Motivated by deep learning regimes with multiple interacting yet distinct model components, we introduce learning diagrams, graphical depictions of training setups that capture parameterized learning as data rather than code. A learning diagram compiles to a unique loss function on which component models are trained. The result of training on this loss is a collection of models whose predictions ``agree" with one another. We show that a number of popular learning setups such as few-shot multi-task learning, knowledge distillation, and multi-modal learning can be depicted as learning diagrams. We further implement learning diagrams in a library that allows users to build diagrams of PyTorch and Flux.jl models. By implementing some classic machine learning use cases, we demonