. An advantage is that the LOSN is an efficient shared weight encoding of N! perceptrons, relative to N inputs. Open source codes are provided to facilitate reproducible research. Experiments are conducted to both validate the method and show its non-linear geometric expression.

Data stream processing has gained much attention lately, in the era of big data. Streaming clustering is an effective tool to recognize normal baseline and to detect outliers in sequentially presented data. Perhaps more importantly would be the ability to predict that incoming data indicates movement towards a likely anomaly. In this paper, a Gaussian Mixture Model (GMM) is employed to represent different patterns in the data stream. The Sequential Possibilistic One-Means (SP1M) is used for initialization, and is incorporated into the GMM framework to recognize new mixture components in the data stream. The new proposed algorithm is called Sequential Possibilistic Gaussian Mixture Model (SPGMM). Furthermore, two methods of trajectory analysis, the “maximum typicality decline” and the “trend value measurement,” are used together with SPGMM to detect early signs of pattern changes before unusual pattern data arrive in the stream. The proposed SPGMM is tested on synthetic and real-world datasets, and is shown to have excellent performance on predicting early signs of pattern changes in these sequential streams.

The quality of sleep has a significant impact on health and life. This study adopts the structure of hierarchical classification to develop an automatic sleep stage classification system using ballistocardiogram (BCG) signals. A leave-one-subject-out cross validation (LOSO-CS) procedure is used for testing classification performance. Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM), and Deep Neural Networks DNNs are complementary in their modeling capabilities; while CNNs have the advantage of reducing frequency variations, LSTMs are good at temporal modeling. A transfer learning (TL) technique is used to pre-train our CNN model on posture data and then fine-tune it on the sleep stage data. We used a ballistocardiography (BCG) bed sensor to collect both posture and sleep stage data to provide a non-invasive, in-home monitoring system that tracks changes in health of the subjects over time. Polysomnography (PSG) data from a sleep lab was used as the ground truth for sleep stages, with the emphasis on three sleep stages, specifically, awake, rapid eye movement (REM) and non-REM sleep (NREM). Our results show an accuracy of 95.3%, 84% and 93.1% for awake, REM and NREM respectively on a group of patients from the sleep lab.

In this paper, we study the internal incremental Davies-Bouldin (iiDB) cluster validity index in the context of streaming data analysis. We extend the original index to a more general version parameterized by the exponent of membership weights. Then we illustrate how the iiDB can be used to analyze and understand the performance of the Extended Robust Online Streaming Clustering (EROLSC) algorithm. We give examples that illustrate the appearance of a new cluster, the effect of different cluster sizes, handling of outlier data samples, and the effect of the input order on the resultant cluster history.

The Possibilistic C-Means (PCM) was developed as an extension of the Fuzzy C-Means (FCM) by abandoning the membership sum-to-one constraint. In PCM, each cluster is independent of the other clusters, and can be processed separately. Thus, the Sequential Possibilistic One-Means (SP1M) was proposed to find clusters sequentially by running P1M C times. One critical problem in both PCM and SP1M is how to determine the parameter η. The Sequential Possibilistic One Means with Adaptive Eta (SP1M-AE) was developed to allow η to change during iterations. In this paper, we introduce a new dynamic adaption mechanism for the parameter η in each cluster and apply it into SP1M. The resultant algorithm, called the Sequential Possibilistic One-Means with Dynamic Eta (SP1M-DE) is shown to provide superior performance over PCM, SP1M, and SP1M-AE in determining correct clustering results.

Online clustering has attracted attention due to the explosion of ubiquitous continuous sensing. Streaming clustering algorithms need to look for new structures and adapt as the data evolves, such that outliers are detected, and that new emerging clusters are automatically formed. The performance of a streaming clustering algorithm needs to be monitored over time to understand the behavior of the streaming data in terms of new emerging clusters and number of outlier data points. Small datasets with 2 or 3 dimensions can be monitored by plotting the clustering results as data evolves. However, as the size and dimensions of streaming data increase, plotting the clustering result becomes unfeasible. Therefore, incremental internal Validity Indices (iCVIs) could be applied for monitoring the performance of an online clustering algorithm. In this paper, we study the internal incremental Davies-Bouldin (iDB) cluster validity index in the context of big streaming data analysis. Also, we study the effect of large number of samples on the values of the iCVI (iDB). Finally, we propose a way to project streaming data into a lower space for cases where the distance measure does not perform as expected in the high dimensional space.

Presents a brief historical review of the various Editors in Chief of the IEEE Transactions on Fuzzy Systems.

Predicting early signs of illness in older adults by utilizing a continuous, unobtrusive nursing home monitoring system has been shown to increase the quality of life and decrease the cost of care. Illness prediction is based on sensor data such as motion and bed and uses algorithms such as support vector machine (SVM) or k-nearest neighbor (kNN). One of the greatest challenges in developing prediction algorithms for sensor networks is utilizing knowledge from previous residents for predicting behavior in new ones. In this paper, we employ a transfer learning approach for addressing the cross resident training problem. We validate our method by conducting a retrospective study on three residents from TigerPlace, a retirement community in Columbia, MO, where apartments are fitted with wireless networks of motion and bed sensors. The ground truth, the daily presence or absence of the illness, was manually evaluated using nursing visit reports from an homegrown electronic medical record (EMR) system. In this study, transfer learning SVM approach outperformed other three methods, regular SVM, one class SVM, and one class kNN, resulting in average areas under the curve (AUCs) of 0.74, 0.52, 0.60 and 0.62 for three residents, respectively.

Eldercare monitoring using non-wearable sensors is a candidate solution for improving care and reducing costs. Abnormal sensor patterns produced by certain resident behaviors could be linked to early signs of illness. We propose an unsupervised method for detecting abnormal behavior patterns based on a new context preserving representation of daily activities. A preliminary analysis of the method was conducted on data collected in TigerPlace, an eldercare facility that promotes aging-in-place. Sensors firings of each day are converted into sequences of daily activities. Using the proposed method, a day with hundreds of sequences is converted into a single data point representing that day and preserving the context of the daily routine at the same time. We obtained an average Area Under the Curve (AUC) of 0.9 in detecting days where elder adults need to be assessed.

Fuzzy c-means (FCM) clustering is known to be sensitive to outliers and noise. Possibilistic c-means (PCM) has been reported to be more robust against outliers and noise but may yield coincident clusters. We introduce a variant of PCM called sequential possibilistic one-means (SP1M) that finds clusters sequentially, takes into account the previously found clusters for initialization, and discards coincident clusters. Experiments with the well-known BIRCH benchmark data set and two variants of BIRCH indicate that SP1M is able to find a significantly larger percentage of the clusters contained in the data, with about twice as many cluster update steps, but significantly faster than FCM and PCM.

In this paper, we present two greedy, myopic algorithms for solving the partially observable travelling salesman problem. Although not optimal from a decision-theoretic viewpoint, these strategies are shown to perform reasonably well under the uncertain conditions of the environment. The first algorithm is a strictly greedy algorithm and has no tunable parameters, whereas the second algorithm uses Monte Carlo sampling to determine likely configurations of the environment and applies value iteration to pick an action. We present both approaches with illustrative examples and empirically demonstrate their relative strengths and weaknesses.

The Multiple Instance Choquet integral (MICI) for classifier fusion and an evolutionary algorithm for parameter estimation is presented. The Choquet integral has a long history of providing an effective framework for non-linear fusion. However, previous methods to learn an appropriate measure for the Choquet integral required accurate and precise training labels. In many applications, data-point specific labels are unavailable and infeasible to obtain. The proposed MICI algorithm allows for training with uncertain labels in which class labels are provided for sets of data points (i.e., “bags”) instead of individual data points (i.e., “instances”). The proposed algorithm is able to fuse multiple two-class classifier outputs by learning a monotonic and normalized fuzzy measure from uncertain training labels using an evolutionary algorithm. It produces enhanced classification performance by computing Choquet integral with the learned fuzzy measure. Results on both simulated and real hyperspectral data are presented in the paper.

A Gaussian mixture model (GMM), coupled with possibilistic clustering is used to build an adaptive system for analyzing streaming multi-dimensional activity feature vector with the goal of identifying signs of early diseases. The system is based on temporal analysis, including outlier detection, customization and adaption to new changes, together with the creation of new components for GMM in the case of emerging new normal patterns. On the other hand, an alert will be fired when detecting unexpected behavior patterns. When dealing with streaming data from embedded sensors in an eldercare environment, every resident has their unique behavior pattern. Therefore, number of Gaussians for the GMM needs to be individually determined. For this reason, possibilistic C-Means (PCM) and Automatic Merging possibilistic Clustering Method (AMPCM) are combined together to cluster the initial data points, detect anomalies and initialize the GMM. The system achieves our goals when tested on the synthetic datasets simulating an extended period of time. We hope that by applying the proposed system in real datasets, it will help by detecting health changes before real health issue happens.

As the number of features in pattern recognition applications continuously grows, new algorithms are necessary to reduce the dimensionality of the feature space while producing comparable results. For example, a dynamic area of research, activity recognition, produces large quantities of high-velocity, high-dimensionality data that require real time classification. While dimensionality reduction approaches such as principle component analysis (PCA) and feature selection work well for datasets of reasonable size and dimensionality, they fail on big data. A possible approach to classification of high-dimensionality datasets is to combine a typical classifier, fuzzy k-nearest neighbor in our case (FKNN), with feature reduction by random projection (RP). As opposed to PCA where one projection matrix is computed based on least square optimality, in RP, a projection matrix is chosen at random multiple times. As the random projection procedure is repeated many times, the question is how to aggregate the values of the classifier obtained in each projection. In this paper we present a fusion strategy for RP FKNN, denoted as RPFKNN. The fusion strategy is based on the class membership values produced by FKNN and classification accuracy in each projection. We test RPFKNN on several synthetic and activity recognition datasets.

The Johnson-Lindenstrauss (JL) lemma, with known probability, sets a lower bound q0on the dimension for which a random projection of p-dimensional vector data is guaranteed to be within (1±ε) of being an isometry in a randomly projected downspace. We study several ways to identify a “good” rogue random projection when the target downspace has dimensions below the JL limit. The tools used towards this end are Pearson and Spearman correlation coefficients, and a visual imaging method (a cluster heat map) that usually reveals cluster structure in spaces of any dimension. We use four synthetic data sets and the ubiquitous Iris data to study our procedures for tracking the reliability of RRPs. Unsurprisingly, rogue random projection is quite unpredictable. At its best, it is every bit as good as Principal Components Analysis, but at it's worst, it is awful. Pearson and Spearman correlations do signal good and bad projections, but the visual imaging method seems even more effective in determining the quality of RRPs.

Linguistic summaries provide a promise for extracting useful information from large datasets and present them in the form of natural language. Their applications can be found in various disciplines such as eldercare, financial time series etc. In this work we focus on linguistic protoform summaries and point out at some problems associated with the truth value computation methods present in literature. We develop a technique which produces more intuitive truth values for three different kinds of linguistic protoform summaries and illustrate this with help of some examples. Moreover, we show through a mathematical proof that our method is very robust and the truth values always follow the semantic order of the language they are representing.

Many contemporary biomedical applications such as physiological monitoring, imaging, and sequencing produce large amounts of data that require new data processing and visualization algorithms. Algorithms such as principal component analysis (PCA), singular value decomposition and random projections (RP) have been proposed for dimensionality reduction. In this paper we propose a new random projection version of the fuzzy c-means (FCM) clustering algorithm denoted as RPFCM that has a different ensemble aggregation strategy than the one previously proposed, denoted as ensemble FCM (EFCM). RPFCM is more suitable than EFCM for big data sets (large number of points, n). We evaluate our method and compare it to EFCM on synthetic and real datasets.

This paper presents an approach to designing a strategy for the game of Geister using the three main research areas of computational intelligence. We use a goal-based fuzzy inference system to evaluate the utility of possible actions and a neural network to estimate unobservable features (the true natures of the opponent ghosts). Finally, we develop a coevolutionary algorithm to learn the parameters of the strategy. The resulting autonomous gameplay agent was entered in a global competition sponsored by the IEEE Computational Intelligence Society and finished second among eight participating teams.

Complex activities such as instrumental activities of daily living (IADLs) can be identified by creating a hierarchical model of fuzzy rules. In this work, we present a framework to model a specific IADL — "making the bed". For this activity recognition, the need for a three level Fuzzy Inference System (FIS) model is shown. Simple features such as bounding box parameters were extracted from the foreground images and combined with 3D features extracted from the Kinect depth data. This was then fed as input to the three layered FIS for further analysis. Data collected from several participants were tested and evaluated. Such a framework can be used to model several other IADLS as well as basic activities of daily living (ADLs). Analysis of ADLs can be used to compare daily patterns in older adults to measure changes in behavior. This can then be used to predict health changes to assist older adults in leading independent lifestyles for longer time periods.

The fuzzy integral (FI) is an extremely flexible aggregation operator. It is used in numerous applications, such as image processing, multicriteria decision making, skeletal age-at-death estimation, and multisource (e.g., feature, algorithm, sensor, and confidence) fusion. To date, a few works have appeared on the topic of generalizing Sugeno's original real-valued integrand and fuzzy measure (FM) for the case of higher order uncertain information (both integrand and measure). For the most part, these extensions are motivated by, and are consistent with, Zadeh's extension principle (EP). Namely, existing extensions focus on fuzzy number (FN), i.e., convex and normal fuzzy set- (FS) valued integrands. Herein, we put forth a new definition, called the generalized FI (gFI), and efficient algorithm for calculation for FS-valued integrands. In addition, we compare the gFI, numerically and theoretically, with our non-EP-based FI extension called the nondirect FI (NDFI). Examples are investigated in the areas of skeletal age-at-death estimation in forensic anthropology and multisource fusion. These applications help demonstrate the need and benefit of the proposed work. In particular, we show there is not one supreme technique. Instead, multiple extensions are of benefit in different contexts and applications.

We present an approach for activity state recognition implemented on data collected from various sensors-standard web cameras under normal illumination, web cameras using infrared lighting, and the inexpensive Microsoft Kinect camera system. Sensors such as the Kinect ensure that activity segmentation is possible during the daytime as well as night. This is especially useful for activity monitoring of older adults since falls are more prevalent at night than during the day. This paper is an application of fuzzy set techniques to a new domain. The approach described herein is capable of accurately detecting several different activity states related to fall detection and fall risk assessment including sitting, being upright, and being on the floor to ensure that elderly residents get the help they need quickly in case of emergencies and ultimately to help prevent such emergencies.

We present a model for the analysis of time series sensor data collected at an eldercare facility. The sensors measure restlessness in bed and bedroom motion of residents during the night. Our model builds sets of linguistic summaries from the sensor data that describe different events that may occur each night. A dissimilarity measure produces a distance matrix D between selected sets of summaries. Visual examination of the image of a reordered version of D provides an estimate for the number of clusters to seek in D. Then, clustering with single linkage or non-Euclidean relational fuzzy c-means produces groups of summaries. Subsequently, each group is represented by a linguistic medoid prototype. The prototypes can be used for resident monitoring, two types of anomaly detection, and interresident comparisons. We illustrate our model with real data for two residents collected at TigerPlace: the “aging in place” facility in Columbia, MO, USA.

We present algorithms to segment the activities of sitting and standing, and identify the regions of sit-to-stand (STS) transitions in a given image sequence. As a means of fall risk assessment, we propose methods to measure STS time using the 3-D modeling of a human body in voxel space as well as ellipse fitting algorithms and image features to capture orientation of the body. The proposed algorithms were tested on ten older adults with ages ranging from 83 to 97. Two techniques in combination yielded the best results, namely the voxel height in conjunction with the ellipse fit. Accurate STS time was computed on various STSs and verified using a marker-based motion capture system. This application can be used as part of a continuous video monitoring system in the homes of older adults and can provide valuable information to help detect fall risk and enable early interventions.

We present a unique occlusion and foreground overlap detection technique from depth sensor data using a fuzzy rule-based system. Features such as bounding box parameters and skeletonization were extracted from the foreground images and then input to the Fuzzy Inference System. Overlap and occlusion confidence measures were taken for each frame in the image sequence and compared against the extracted ground truth. This technique can help filter out occluded regions in the image sequence which, in an Eldercare environment, can then be used to compute accurate estimates of fall risk parameters such as stride time, stride length, and walking speed on a daily basis in in order to monitor the well-being of older adults in an ambient assisted living facility.

Linguistic summaries of sensor data have been shown to be valuable as a communication tool with health care providers in an eldercare environment. Additionally, we have developed a metric distance for our particular form of linguistic protoform summaries (LPS). This has allowed the creation of linguistic prototypes from clusters of summaries over some temporal range. Using that, we present a method for detecting anomalies, as observations considerably different from the linguistic prototypes in a moving temporal window. Two case studies from an eldercare environment demonstrate the utility of this approach.

We describe a new cluster validity framework (CVF) that compares structure in the data (in dissimilarity form) to the structure of dissimilarity matrices induced by a matrix transformation of the partition being tested. As part of this framework, we show two possible cluster validation measures: one, visual cluster validity, that that uses visual comparison and another one, correlation cluster validity, based on correlation. Unlike many existing measures, the measures we propose can be applied to crisp or soft partitions obtained by any relational or object data clustering algorithm. We illustrate the new measures and compare them to several well-known existing measures using real and artificial data sets.

In this paper, we present an approach for modeling and comparing small sets of 2-D objects based on their spatial relationships. This situation can arise in the conflation of a hand- or machine-drafted map to a satellite image, or in the correspondence problem of matching two images taken under different viewing conditions. We focus on the specific problem of matching a sketched map containing several 2-D objects to hand-segmented satellite imagery. We define a similarity measure between the spatial configurations of two object sets, which uses attributed relational graphs to represent scene information. Objects are represented as graph nodes and edges are defined by the histograms of forces between object pairs. We develop a memetic algorithm based on a (μ+λ) evolution strategy to solve this scene-matching problem with three domain-specific local search operators that are compared experimentally.

In this paper, we consider the problem of evaluating the similarity of two sets of linguistic summaries of sensor data. Huge amounts of available data cause a dramatic need for summarization. In continuous monitoring, it is useful to compare one time interval of data with another, for example, to detect anomalies or to predict the onset of a change from a normal state. Assuming that summaries capture the essence of the data, it is sufficient to compare only those summaries, i.e., they are descriptive features for recognition. In previous work, we developed a similarity measure between two individual summaries and proved that the associated dissimilarity is a metric. Additionally, we proposed some basic methods to combine these similarities into an aggregate value. Here, we develop a novel parameter free method, which is based on fuzzy measures and integrals, to fuse individual similarities that will produce a closeness measurement between sets of summaries. We provide a case study from the eldercare domain where the goal is to compare different nighttime patterns for change detection. The reasons for studying linguistic summaries for eldercare are twofold: First, linguistic summaries are the natural communication tool for health care providers in a decision support system, and second, due to the extremely large volume of raw data, these summaries create compact features for an automated reasoning for detection and prediction of health changes as part of the decision support system.

We have developed a fully automated system for change detection of high-resolution satellite imagery. Our system, GeoCDX, is sensor-agnostic, resolution-independent and designed to process the very large volumes of data collected by modern high resolution panchromatic and multispectral imaging satellites. GeoCDX performs fully automated coregistration of imagery; extracts high-level features from the satellite imagery; performs change detection processing to pinpoint locations of change; clusters image tiles to group similar regions of change; and presents results in a variety of ways in an easy-to-use web application that facilitates online discovery, analysis, and dissemination of the change detection results. We applied GeoCDX to 4121 image pairs and successfully coregistered over 91% of the pairs covering a total area greater than 370 000 km2; GeoCDX decreased the average coregistration error from 9.6 ± 8.6 m to 1.8 ± 1.2 m. We show that for some pairs, GeoCDX provides up to a 50% increase in users' efficiency compared to manually performing change detection in common GIS software. Moreover, the change detection assessment performed using GeoCDX was on average four times more accurate compared to the manual approach in large part due to the use of our change intensity map that provides visual cues to the user during exploitation. Finally, change detection analysis using GeoCDX resulted in a missed detection rate of less than 2%.

In this paper, we propose a webcam-based system for in-home gait assessment of older adults. A methodology has been developed to extract gait parameters including walking speed, step time, and step length from a 3-D voxel reconstruction, which is built from two calibrated webcam views. The gait parameters are validated with a GAITRite mat and a Vicon motion capture system in the laboratory with 13 participants and 44 tests, and again with GAITRite for 8 older adults in senior housing. Excellent agreement with intraclass correlation coefficients of 0.99 and repeatability coefficients between 0.7% and 6.6% was found for walking speed, step time, and step length given the limitation of frame rate and voxel resolution. The system was further tested with ten seniors in a scripted scenario representing everyday activities in an unstructured environment. The system results demonstrate the capability of being used as a daily gait assessment tool for fall risk assessment and other medical applications. Furthermore, we found that residents displayed different gait patterns during their clinical GAITRite tests compared to the realistic scenario, namely a mean increase of 21% in walking speed, a mean decrease of 12% in step time, and a mean increase of 6% in step length. These findings provide support for continuous gait assessment in the home for capturing habitual gait.

Rapid detection of landmines and explosive hazards is a critical issue for modern military operations. Due to the varied nature of the objects of interest and the complexity of the surroundings, one approach is to utilize the superior recognition capabilities of the human brain in the detection process. We are developing frameworks and algorithms to process image video data from an RGB camera, mounted on a moving vehicle, and to provide cueing capability for a human-in-the-loop detection system. Feedback from the human operator is embedded into the system memory to aid future detection processes (causal). Due to the inherent variation of different objects of interest terms of color and texture appearance, and the inherent variation and complexity of the surroundings, we introduce a classification algorithm that operates on local decision boundaries. Each decision boundary is learned using the support vector machine (SVM) technique. Given test data, the K-nearest neighbor (KNN) method is used to pre-select the nearest training set to localize the scope of SVM training, giving us the local decision boundary.

This paper proposes a method for segmenting an unstructured dirt road in color space images using color and texture analysis. A support vector machine (SVM) classifier was trained on samples of on and off road patches from a similar road. Image patches were classified at sparse intervals at a fixed distance from the vehicle. Each patch is described by the Histogram of oriented gradients (HOG), the Local Binary Patters (LBP), a histogram of the color channel, and a histogram of a non linear color transform. The classified patches were transformed to the next frame of the sequence using the scale invariant feature transform (SIFT) to reduce reclassification of image patches. Morphological opening and closing were used to transform the points into a mask, and reduce errors. Experimental results indicated that the algorithm can accurately segment road images given a set of training data from similar road utilizing only color imagery.

In this paper we describe a method for detecting buried objects of interest using a forward looking infrared camera (FLIR) installed on a moving vehicle. Infrared (IR) detection of buried targets is based on the thermal gradient between the object and the surrounding soil. The processing of FILR images consists in a spot-finding procedure that includes edge detection, opening and closing. Each spot is then described using texture features such as histogram of gradients (HOG) and local binary patterns (LBP) and assigned a target confidence using a support vector machine (SVM) classifier. Next, each spot together with its confidence is projected and summed in the UTM space. To validate our approach, we present results obtained on 6 one mile long runs recorded with a long wave IR (LWIR) camera installed on a moving vehicle.

In prior work, Grabisch put forth a direct (i.e., result of the Extension Principle) generalization of the Sugeno fuzzy integral (FI) for fuzzy set (FS)-valued normal (height equal to one) integrands and number-based fuzzy measures (FMs). Grabisch's proof is based in large on Dubois and Prade's analysis of functions on intervals, fuzzy numbers (thus normal FSs) and fuzzy arithmetic. However, a case not studied is the extension of the FI for sub-normal FS integrands. In prior work, we described a real-world forensic application in anthropology that requires fusion and has sub-normal FS inputs. We put forth an alternative non-direct approach for calculating FS results from sub-normal FS inputs based on the use of the number-valued integrand and number-valued FM Sugeno FI. In this article, we discuss a direct generalization of the Sugeno FI for sub-normal FS integrands and numeric FMs, called the Sub-normal Fuzzy Integral (SuFI). To no great surprise, it turns out that the SuFI algorithm is a special case of Grabisch's generalization. An algorithm for calculating SuFI and its mathematical properties are compared to our prior method, the Non-Direct Fuzzy Integral (NDFI). It turns out that SuFI and NDFI fuse in very different ways. We assert that in some settings, e.g., skeletal age-at-death estimation, NDFI is preferred to SuFI. Numeric examples are provided to stress important inner workings and differences between the FI generalizations.

A popular clustering model is hard c-means (HCM). For many data sets the HCM objective function has local extrema, so HCM optimization often yields suboptimal clusterings. The effect of local extrema can be reduced by fuzzification, leading to the well-known fuzzy c-means (FCM) model with the fuzziness parameter m >; 1. In this paper we use FCM to optimize the HCM model, even though we actually optimize a different objective function. This work is motivated by a popular approach to avoid local extrema in HCM which approximates the minimum operator in HCM by the harmonic means, leading to c-harmonic means (CHM), which was recently shown to be equivalent to FCM for m = 2. Generalizing the harmonic means in CHM to generalized means yields a clustering model that we call c-generalized means (CGM), which is equivalent to FCM for arbitrary m >; 1. Numerical experiments with the BIRCH and Lena data sets show that FCM/CGM (with optimal m) often yields significantly better HCM clusterings than HCM itself or CHM.

Linguistic summarization of time series can glean meaningful information from huge amounts of data. However, in situations like continuous monitoring, even linguistic summaries become difficult for a person to understand. In this paper, we develop an approach to generate linguistic prototypes from a group of time blocks that represent a normal condition. Then the set of summaries for new time blocks are compared to the prototypes to flag anomalous conditions, thereby reducing the burden on the human. Case studies from an eldercare environment demonstrate the utility of this approach.

Human geography is a phrase that is used to indicate the augmentation of standard geographic layers of information about an area with behavioral variations of the people in the area. In particular, the actions of people can be attributed to both local and regional variations in physical (i.e., terrain) and human (e.g., income, political, cultural) variables. For example, in disaster planning, response, and relief, it is important to understand how individuals and groups of people will move in the environment. Different groups may have different objectives, the time scales are longer, and other factors like food and mobility need to be addressed. Mathematical models with graphics realizations, particularly agent-based models, are an important way to simulate human response to stress. In this paper, we extend a standard mathematical model of agent evacuation to people on an island under the threat of a hurricane.

Many agent based models for disaster crowd behavior in closed spaces have been described in the literature. In this paper we propose an extension of the confined space models based on the bounded rationality theory (BRT) that is able to model crowd behavior during large area events with longer time constants, such as natural disasters. We model the BRT factor selection process using an ordered geometric average approach (OGA). Then, we present two examples of crowd behavior related to the evacuation of a hypothetical island.

In this paper, two rumor spreading models to investigate information spread in disaster scenarios are described. In the experiments shown, the impact of various scenario parameters were examined in terms of percentage of agents able to reach a shelter within a prescribed amount of time. Future work will include adding rumors for information other than the availability of evacuation shelters. For example, additional rumors on traffic or road closings and conditions will be included. The inclusion of traffic and road information will cause agents to consider and update paths to evacuation shelters based on each agent's individual knowledge of the road structure and the information that gets passed to them. Furthermore, in the second rumor-spreading model, agents have some level of skepticism about the rumors. They must hear a rumor several times before trusting the information. The level of an agent's skepticism or how an agent perceives information may be related to personality. Future work will incorporate personality traits into each agent and these traits will be used to modulate how agents perceive and make use of the rumors they hear.

Herein, we put forth a new similarity measure for anomaly detection and for comparing human behaviors based on the theories of learning automata, comparison of soft partitions, and temporal probabilistic order relations. In particular, focus is placed on monitoring individuals in a home setting for their own well-being. This work is a high-level investigation focused on the structure of human behavior. Examples demonstrate the utility of this approach for (1) understanding the similarity of pairs of behaviors for an individual (or alternatively between individuals) and (2) detecting significant change between changing behavior and a baseline model. In the context of eldercare, significant change in behavior can be a precursor to cognitive and/or functional health related problems. Simulated resident behavior is used to show different scenarios and the response of the proposed measure. © 2012 Wiley Periodicals, Inc.

Creating linguistic summaries of data has been a goal of the artificial and computational intelligence communities for many years. Summaries of written text have garnered the most attention. More recently, creating summaries of imagery and other sensed data has become important as a means of compressing large amounts of data and communicating with humans. In this paper, we consider the question of comparing sets of summaries generated from sensed data. In an earlier work, we developed a metric between individual protoform-based summaries; and here, as a next step, we propose aggregation methods to fuse these individual distances. We provide a case study from eldercare where the goal is to compare different nighttime patterns for change detection. © 2012 Wiley Periodicals, Inc.

In this paper, we present an improved evolutionary method for the task of locating a group of buildings based solely on their relative spatial relationships. This problem arises in the general text-to-sketch problem of conflating a hand or machine drafted sketch of building locations to a satellite image. We use the histograms of forces to capture the relative position information between buildings and develop a method to compare building sets. This represents an extension to our previous work, allowing for larger placement perturbations and changes in orientation.

Previously, we introduced a novel method to estimate adult skeletal age-at-death using the Sugeno fuzzy integral (FI). Specifically, we took a multi-hypothesis testing approach to make the classical FI yield a fuzzy set (FS)-valued result, which is not guaranteed to be normal or convex, based on interval-valued sources of information (aging methods). We showed quantitative results for summarizing the FS and comparing the single decision to a known age-at-death. In this article, we extend our prior work and present formulas to measure the uncertainty in the resultant FSs. We generate linguistic descriptions to establish domain standardization for the goal of assisting forensic and biological anthropologists. Specifically, we introduce fuzzy class definitions for age-at-death FSs and we present an OWA contrast approach to measure the degree of specificity in age-at-death FSs.

Previously, we presented a method for comparing soft partitions (i.e. crisp, probabilistic, fuzzy and possibilistic) to a known crisp reference partition. Many of the classical indices that have been used with outputs of crisp clustering algorithms were generalized so that they are applicable for candidate partitions of any type. In particular, focus was placed on generalizations of the Rand index. In this article, we extend our prior work by (1) investigating the behavior of the soft Rand for comparing non-crisp, specifically possibilistic, partitions and (2) we demonstrate how the possibilistic Rand and visual assessment of (cluster) tendency (VAT) algorithm can be used to discover the number of actual clusters and coincident clusters for outputs from the possibilistic c-means (PCM) algorithm.

In this paper, we propose a linguistic summarization procedure for describing long-term trends of change in human behavior. Our objective consists of defining methods that provide information to elders, caregivers, social workers or even family in an understandable language. We adapt a measure that we defined in previous work on soft cluster partition similarity for comparing behaviors that are adapted over time. From that measure, we are able to produce a time series that numerically describes change in behavior over time. In this article, the resulting time series is partitioned and linguistically summarized depending on a user's (caregiver, social worker, etc.) desired time resolution. Simulated resident behavior is used in order to explore a range of different scenarios and the response of the proposed linguistic summarization process is investigated.

A common question asked about unlabeled data sets is how many subsets (or clusters) of objects are represented in the data? The answer to this question is usually obtained by first clustering the data, and then employing a cluster validity measure to validate one or more candidate partitions of the objects. In this paper we describe an universal cluster validity measure that, unlike most existing measures, can be applied to partitions obtained by any relational or object data clustering algorithm. We illustrate the new measure, and compare it to several well known existing measures using a variety of artificial data sets.

Ubiquitous passive, as well as active, monitoring of elders is a growing field of research and development with the goal of allowing seniors to live safe active independent lives with minimal intrusion. Much useful information, fall detection, fall risk assessment, activity recognition, early illness detection, etc. can be inferred from the mountain of data. Healthcare must be human centric and human friendly, and so, methods to consolidate the data into linguistic summaries for enhanced communication and problem detection with elders, family and healthcare providers is essential. Long term trends can be most easily identified using summarized information. This paper explores the soft computing methodology of protoforms to produce linguistic summaries of one dimensional data, motion and restlessness. The technique is demonstrated on a 15 month sensor collection for an elder participant.

This letter presents a system to solve the vector-to-imagery building conflation problem. To drive the system, structure outlines in high-resolution images are extracted via a shape-driven level set scheme. Shape and relative position features are then computed for the image-extracted buildings and for vector graphics buildings from a geospatial information system (GIS). These two features are used by a graph-matching procedure that finds correspondences between the image-extracted buildings and those from a GIS. Extensions of our system to vector-to-vector building conflation, generic polygonal object conflation, and image-to-image registration are also possible.

The Geospatial Change Detection and exploitation (GeoCDX) is a fully automated system for detection and exploitation of change between multitemporal high-resolution satellite and airborne images. Overlapping multitemporal images are first organized into 256 m × 256 m tiles in a global grid reference system. The system quantifies the overall amount of change in a given tile with a tile change score as an aggregation of pixel-level changes. The tiles are initially ranked by these change scores for retrieval, review, and exploitation in a Web-based application. However, the ranking does not account for the wide variety of change types that are typically observed in the top-ranked change tiles. To automatically organize the wide variety of change patterns observed in multitemporal high-resolution imagery, we perform tile clustering using the competitive agglomeration (CA) algorithm stabilized using the fuzzy c-means (FCM) algorithm. Each resulting cluster contains tiles with a visually similar type of change. By visual inspection of these tile clusters, GeoCDX users can quickly find certain types of change without having to sift through a large number of tiles initially organized solely by their tile change score, thereby reducing the time it takes for users to discover and exploit the change pattern(s) of greatest interest to a given application (e.g., urban growth, disaster assessment, facility monitoring, etc.). The tile clusters also provide a high-level overview of the various types of change that occur between the two observations. This overview is compared with a similar yet more limited view offered by a relevance feedback tool that requires a user to select sample tiles for use as samples in the reranking process.

This paper presents an approach to the task of locating a group of buildings based solely on their relative spatial relationships. This situation can occur in the problem of conflation of a hand or machine drafted map to a satellite image or in matching of two images taken under different viewing conditions (the correspondence problem). Of importance to us is the general text-to-sketch problem where a sketch of building locations must be matched to actual satellite imagery. Information about the nature of these relative positions is captured by the histograms of forces. In this paper, we consider a modified genetic algorithm that allows us to search for a specific group of buildings within a large geospatial database using the histograms of forces in the matching process. A novel mutation operator is introduced to adapt the standard GA to this environment.

For reasons such as computational complexity, spatial and temporal information reduction, and human understandability, it is important that computer vision systems be equipped with the means to summarize their content in a natural language. Such rich descriptions are of use by both humans and computers for describing, recognizing, and tracking objects, activity, and their interactions at a desired level of abstraction. A genetic algorithm is introduced here for segmenting non-human objects deemed relevant to human activity analysis in stereo vision acquired voxel environments. This approach is of use in an Eldercare setting as it relates to monitoring the “well-being” of residents through acquiring and detecting deviations in patterns of typical behavior as well as recognizing abnormal events, such as fall detection.

The ability to rise from a chair is an important parameter to assess the balance deficits of a person. In particular, this can be an indication of risk for falling in elderly persons. Our goal is automated assessment of fall risk using video data. Towards this goal, we present a simple yet effective method of detecting transition, i.e. sit-to-stand and stand-to-sit, from image frames using fuzzy clustering methods on image moments. The technique described in this paper is shown to be robust even in the presence of noise and has been tested on several data sequences using different subjects yielding promising results.

We model anomalies in wireless sensor networks with ellipsoids that represent node measurements. Elliptical anomalies (EAs) are level sets of ellipsoids, and classify them as type 1, type 2 and higher order anomalies. Three measures of (dis)similarity between pairs of ellipsoids convert model ellipsoids into dissimilarity data. Clusters in the dissimilarity data may correspond to normal and anomalous measurements and nodes in the network. Assessment of (clustering) tendency is facilitated by visual inspection of (VAT/iVAT) images. Two examples illustrate the potential for anomaly detection.

Fuzzy integrals have been used to fuse the evidence or opinions from a variety of sources. These integrals are nonlinear combinations of the support functions and the (possibly subjective) worth of subsets of the sources of information, realized by a fuzzy measure. There have been many applications and extensions of fuzzy integrals and this paper proposes a fuzzy Choquet integral, where the integrand takes an interval type-2 fuzzy number and the fuzzy measure is real number-valued. Interval type-2 fuzzy numbers encode the second-order uncertainty in a fuzzy number. Type-2 fuzzy numbers have been been shown to be useful in many applications, including computing with words and control systems. We illustrate our method on several numerical examples as well as on a bioinformatics application.

The hard, fuzzy and possibilistic c-means clustering algorithms are widely used for partitioning a set of n objects into c groups. There are cases, however, when more than one type of partition is necessary to correctly describe the belongingness of an object to a group. Previously, Pal, Pal and Bezdek listed some of these cases and proposed a method to simultaneously produce both memberships and typicalities for a set of vectorial object data: the fuzzy possibilistic c-means (FPCM) clustering algorithm. However, FPCM is not directly applicable when the data are represented by object-object relationships. In this paper, we reformulate FPCM so that it can work with A-norm relational data. Extensions and properties of the relational clustering algorithm are also considered.

GeoCDX (Geospatial Change Detection and eXploitation) is an integrated system for detecting change between multi-temporal, high-resolution satellite or airborne images. Overlapping images are organized into 256×256 meter tiles in a global grid system. A tile change score measures the amount of change in the tile which is the aggregation of pixel-level change score. The tiles are initially ranked by these change scores. However, this ranking does not account for the wide variety of change types. To learn the change patterns in the data, we apply the fuzzy c-means clustering algorithm to the tiles. Each resulting cluster contains tiles with similar type of change. Users looking for certain types of change can review the tile clusters rather than the more time consuming process of searching through the tile list based on the initial ranking. The clusters also provide users an overview of various types of change found in the scene.

When clustering produces more than one candidate to partition a finite set of objectsO, there are two approaches to validation (i.e., selection of a “best” partition, and implicitly, a best value for c , which is the number of clusters inO). First, we may use an internal index, which evaluates each partition separately. Second, we may compare pairs of candidates with each other, or with a reference partition that purports to represent the “true” cluster structure in the objects. This paper generalizes many of the classical indices that have been used with outputs of crisp clustering algorithms so that they are applicable for candidate partitions of any type (i.e., crisp or soft, with soft comprising the fuzzy, probabilistic, and possibilistic cases). Space prevents inclusion of all of the possible generalizations that can be realized this way. Here, we concentrate on the Rand index and its modifications. We compare our fuzzy-Rand index with those of Campello, Hullermeier and Rifqi, and Brouwer, and show that our extension of the Rand index is O(n), while the other three are all O(n2). Numerical examples are given to illustrate various facets of the new indices. In particular, we show that our indices can be used, even when the partitions are probabilistic or possibilistic, and that our method of generalization is valid for any index that depends only on the entries of the classical (i.e., four-pair types) contingency table for this problem.

This paper addresses thecomputing-with-wordsparadigm by presenting an ontological self-organizing map (OSOM), which produces visualization and summarization information about datasets composed of words, namely, ontological data. The specific data that are used in this paper are the Gene Ontology (GO) annotations of genes and gene products. The OSOM is an extension of the SOM, which was initially developed by Kohonen. We adapt the SOM by integrating ontology-based similarity measures and relational-clustering distance measures. We also develop a novel prototype update. We present results on two datasets composed of GO annotations of genes and gene products. An OSOM-based summarization, which produces the term-based summarizations of the trained OSOM network, is also demonstrated. The results show that the OSOM-based visualization method correctly shows the cluster tendency of the genes and gene products and that the summarization provides useful information about the mapped groups of genes and gene products.

Numerous computational schemes have arisen over the years that attempt to learn information about objects based upon the similarity or dissimilarity of one object to another. One such scheme, clustering, looks for self-similar groups of objects. To use clustering algorithms, an investigator must often havea prioriknowledge of the number of clusters, i.e.,$c$, to search for in the data. Moreover, it is often convenient to have ways to rank the returned results, either for a single value of$c$, a range of$c$’s different clustering methods, or any combination thereof. However, the task of assessing the quality of the results, so that$c$may be determined objectively, is currently ill-defined for object–object relationships. To bridge this gap, we generalize three well-known validity indices: the modified Hubert’s Gamma, Xie–Beni, and the generalized Dunn’s indices, to relational data. In doing so, we develop a framework to convert many other validity indices to a relational form. Numerical examples on 12 datasets (samples from four normal mixtures, four real-world object datasets, and four real-world “pure relational” datasets) using the relational duals of the hard, fuzzy, and possibilistic$c$-means cluster algorithms are offered to illustrate and evaluate the new indices.

Clustering aims to identify groups of similar objects. To evaluate the results of cluster algorithms, an investigator uses cluster-validity indices. While the theory of cluster validity is well established for vector object data, little effort has been made to extend it to relationship-based data. As such, this paper proposes a theory of reformulation for object-data validity indices so that they can be used to rank the results produced by the relational -means clustering algorithms. More specifically, we create a class of relational validity indices, which is called dual-relational indices, that are guaranteed under certain, but easily met, constraints to produce the same results and, hence, the same cluster counts, as their object-data counterparts.

Video-based tracking of contours on the human body has been shown to be useful for many applications, including gait and gesture recognition, posture estimation, and activity analysis. We present a contour tracking method that incorporates a novel edge feature and fuzzy contour template. We apply our method in tracking the motions of older adults exercising in a gym environment. The output of our system is a dynamic fuzzy representation of the spine angle of the subject. We show that the method described in this paper is capable of tracking contours even in cases where human silhouette extraction is poor.

The existence of BLAST sequence comparison algorithm and microarray technology are among the reasons that make bioinformatics the domain with the most abundant large relational datasets. For example, by BLAST-ing the genes of the human genome (around 30,000 genes) we obtain a 30,000 by 30,000 distance matrix. This matrix can not be currently stored in the memory of a typical desktop PC. In the same time, clustering the resulting matrix using a fuzzy relational clustering algorithm such as Non-Euclidean Fuzzy C-means (NERFCM) requires prior knowledge of the number of clusters existent in the data set. The question is, how can we evaluate the number of clusters if we can't even load the matrix in the memory our PC? To address this problem, we propose to extend the correlation cluster validity (CCV) that we introduced in a previous paper, denoting the new validity measure as eCCV. eCCV consists of two steps: first sampling of the large matrix followed by the estimation of the number of cluster employing CCV of the sampled data. The sampling strategy produces also a significant processing speedup. We illustrate eCCV properties on a large synthetic dataset and on a large subset of human genes obtained from the RefSeq database.

Humans are endowed with innate faculties, which allow for reasoning in noisy or uncertain environments, that far surpass the current abilities of computing systems. One such example is the notion of forming a ldquosketchrdquo of some real-world location or route from a series of linguistic descriptions of regions and surrounding landmarks. While mirroring this functionality might seem like a daunting computational task, it is possible, to a certain degree, to mimic many of the underlying humanistic processes. Out of these, the facet that we consider in this paper is iterative object placement from a set of language extracted spatial relations and dependencies.

In this work, we study how continuous video monitoring and intelligent video processing can be used in eldercare to assist the independent living of elders and to improve the efficiency of eldercare practice. More specifically, we construct an advanced silhouette extraction and tracking algorithm for indoor environments. An adaptive learning method was developed to estimate the physical location and moving speed of a person from a single camera view without calibration. Then hierarchical decision tree and dimension reduction methods were used for human action recognition. We extract important ADL (activities of daily living) statistics for automated functional assessment. Our extensive tests over these massive video datasets demonstrate that the proposed automated activity analysis system is very efficient.

This paper presents a new technique for clustering either object or relational data. First, the data are represented as a matrix D of dissimilarity values. D is reordered to D* using a visual assessment of cluster tendency algorithm. If the data contain clusters, they are suggested by visually apparent dark squares arrayed along the main diagonal of an image I(D*) of D*. The suggested clusters in the object set underlying the reordered relational data are found by defining an objective function that recognizes this blocky structure in the reordered data. The objective function is optimized when the boundaries in I(D*) are matched by those in an aligned partition of the objects. The objective function combines measures of contrast and edginess and is optimized by particle swarm optimization. We prove that the set of aligned partitions is exponentially smaller than the set of partitions that needs to be searched if clusters are sought in D. Six numerical examples are given to illustrate various facets of the algorithm. © 2009 Wiley Periodicals, Inc.

As part of an interdisciplinary collaboration on elder-care monitoring, a sensor suite for the home has been augmented with video cameras. Multiple cameras are used to view the same environment and the world is quantized into nonoverlapping volume elements (voxels). Through the use of silhouettes, a privacy protected image representation of the human acquired from multiple cameras, a 3-D representation of the human is built in real time, called voxel person. Features are extracted from voxel person and fuzzy logic is used to reason about the membership degree of a predetermined number of states at each frame. Fuzzy logic enables human activity, which is inherently fuzzy and case-based, to be reliably modeled. Membership values provide the foundation for rejecting unknown activities, something that nearly all current approaches are insufficient in doing. We discuss temporal fuzzy confidence curves for the common elderly abnormal activity of falling. The automated system is also compared to a ground truth acquired by a human. The proposed soft computing activity analysis framework is extremely flexible. Rules can be modified, added, or removed, allowing per-resident customization based on knowledge about their cognitive and functionality ability. To the best of our knowledge, this is a new application of fuzzy logic in a novel approach to modeling and monitoring human activity, in particular, the well-being of an elderly resident, from video.

As the availability of various geospatial data increases, there is an urgent need to integrate multiple datasets to improve spatial analysis. However, since these datasets often originate from different sources and vary in spatial accuracy, they often do not match well to each other. In addition, the spatial discrepancy is often nonsystematic such that a simple global transformation will not solve the problem. Manual correction is labor-intensive and time-consuming and often not practical. In this paper, we present an innovative solution for a vector-to-imagery conflation problem by integrating several vector-based and image-based algorithms. We only extract the different types of road intersections and terminations from imagery based on spatial contextual measures. We eliminate the process of line segment detection which is often troublesome. The vector road intersections are matched to these detected points by a relaxation labeling algorithm. The matched point pairs are then used as control points to perform a piecewise rubber-sheeting transformation. With the end points of each road segment in correct positions, a modified snake algorithm maneuvers intermediate vector road vertices toward a candidate road image. Finally a refinement algorithm moves the points to center each road and obtain better cartographic quality. To test the efficacy of the automated conflation algorithm, we used U.S. Census Bureau's TIGER vector road data and U.S. Department of Agriculture's 1-m multi-spectral near infrared aerial photography in our study. Experiments were conducted over a variety of rural, suburban, and urban environments. The results demonstrated excellent performance. The average correctness measure increased from 20.6% to 95.5% and the average root-mean-square error decreased from 51.2 to 3.4 m.

As the size and operator complexity of a fuzzy logic system increases, computational tractability becomes a problem. There is a significant amount of parallelism in both the creation of the fuzzy rule base and in fuzzy inference. Traditional processors (CPUs) cannot take full advantage of this natural parallelism graphics processing units (GPUs) speed up rule construction and inference by utilizing up to 128 processing units operating in parallel. Normally, these processors are used to perform high speed graphics calculations for video games, movies, and other areas of intense graphical work. In this paper, a method is discussed for speeding up fuzzy logic by structuring it into a format such that it resembles the standard rendering procedure for a graphics pipeline based on rasterization.

Video cameras are a relatively low-cost, rich source of information that can be used for ldquowell-beingrdquo assessment and abnormal event detection for the goal of allowing elders to live longer and healthier independent lives. We previously reported a soft-computing fall detection system, based on two levels from a hierarchy of fuzzy inference using linguistic summarizations of activity acquired temporally from a three dimensional voxel representation of the human found by back projecting silhouettes acquired from multiple cameras. This framework is extremely flexible and rules can be modified, added, or removed, allowing for per-resident customization based on knowledge about their cognitive and physical ability. In this paper, we show the flexibility of our activity analysis framework by extending it to additional common elderly activities and contextual awareness is added for reasoning based on location or static objects in the apartment.

This paper presents an ontological self-organizing map (OSOM), which is used to produce visualization and functional summarization information about gene products using gene ontology (GO) similarity measures. The OSOM is an extension of the self-organizing map as initially developed by Kohonen, which trains on data composed of sets of terms. Term-based similarity measures are used as a distance metric as well as in the update of the OSOM training procedure. We present an OSOM-based visualization method that shows the cluster tendency of the gene products. Also demonstrated is an OSOM-based functional summarization which produces the most representative term(s) (MRT) from the GO for each OSOM prototype and, subsequently, each gene product cluster. We validated the results of our method by applying the OSOM to a well-studied set of gene products.

Many important applications in biology have underlying datasets that are relational, that is, only the (dis)similarity between biological objects (amino acid sequences, gene expression profiles, etc.) is known and not their feature values in some feature space. Examples of such relational datasets are the gene similarity matrices obtained from BLAST, gene expression data, or gene ontology (GO) similarity measures. Once a relational dataset is obtained, a common question asked is how many groups of objects are represented in the original dataset. The answer to this question is usually obtained by employing a clustering algorithm and a cluster validity measure. In this article we describe a cluster validity measure for non-Euclidean relational fuzzy c-means that is based on the correlation between a relation induced on the data by the cluster memberships and the original relational data. This validity measure can be applied to partitions made by any fuzzy relational clustering algorithm. We illustrate our measure by validating clusters in several dissimilarity matrices for a set of 194 gene products obtained using BLAST and GO similarities.

This paper addresses the relationship between the visual assessment of cluster tendency (VAT) algorithm and Dunnpsilas cluster validity index. We present an analytical comparison in conjunction with numerical examples to demonstrate that the effectiveness of VAT in showing cluster tendency is directly related to Dunnpsilas index. This analysis is important to understanding the underlying theory of VAT and VAT-based algorithms and, more generally, other algorithms that are based on, or similar to, Primpsilas Algorithm.

Conventional clustering techniques provide a static snapshot of each vectorpsilas commitment to every group. With additive datasets, however, existing methods may not be sufficient for adapting to the presence of new clusters or even the merging of existing data-dense regions. To overcome this deficit, we explore the use of growing neural gas for temporal clustering and provide evidence that this new algorithm is capable of detecting cluster structures that incrementally emerge.

The demand for high-resolution commercial satellite imagery (HR-CSI) has increased significantly over the last 5 years for a wide variety of applications. This demand has driven an increase in volume, frequency of acquisition, and spatial resolution of HR-CSI. In turn, this has spurred the need for more accurate and time-efficient processing tools for analyzing geospatial information to support user-specific applications. One such application is change detection between multi-temporal HR-CSI data. The significant increase in quantity and quality of multi-temporal HR-CSI data makes traditional manual analysis impractical. Thus, there is a need for a fully automated change detection system that not only identifies areas of change, but also allows users to filter, sort through, and analyze areas of change quickly and efficiently. Here we describe a tool - GeoCDX (Geospatial Change Detection and Exploitation) - to meet this need. GeoCDX is an integrated system that performs image ingestion and registration, feature extraction, and change analysis. The change detection results from GeoCDX are web accessible with additional interfaces to Google Earth™ (GE) and Google Maps™ (GM). In the near future GeoCDX will be integrated with its sister system GeoIRIS (Geospatial Information Retrieval and Indexing System). This integration will produce a very powerful HR-CSI analysis package with the change detection capabilities of GeoCDX and the content-based image retrieval system of GeoIRIS.

There are many function optimization algorithms based on the collective behavior of natural systems -ParticleSwarmOptimization(PSO) andAntColonyOptimization(ACO) are two of the most popular. This paper presents a new adaptation of the PSO algorithm, entitled Roach Infestation Optimization (RIO), that is inspired by recent discoveries in the social behavior of cockroaches. We present the development of the simple behaviors of the individual agents, which emulate some of the discovered cockroach social behaviors. We also describe a ldquohungryrdquo version of the PSO and RIO, which we aptly call Hungry PSO and Hungry RIO. Comparisons with standard PSO show that Hungry PSO, RIO, and Hungry RIO are all more effective at finding the global optima of a suite of test functions.

In this work, we study how continuous video monitoring and intelligent video processing can be used in eldercare to assist the independent living of elders and to improve the efficiency of eldercare practice. More specifically, we develop an automated activity analysis and summarization for eldercare video monitoring. At the object level, we construct an advanced silhouette extraction, human detection and tracking algorithm for indoor environments. At the feature level, we develop an adaptive learning method to estimate the physical location and moving speed of a person from a single camera view without calibration. At the action level, we explore hierarchical decision tree and dimension reduction methods for human action recognition. We extract important ADL (activities of daily living) statistics for automated functional assessment. To test and evaluate the proposed algorithms and methods, we deploy the camera system in a real living environment for about a month and have collected more than 200 hours (in excess of 600 G bytes) of activity monitoring videos. Our extensive tests over these massive video datasets demonstrate that the proposed automated activity analysis system is very efficient.

As the number of data points, feature dimensionality, and number of centers for clustering algorithms increase, computational tractability becomes a problem. The fuzzy c-means has a large degree of inherent algorithmic parallelism that modern CPU architectures do not exploit. Many pattern recognition algorithms can be sped up on a graphics processing unit (GPU) as long as the majority of computation at various stages and the components are not dependent on each other. We present a generalized method for offloading fuzzy clustering to a GPU, while maintaining control over the number of data points, feature dimensionality, and the number of cluster centers. GPU-based clustering is a high-performance low-cost solution that frees up the CPU. Our results show a speed increase of over two orders of magnitude for particular clustering configurations and platforms.

A novel algorithm for discriminative training of Choquet-integral-based fusion operators is described. Fusion is performed by Choquet integration of classifier outputs with respect to fuzzy measures. The fusion operators are determined by the parameters of fuzzy measures. These parameters are found by minimizing a minimum classification error (MCE) objective function. The minimization is performed with respect to a special class of measures, the Sugeno lambda-measures. An analytic expression is derived for the gradient of the Choquet integral with respect to the Sugeno lambda-measure. The new algorithm is applied to a landmine detection problem, and compared to previous techniques.

This paper explores several novel approaches to solve the Morris water maze task. In this spatial memory task, the robot must learn how to associate perceptual information with a particular location to aid in navigating to the goal. A self-organizing feature map (SOFM) is used to discretize the perceptual space. The robot must then learn to associate these perceptual states with an action used to navigate through the environment. Two navigational approaches are proposed. The first approach involves computing a probabilistic graph between SOFM nodes and then searching the graph to locate a path to the goal. The second approach uses temporal difference learning to learn the association between an SOFM node and an action that will direct it to the goal. The paper compares the effectiveness of these two approaches and discusses their respective utility.

The goal of this work is to determine the object correspondence between a sketched map and the scene depicted by the sketch, e.g., as represented by an occupancy grid map (OGM) built by a robot. We describe a novel method based on spatial relations for accomplishing this task. Our method is based on using the histogram of forces as scene descriptors. We generate a correspondence map between two scene descriptors and evaluate its confidence. From this map, we generate a one-to-one object correspondence map for the two scenes such that the object correspondence confidence value is maximized. Challenges include the fact that the two scenes may differ in terms of the shape and size of the objects, their orientation, and the objects might be shifted due to translation. The approach is evaluated using several hand drawn sketches that were collected as a part of a user study. We believe that the ability to perform scene matching will make our sketch interface more robust and easier to use, thereby providing us with a more intuitive way of communicating with the robots

Heterogeneous genetic and epigenetic alterations are commonly found in human non-Hodgkin's lymphomas (NHL). One such epigenetic alteration is aberrant methylation of gene promoter-related CpG islands, where hypermethylation frequently results in transcriptional inactivation of target genes, while a decrease or loss of promoter methylation (hypomethylation) is frequently associated with transcriptional activation. Discovering genes with these relationships in NHL or other types of cancers could lead to a better understanding of the pathobiology of these diseases. The simultaneous analysis of promoter methylation using Differential Methylation Hybridization (DMH) and its associated gene expression using Expressed CpG Island Sequence Tag (ECIST) microarrays generates a large volume of methylation-expression relational data. To analyze this data, we propose a set of algorithms based on fuzzy sets theory, in particular Possibilistic c-Means (PCM) and cluster fuzzy density. For each gene, these algorithms calculate measures of confidence of various methylation-expression relationships in each NHL subclass. Thus, these tools can be used as a means of high volume data exploration to better guide biological confirmation using independent molecular biology methods.

There has been significant amount of study on the use of ground-penetrating radar (GPR) for land-mine detection. This paper presents our analysis of GPR data collected at a U.S. Army test site using a new approach based on frequency subband processing. In this approach, from the radar data that have over 2.5 GHz of bandwidth, we compute separate radar images using the one wide (2 GHz) and four narrow (0.6 GHz) frequency subbands. The results indicate that signals for different frequency subbands are significantly different and give very different performance in land-mine detection. In addition, we also examine a number of features extracted from the GPR data, including magnitude and local-contrast features, ratio between copolarization and cross-polarization signals, and features obtained using polarimetric decomposition. Feature selection procedures are employed to find subsets of features that improve detection performance when combined. Results of land-mine detection, including performance on blind test lanes, are presented

Extracting a human silhouette from an image is the enabling step for many high-level vision processing tasks, such as human tracking and activity analysis. Although there are a number of silhouette extraction algorithms proposed in the literature, most approaches work efficiently only in constrained environments where the background is relatively simple and static. In a previous paper, we addressed some of the challenges in silhouette extraction and human tracking in a real-world unconstrained environment where the background is complex and dynamic. We extracted features from image regions, accumulated the feature information over time, fused high-level knowledge with low-level features, and built a time-varying background model. A problem with our system is that by adapting the background model, objects moved by a human are difficult to handle. In order to reinsert them into the background, we run the risk of cutting off part of the human silhouette, such as in a quick arm movement. In this paper, we develop a fuzzy logic inference system to detach the silhouette of a moving object from the human body. Our experimental results demonstrate that the fuzzy inference system is very efficient and robust.

This paper addresses the problem of constructing a summarization of groups of patients that are found by clustering a hospital database where diagnoses are encoded in a controlled medical vocabulary, called ICD-9. Our method finds the "most representative terms" (MRTs) for a patient cluster by using weights from a fuzzy partition matrix generated by fuzzy clustering the patient similarity matrix. We present a novel approach to computing patient similarity by using OWA operators. Finally, we apply our method to a set of 2077 cardiology patients.

This paper describes the application of fuzzy logic to the Short Physical Performance Battery (SPPB) test, a series of timed physical activities that have been created to evaluate, discriminate, and predict physical functional performance for both research and clinical purposes, primarily for physically impaired older adults. The original scoring system of SPPB test uses crisp time boundaries to assign the subject to discrete classes of performance. The crisp (and somewhat arbitrary) nature of the crisp thresholds can easily produce anomalies. Fuzzy Logic theory allows the natural description, in linguistic terms, of input/output relationships rather than relying on precise numerical threshold values. This advantage, dealing with the complicated systems in simple way, is the main reason why fuzzy logic theory is widely applied. In this paper, we offer a new approach for scoring the SPPB test. We demonstrate that in the proposed system, the Fuzzy Short Physical Performance Battery (FSPPB), we can improve the sensitivity and data distribution of the scoring system for the SPPB test. We present the procedures of constructing a fuzzy inference system using fuzzy logic to score the SPPB test and compare the original scoring system with our fuzzy scoring system. As part of a large project in technology for Eldercare, our goal is to accurately measure trends in physical performance of seniors over time.

Many biological systems and objects are intrinsically fuzzy. Fuzzy set theory and fuzzy logic are ideal frameworks for describing some biological systems/objects and providing suitable computational methods for a widely range of bioinformatics problems. In this paper, we present two examples of using fuzzy set theory in bioinformatics, one in fuzzy measurement of ontological similarity and its application in bioinformatics, and the other in the application of the fuzzy k-nearest neighbor algorithm in protein secondary structure prediction. We also review other "fuzzy" methods for bioinformatics applications.

One of the key components for natural interaction between humans and robots is the ability to understand the spatial relationships that exist in the natural world. Previous research has shown that modeling the 2D spatial relationships of FRONT, BEHIND, LEFT, RIGHT, and BETWEEN can be accomplished with results consistent with that of a human being. Upcoming research will involve a human subject study to investigate the use of spatial relationships in 3D space. This will be the first step in extending previous research of the 2D spatial relations into a 3D representation through the use of 3D object point clouds generated by the SIFT algorithm and stereo vision. This will allow for the enrichment of our human-robot dialog to include phrases such as "Bring me the coffee cup on top of the desk and to the right of the computer.

Extracting a human silhouette from an image is the enabling step for many high-level vision processing tasks, such as human tracking and activity analysis. Although there are a number of silhouette extraction and human tracking algorithms proposed in the literature, most approaches work efficiently only in constrained environments where the background is relatively simple and static. In this work, we propose to address the challenges in silhouette extraction and human tracking in a real-world unconstrained environment where the background is complex and dynamic. We extract features from image regions, accumulate the feature information over time, fuse the high-level knowledge with low-level features, and build a time-varying background model. We develop a fuzzy decision process to detach foreground moving objects from the human body. Our experimental results demonstrate that the algorithm is very efficient and robust.

This paper describes our analysis of using extra constraint terms regarding relations between cluster prototypes in possibilistic c-shell clustering. The extra constraints are implemented as additional terms in the cost function. This allows users of these algorithms to incorporate additional knowledge regarding properties cluster prototype into the clustering process. Our analysis here focuses on the use of one extra term for locating circles (shell clustering with circular prototypes) with similar radii. An adjustable factor is used to control the strength of this constraint. For possibilistic clustering, this couples the update procedure of the otherwise independent prototypes. Our experiments, using both simulation and real image data, indicate that this is especially useful in locating actual clusters when the available data are noisy.

The standard method for comparing gene products (proteins or RNA) is to compare their DNA or amino acid sequences. Additional information about some gene products may come from multiple sources, including the set of Gene Ontology (GO) annotations and the set of journal abstracts related to each gene product. Gene product similarity measures can be based on evaluating sets of descriptor terms found in the GO taxonomy, and/or the index term sets of the related documents (MeSH annotations). While our techniques can be applied to term sets from any taxonomy, we restrict our examples in this article to GO annotations. We investigate the use of linear order statistics (LOS) to build similarity relations on pairs of terms that are used in the GO as linguistic descriptors of genes and gene products. One of our objectives is to investigate the construction and utility of visual assessments of relational data (in this case, dissimilarity matrices) for discovering tendencies of groups of gene products to "cluster together". We use gene product data derived from a group of 194 gene products representing three protein families extracted from ENSEMBL. Our examples suggest that LOS similarity measures are more effective than traditional sequence-based similarity measures at capturing relationships between pairs of gene products in ENSEMBL families when annotation information is available. We show examples of how these similarity measures can assist in knowledge discovery and gene product family validation.

One of the most important objects in bioinformatics is a gene product (protein or RNA). For many gene products, functional information is summarized in a set of Gene Ontology (GO) annotations. For these genes, it is reasonable to include similarity measures based on the terms found in the GO or other taxonomy. In this paper, we introduce several novel measures for computing the similarity of two gene products annotated with GO terms. The fuzzy measure similarity (FMS) has the advantage that it takes into consideration the context of both complete sets of annotation terms when computing the similarity between two gene products. When the two gene products are not annotated by common taxonomy terms, we propose a method that avoids a zero similarity result. To account for the variations in the annotation reliability, we propose a similarity measure based on the Choquet integral. These similarity measures provide extra tools for the biologist in search of functional information for gene products. The initial testing on a group of 194 sequences representing three proteins families shows a higher correlation of the FMS and Choquet similarities to the BLAST sequence similarities than the traditional similarity measures such as pairwise average or pairwise maximum.

In this work, we propose a hidden Markov model (HMM), called the linguistic HMM, suitable for processing sequences of fuzzy vectors. A fuzzy vector B is an n-tuple of fuzzy numbers. Since fuzzy numbers are often associated with linguistic terms, such as "small," "medium," etc., a fuzzy vector can also be called a linguistic vector. Similarly, an HMM that processes linguistic vectors can be called a "linguistic HMM." The derivation of the linguistic HMM (LHMM) from the continuous HMM is performed using the extension principle and the decomposition theorem. We prove that a LHMM behaves in the same fashion as the CHMM in the degenerate linguistic case when the fuzzy numbers are singletons (real numbers). We also provide an example where an LHMM was used for the recognition of a play (pick-and-shoot) during a basketball game. The positions of the players were described using spatial fuzzy relations. For the recognition experiment, we generated two sets of 100 sequences containing pick-and-shoot and non pick-and-shoot sequences, respectively. The LHMM results obtained for the fuzzy sequences were compared to the CHMM results obtained on a crisp version of the same sequences. The results obtained showed that the fuzzy spatial relations together with the LHMM provide a better description of the movement than the CHMM.

Recent years have seen an explosive growth in the amount of biological data available for analysis. The large volume of data collected makes it necessary to automatically classify and sort such data on a very large scale. Typically, investigators use computational sequence analysis tools to assign functions to newly found gene products. The problem is to find the functions of a (unknown) gene product given its amino acid sequence. In this work we search for functional similarity between gene products by matching the functional domains that they contain. The domain-based approach addresses the main problem of sequence-based similarity, i.e., when the region of a gene product that is matched by a query sequence is not related to the function of that gene product. We use the hidden Markov representation of a gene product domain as described in the PFAM database, and then infer annotations that come from the Gene Ontology. To compute domain similarity between two gene products we introduce a fuzzy Jaccard similarity measure. We tested our domain-based similarity for the functional annotation of a set of 194 gene products extracted from the ENSEMBL Web site. We compared the domain similarity approach to the traditional way of performing functional annotation using a sequence-based similarity (BLAST and Smith-Waterman). The annotation was performed in all cases using a fuzzy K-nearest neighbor algorithm. We found that our domain-based annotation was better than the most common BLAST approach, but not as good as complex Smith-Waterman technique. The domain-based annotation has about 70% correct annotation rate at 17% false annotation rate

In this paper, we discuss an important aspect of cognitive mobile robotics stemming from a new project in which an adaptive working memory is investigated for robot control and learning. Specifically, our approach is built on the premise that qualitative spatial reasoning is an appropriate framework to pose, learn, and solve navigational tasks. As such, the robot must be able to acquire and maintain landmarks in a form that facilitates learning and subsequent travel. Much research on landmark recognition has focused on either point landmarks or on landmark objects that come from segmentation and feature extraction. Here, we combine these approaches in the following sense. Potential landmark points are acquired in the point mode, but aggregations of them are utilized to represent "interesting" objects that can then be maintained throughout the path. In this paper, we investigate whether consistent aggregations can be maintained and thus serve as candidate chunks for the working memory system. The approach was tested on a video sequence of 1200 frames. Examples from this outdoor video are shown to corroborate the approach.

Advances in a scene matching approach based on objects spatial relationships are discussed. Objects spatial relationships are captured using force histograms, which are used as affine-invariant image descriptors. Object mapping across images is performed by finding the best correspondence map between image descriptors. Due to a very large search space, the particle swarm optimization method is used to facilitate more efficient search. The image descriptors map is then translated into an object map identifying the correspondences between objects in the two images.

The mountain clustering method and the subtractive clustering method are useful methods for finding cluster centers based on local density in object data. These methods have been extended to shell clustering. In this article, we propose a relational mountain clustering method (RMCM), which produces a set of (proto) typical objects as well as a crisp partition of the objects generating the relation, using a new concept that we call relational density. We exemplify RMCM by clustering several relational data sets that come from object data. Finally, RMCM is applied to web log analysis, where it produces useful user profiles from web log data. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 375–392, 2005.

In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification.

One of the most important objects in bioinformatics is a gene product (a protein or an RNA). Besides the gene sequence and expression values found following a microarray experiment, for many gene products, additional functional information comes from the set of gene ontology (GO) annotations and the set of journal abstracts related to the gene product. For these genes, it is reasonable to include similarity measures based on the terms found in the GO and/or the index term sets of the related documents (MeSH annotations). We propose a fuzzy measure-based similarity (FMS) for computing the similarity of two gene products annotated with terms from ontology. The advantage of FMS is that it takes into consideration the context of the whole set when computing the similarity. For the case when the two gene products are not annotated by common ontology terms, we propose a method that avoids a zero similarity result. In dealing with large groups of documents describing the objects under consideration, not only do we determine the similarity between the document pairs, but, by introducing the Choquet integral to the scenario, we can fuse this partial agreement function on pairs of documents into a single value relating the gene products. We present examples of FMS calculation for specific situations where two genes are described by a set of terms from the gene ontology, comparing our measures to others from the literature.

Earlier we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM imposes a constraint on the sum of typicalities over a cluster that leads to unrealistic typicality values for large data sets. Here we propose a new model called possibilistic fuzzy c-means (PFCM). PFCM produces memberships and possibilities simultaneously, along with the cluster centers. PFCM addresses the noise sensitivity defect of FCM, overcomes the coincident clusters problem of possibilistic c-means (PCM) and eliminates the row sum constraints of FPCM. Our numerical examples show that PFCM compares favorably to all of the previous models.

In this paper we develop a hidden Markov model (HMM), called the linguistic HMM (LHMM), suitable for processing sequences of fuzzy vectors. A fuzzy vector B is an n-tuple of fuzzy numbers. Since fuzzy numbers are often associated with linguistic terms, such as "small," "medium," etc., a fuzzy vector can also be called a linguistic vector. The derivation of the linguistic HMM (LHMM) from the numeric HMM is done using the extension principle and the decomposition theorem. We show that the LHMM behaves in the same way as the HMM in the degenerate linguistic case when the fuzzy numbers are singletons (real numbers). We also derive the related algorithms for LHMM training (linguistic Baum-Welch) and for LHMM recognition (linguistic Viterbi). Several examples of LHMM training and recognition are given.

By utilizing morphological shared-weight neural networks (MSNN) that have been trained for face recognition, common access restriction points can be enhanced to identify particular individuals of interest. A trained MSNN is a computational intelligence structure that learns representation of a specific face that encodes in its connection weights the feature extraction and classification abilities needed to identify an instance of that face. It has been shown effective in analyzing images that contain the target in a group of faces, even with the target face at varying orientations and lighting, as well as occluded target faces. The experiments presented here show the possible application of the MSNN to perform watch-list scanning of faces as individuals pass through access screening areas.

Previously, we introduced a method for estimating the linguistic direction of motion of an object in a scene by processing a temporal sequence of linguistic descriptions of its position relative to a stationary object. This method relies on the observation of "regular" descriptions generated through a fuzzy logic system based on the histogram of forces. These descriptions may not exist if the distance between the two objects is too close. In this paper, we use fuzzy sets to generate degrees of activation for the estimated directions of motion. Temporal fusion is applied on these values over a fixed time window using weights calculated from linguistic information on the distance between the objects. The new dynamic linguistic descriptions are determined based on the present as well as the past estimates.

To identify the source of Escherichia coli (E.coli) fecal bacterial contamination, we propose a fuzzy dissimilarity measure to calculate the similarity between the E.coli DNA patterns. The fuzzy dissimilarity measure preserves the dimension of the DNA patterns and at the same time allows variation among same host patterns. The fuzzy dissimilarity measure produces a dissimilarity matrix, a form of relational data. For classification of this type of data representation we present a weighted k-nearest neighbor algorithm. The weighted k.nearest neighbor technique uses the classical k-nearest neighbor rule but solves the problem of 'tie' between multi-classes. In addition, we suggest an ensemble data set method for sample sets with a large range of class sizes. The proposed system showed potential as a stable system in detecting fecal bacterial hosts and as a base for future studies in interpreting DNA patterns.

Screening infants for eye problems is loaded with uncertainty. Babies are unable to describe symptoms and in general may not be cooperative. In an ongoing research project, we are developing methods to screen infants for amblyopia, a common, but treatable, eye problem. The approach consists of processing a sequence of digital frames of the baby, searching for the few images where the infant "fixes" on a light positioned by the camera. Measurements made on the detected pupils are used to produce fuzzy confidence values that are fused together to create an overall confidence of fixation (the key factor in determining amblyopia). One of the most important and difficult factors in this calculation is the determination of the Hirschberg points - points of reflection of the light source off the front of the eye- if they exist at all. The criteria for detection are best thought of as fuzzy rules and methods to score potential Hirschberg points are developed. Results are shown on a variety of imagery collected in a clinical setting.

Numerical data from human sources is often used in management studies. MBAs' attitudes and perceptions about the commitment to their school were collected. In an earlier paper, the utility allowing respondents to draw fuzzy membership functions over the set of questionnaire answers was explored. This response format produced good qualitative information. In this paper, we look at a quantitative analysis of these linguistic responses. In particular, we develop a linguistic nearest prototype and computational efficient linguistic Hard C-Means for vectors of fuzzy sets and apply these algorithms to such "linguistic vectors" derived from a set of forty-nine subjects answering questions about students' commitment to their university.

The paper is concerned with a linguistic fuzzy c-means (FCM) algorithm with vectors of fuzzy numbers as inputs. This algorithm is based on the extension principle and the decomposition theorem. It turns out that using the extension principle to extend the capability of the standard membership update equation to deal with a linguistic vector has a huge computational complexity. In order to cope with this problem, an efficient method based on fuzzy arithmetic and optimization has been developed and analyzed. We also carefully examine and prove that the algorithm behaves in a way similar to the FCM in the degenerate linguistic case. Synthetic data sets and the iris data set have been used to illustrate the behavior of this linguistic version of the FCM.

One of the popular fuzzy set theoretic technologies is the fuzzy integral. It combines numeric confidence from information sources with the worth of subsets of those sources. But sometimes, we encounter data that has a higher order of uncertainty, e.g., confidence values, locations, etc., that can only be expressed in linguistic terms. It is our belief that dealing with this type of data through the extended version of the regular algorithms produces meaningful analyses. The regular algorithms are extended using the extension principle. While we have reported success in applying the extended Choquet integral on landmine detection problems, there is a need to study the behavior of the linguistic fuzzy integrals. In this paper, we examine the extended version of the Choquet and Sugeno fuzzy integrals on a synthetic data set to gain insight into the effect of varying conditions on the final results.

This paper examines object pair matching within LADAR (laser radar) imagery. By manipulating the three-dimensional data contained within a LADAR range image, it is possible to create a version of the scene as seen from above. In the transformed view, a fuzzy region represents each object, and the spatial relationship between two objects is represented by a force histogram. Matching two scenes then comes down to comparing force histograms. Each comparison gives a degree of similarity between the two object pairs considered, as well as an assessment of the pose parameters. These values can finally be combined to find a correct scene matching. Experiments on synthetic data as well as on real data demonstrate the applicability of our approach.

We show how linguistic expressions can be generated to describe the spatial relations between a mobile robot and its environment, using readings from a ring of sonar sensors. Our work is motivated by the study of human-robot communication for non-expert users. The eventual goal is to use these linguistic expressions for navigation of the mobile robot in an unknown environment, where the expressions represent the qualitative state of the robot with respect to its environment, in terms that are easily understood by human users. In the paper, we describe the histogram of forces and its application to sonar sensors on a mobile robot. Several environment examples are also included with the generated linguistic descriptions.

Differential white cell counts from bone marrow preparations are very useful in evaluation of various hematologic disorders. It is tedious to locate, identify, and count these classes of cells, even by skilled hands. Automation of classification and counting would be of great benefit. However, the class structure of bone marrow or peripheral blood cells is not discrete; it represents a biological continuum of maturation levels. Because of this, there is uncertainty and overlap in characteristics of adjacent cell classes such that traditional pattern recognition techniques have difficulty in arriving at accurate cell counts. The authors investigate soft counting networks that are trained to produce accurate overall class counts by allowing cells to have degrees of membership in multiple cell classes. This approach is applied to a bone marrow cell library and is compared with other standard recognition algorithms.

We present a new approach for object boundary extraction, called the watersnake. It is a two-step snake algorithm whose energy functional is minimized by the dynamic programming method. It is more robust to local minima because it finds the solution by searching the entire energy space. To reduce the complexity of the minimization process, the watershed transformation and a coarse-to-fine strategy are used. The new technique is compared to standard methods for accuracy in synthetic data and is applied to segmentation of white blood cells in bone marrow images.

As described by Zadeh, recognition technology refers to systems that incorporate new sensors, novel signal processing, and soft computing. In this paper, we discuss these principles applied to the problem of land mine detection. We describe a complex recognition system that is evolving from basic research into a fielded system. Some components of this system have been field tested with excellent results, whereas other components have achieved such results in the laboratory. Fuzzy set-based information fusion algorithms are central to the excellent results obtained. Multiple-detection algorithms are applied to signals acquired from an innovative ground penetrating radar that produces volumetric sub-surface imagery. The outputs of the detection algorithms are combined using the fuzzy logic and Sugeno and Choquet fuzzy integrals to produce overall detection scores. Experimental results are provided on training data and on completely blind test data collected in the field and scored by the US Army.

In this paper, we present an image understanding system using fuzzy sets and fuzzy measures. This system is based on a symbolic object-oriented image interpretation system. We apply a simple, powerful three-dimensional (3-D) recursive filter to tracking moving objects in a dynamic image sequence. This filter has a time-varying 3-D frequency-planar passband that is adapted in a feedback system to automatically track moving objects. However, as objects in the image sequence are not well-defined and are engaged in dynamic activities, their shapes and trajectories in most cases can be described only vaguely. In order to handle these uncertainties, we use fuzzy measures to capture subtle variations and manage the uncertainties involved. This enables us to develop an image understanding system that produces a very natural output. We demonstrate the effectiveness of our system with complex real traffic scenes.

Fuzzy set methods have been used to model and manage uncertainty in various aspects of image processing, pattern recognition, and computer vision. High-level computer vision applications hold a great potential for fuzzy set theory because of its links to natural language. Linguistic scene description, a language-based interpretation of regions and their relationships, is one such application that is starting to bear the fruits of fuzzy set theoretic involvement. In this paper, we are expanding on two earlier endeavors. We introduce new families of fuzzy directional relations that rely on the computation of histograms of forces. These families preserve important relative position properties. They provide inputs to a fuzzy rule base that produces logical linguistic descriptions along with assessments as to the validity of the descriptions. Each linguistic output uses hedges from a dictionary of about 30 adverbs and other terms that can be tailored to individual users. Excellent results from several synthetic and real image examples show the applicability of this approach.

Managerial studies often rely on gathering abstract, numerical data from human resources. Data is gathered about employees' attitudes and perceptions regarding organizations and their practices. Models tested using this data account for probabilistic uncertainty in the data, but not for vague uncertainty. In a previous study, Adrian (1998) explored the utility of allowing respondents to draw fuzzy membership functions over the set of questionnaire answers instead of just picking one response. Her results showed good qualitative value can be obtained from this format. In this paper, we look at a quantitative analysis of these linguistic responses. In particular, we develop classification algorithms for vectors of fuzzy sets and apply these algorithms to such "linguistic vectors" derived from a set of eleven subjects answering questions about job satisfaction and organizational commitment.

This correspondence points out several published errors in replicates of the well-known iris data, which was collected by Anderson (1935) but first published by Fisher (1936).

Computer vision applications often involve measuring properties of objects in images. Typically, thresholding or segmentation techniques are used to obtain crisp object boundaries before object properties are computed. In this correspondence, we explore the possibility of using fuzzy definitions for measuring object properties without having to make crisp decisions about object boundaries prematurely. We present theorems which indicate that the use of fuzzy definitions to measure properties in intensity-based image analysis almost always gives accurate results. We also present experimental evidence and reasoning which show that fuzzy definitions are not always useful in feature-based methods.

Many low-vision people have impaired visual function due to macular scotomas. When scotomas involve the fovea, the low-vision patient must use an eccentric retinal area. Training may help some of these patients compensate for their scotomas. Using a scanning laser ophthalmoscope (SLO), ophthalmologists can measure scotomas and train the patients to use an appropriate retinal area for visual tasks. This task is difficult because the patients may move their eyes consciously or unconsciously during inspection or training. We present a Hough-based registration method combined with feature-based SSD technique to help ophthalmologists perform more accurate and efficient eye registration for inspection and training. Mathematical morphology is used to preprocess each frame to extract a small but relevant set of feature points.

In this paper we analyze the neural network implementation of fuzzy logic proposed by Keller et al. [Fuzzy Sets Syst., 45, 1–12 (1992)], derive a learning algorithm for obtaining an optimal α for the net, and, for a special case, we show how one can directly (avoiding training) compute the optimal α. We address how training data can be generated for such a system. Effectiveness of the optimal α is then established through numerical examples. In this regard, several indices for performance evaluation are discussed. Finally, we propose a new architecture and demonstrate its effectiveness with numerical examples. © 1998 John Wiley & Sons, Inc.

The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation method.

Karyotyping involves the visualization and classification of chromosomes into standard classes. In "normal" human metaphase spreads, chromosomes occur in homologous pairs for the autosomal classes 1-22, and X chromosome for females. Many existing approaches for performing automated human chromosome image analysis presuppose cell normalcy, containing 46 chromosomes within a metaphase spread with two chromosomes per class. This is an acceptable assumption for routine automated chromosome image analysis. However, many genetic abnormalities are directly linked to structural or numerical aberrations of chromosomes within the metaphase spread. Thus, two chromosomes per class cannot be assumed for anomaly analysis. This paper presents the development of image analysis techniques which are extendible to detecting numerical aberrations evolving from structural abnormalities. Specifically, an approach to identifying "normal" chromosomes from selected class(es) within a metaphase spread is presented. Chromosome assignment to a specific class is initially based on neural networks, followed by banding pattern and centromeric index criteria checking, and concluding with homologue matching. Experimental results are presented comparing neural networks as the sole classifier to our homologue matcher for identifying class 17 within normal and abnormal metaphase spreads.

Escherichia coli O157:H7 has been found to cause serious health problems. Traditional methods to identify the organism are quite slow, pulsed-held gel electrophoresis (PFGE) images contain "banding pattern" information which can be used to recognize the bacteria. A fuzzy logic rule-based system is used as a guide to find a good feature set for the recognition of E. coli O157:H7. While the fuzzy rule-based system achieved good recognition, the human inspired features used in the rules were incorporated into a multiple neural network fusion approach which gave excellent separation of the target bacteria. The fuzzy integral was utilized in the fusion of neural networks trained with different feature sets to reach an almost perfect classification rate of E. coli O157:H7 PFGE patterns made available for the experiments.

Recently, the possibilistic C-means algorithm (PCM) was proposed to address the drawbacks associated with the constrained memberships used in algorithms such as the fuzzy C-means (FCM). In this issue, Barni et al. (1996) report a difficulty they faced while applying the PCM, and note that it exhibits an undesirable tendency to converge to coincidental clusters. The purpose of this paper is not just to address the issues raised by Barni et al., but to go further and analytically examines the underlying principles of the PCM and the possibilistic approach, in general. We analyze the data sets used by Barni et al. and interpret the results reported by them in the light of our findings.

One of the longest standing problems in medical image analysis is that of the automated recognition of chromosomes from images of a metaphase spread of a cell. This process of visualizing and categorizing the chromosomes within a cell, called karyotyping, is a key factor in many medical procedures. It is a labor intensive activity, and hence, is a great candidate for automation. However, there are many sources of uncertainty in this problem domain, making complete karyotyping a difficult problem. We describe how fuzzy logic is being inserted into a complete karyotyping system to deal with uncertainty in similar chromosome classes.>

Fuzzy logic is applied to the problem of locating and reading street numbers in digital images of handwritten mail. A fuzzy rule-based system is defined that uses uncertain information provided by image processing and neural network-based character recognition modules to generate multiple hypotheses with associated confidence values for the location of the street number in an image of a handwritten address. The results of a blind test of the resultant system are presented to demonstrate the value of this new approach. The results are compared to those obtained using a neural network trained with backpropagation. The fuzzy logic system achieved higher performance rates.>

Evidence Aggregation Networks based on multiplicative fuzzy hybrid operators were introduced by Krishnapuram and Lee. They have been used for image segmentation, pattern recognition, and general multicriteria decision making. One of the drawbacks to these networks is that the training is complex and quite time consuming. In this article, we modify these aggregation networks to implement additive fuzzy hybrid connectives. We study the theoretical properties of two classes of such aggregation operators, one where the union and intersection components are based on multiplication, and the other where these components are derived from Yager connectives. These new networks have similar excellent properties such as backpropagation training and node interpretability for decision making under uncertainty as do their multiplicative precursors. They also have the advantage that training is easier since the derivatives of the additive hybrid operators are not as complex in form. the appropriate training algorithms are derived, and several examples given to illustrate the properties of the networks. © 1994 John Wiley & Sons, Inc.

In image analysis, there have been few effective procedures that deal with a wide class of imagery acquired by different sensors under different environmental conditions. The success of a given classification algorithm is dependent upon pattern familiarity, background, and the image acquisition process. Thus, with the inaccuracies in the acquisition process, as well as incomplete or incorrect knowledge about the pattern classes, one cannot place complete confidence in the classifier outcome. There has been increasing success in making decisions under such uncertain conditions by using a rule-based approach with effective uncertainty management, which involves identifying the causes of uncertainty and developing mathematical models for the same. These are incorporated into the rule structure so that the result would be a set of choices or decisions, with a set of associated certainty values or confidences. This paper proposes a "unified" methodology to combine the uncertainties associated with evidence for a given proposition, which is then systematically propagated down the decision tree. The relative importance of propositions as well as the rules themselves have also been considered. Finally, the methodology has been applied to an ATR problem and the results, when compared to some existing methods, show the overall effectiveness of this approach.>

Fractal geometry is becoming increasingly more important in the study of image characteristics. There are numerous methods available to estimate parameters from images of fractal surfaces. A very general technique to calculate numerous fractal features involves the estimation of the mass density function by box counting. The authors analyze the box-counting method, establish a lower bound for the box size, and indicate how algorithms can be improved to give better estimates of fractal features of images. This provides a theoretical basis for a heuristic approach used by C.A. Pickover and A.L. Khorasani (1986).>

The clustering problem is cast in the framework of possibility theory. The approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values can be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function. The advantages of the resulting family of possibilistic algorithms are illustrated by several examples.>

Properties of objects and spatial relations between objects play an important role in rule-based approaches for high-level vision. The partial presence or absence of such properties and relationships can supply both positive and negative evidence for region labeling hypotheses. Similarly, fuzzy labeling of a region can generate new hypotheses pertaining to the properties of the region, its relation to the neighboring regions, and, finally, hypotheses pertaining to the labels of the neighboring regions. A unified methodology that can be used to characterize both properties and spatial relationships of object regions in a digital image is presented. The methods proposed for computing the properties and relations of image regions can be used to arrive at more meaningful decisions about the contents of the scene.>

Fuzzy logic has been applied in many engineering disciplines. The problem of fuzzy logic inference is investigated as a question of aggregation of evidence. A fixed network architecture employing general fuzzy unions and intersections is proposed as a mechanism to implement fuzzy logic inference. It is shown that these networks possess desirable theoretical properties. Networks based on parameterized families of operators (such as Yager's union and intersection) have extra predictable properties and admit a training algorithm which produces sharper inference results than were earlier obtained. Simulation studies corroborate the theoretical properties.

Methods for modeling and managing uncertainty in computer vision systems have received increased attention in recent years. Automatic target recognition is one application area of computer vision where the demands are particularly acute. In this article, fuzzy logic is proposed as a means of handling uncertainty in an expert system structure for automatic target recognition. A new technique for logical inference is described which is well-suited for this type of application. A prototype system has been developed and tested on multisensor and temporal images. the results are compared to a similar expert system which used a numeric uncertainty calculus.

This article incorporates fuzzy set theory into the task of image segmentation. the basic concept is to allow the fuzzy membership function to model the uncertainty and vagueness of definition of objects in digital images. We define a fuzzy segmentation as a fuzzy c-partition of an image and incorporate this definition and fuzzy criteria into several image segmentation techniques including segmentation by clustering, region growing, and relaxation labelling. the algorithms are tested on digital forward looking infrared (FLIR) images and digital subtraction angiographic images. These techniques are shown to perform at least as well as their crisp or probabilistic counterparts when converted to a crisp partition. However, the real advantage to a fuzzy methodology is that the degree of membership provides a model of uncertainty and can subsequently be used by feature extraction and object recognition algorithms to increase the amount of information available in decision processes.

A method of evidence fusion, based on the fuzzy integral, is developed. This technique nonlinearly combines objective evidence, in the form of a fuzzy membership function, with subjective evaluation of the worth of the sources with respect to the decision. Various new theoretical properties of this technique are developed, and its applicability to information fusion in computer vision is demonstrated through simulation and with object recognition data from forward-looking infrared imagery.>

Any decision procedure that is applied to a given problem involves both the gathering of relevant information from different sources and, when possible, accounting for the reliability of each source or group of sources. Due to insufficient knowledge, it may not be possible to isolate an unreliable or poor source of information. However, if a set of sources provides information to a decision algorithm, the effect of these sources as a group could be analyzed in terms of the relative coherence of the sources within it. A group whose sources are in agreement regarding the same decision is more reliable than one in which the individual sources supported different decisions. A measure of the unreliability of a group is its 'disparity', which could compensate for disagreement within a group. Theory and results to support this group unreliability are presented.>

Many objects in images of natural scenes are so complex and erratic, that describing them by the familiar models of classical geometry is inadequate. In this paper, we exploit the power of fractal geometry to generate global characteristics of natural scenes. In particular we are concerned with the following two questions: 1) Can we develop a measure which can distinguish between different global backgrounds (e.g., mountains and trees)? and 2) Can we develop a measure that is sensitive to change in distance (or scale)? We present a model based on fractional Brownian motion which will allow us to recover two characteristics related to the fractal dimension from silhouettes. The first characteristic is an estimate of the fractal dimension based on a least squares linear fit. We show that this feature is stable under a variety of real image conditions and use it to distinguish silhouettes of trees from silhouettes of mountains. Next we introduce a new theoretical concept called the average Holder constant and relate it mathematically to the fractal dimension. It is shown that this measurement is sensitive to scale in a predictable manner, and hence, provides the potential for use as a range indicator. Corroborating experimental results are presented.

Segmentation, description, and recognition of objects and regions in natural images involve processes containing varying degrees of uncertainty. High-level vision systems can utilize measures of confidence in scene component labeling to prioritize investigation, resolve conflict, allocate resources, etc., if such measures are provided by the midlevel vision subsystem. A methodology based on the theory of fuzzy sets is presented which can be used to produce linguistic, i.e., natural language, confidence measures of object labeling in natural scenes. The linguistic structure models the uncertainty and complexity and allows for easy incorporation of high-level ancillary information, such as weather conditions and sensor motion. The use of the linguistic confidence structure is demonstrated in two applications. The first involves the labeling of objects in multitemporal forward-looking infrared (FLIR) sequences. The second application is in fusion of information from more than one sensor using sensor models. In both cases, new methods for automatically generating the linguistic values from the image data are described. Also, a new linguistic approximation scheme is developed to generate the final natural language result which reflects the nature of the fuzzy arithmetic.

The extended Euclidean algorithm is typically used to calculate multiplicative inverses over finite fields and rings of integers. The algorithm presented here has approximately the same number of average iterations and maximum number of iterations. It is shown, when P is a Mersenne prime, implementation of this algorithm on a processor, designed especially for mod P arithmetic operations, produces a more efficient algorithm with respect to the amount of program statements and number of operations. It is then shown heuristically, when the division and multiplications are performed simultaneously, the Euclidean algorithm has fewer subiterations.

The perceptron algorithm, one of the class of gradient descent techniques, has been widely used in pattern recognition to determine linear decision boundaries. While this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable, it exhibits erratic behavior if the data are not linearly separable. Fuzzy set theory is introduced into the perceptron algorithm to produce a ``fuzzy algorithm'' which ameliorates the convergence problem in the nonseparable case. It is shown that the fuzzy perceptron, like its crisp counterpart, converges in the separable case. A method of generating membership functions is developed, and experimental results comparing the crisp to the fuzzy perceptron are presented.

Classification of objects is an important area of research and application in a variety of fields. In the presence of full knowledge of the underlying probabilities, Bayes decision theory gives optimal error rates. In those cases where this information is not present, many algorithms make use of distance or similarity among samples as a means of classification. TheK-nearest neighbor decision rule has often been used in these pattern recognition problems. One of the difficulties that arises when utilizing this technique is that each of the labeled samples is given equal importance in deciding the class memberships of the pattern to be classified, regardless of their `typicalness'. The theory of fuzzy sets is introduced into theK-nearest neighbor technique to develop a fuzzy version of the algorithm. Three methods of assigning fuzzy memberships to the labeled samples are proposed, and experimental results and comparisons to the crisp version are presented.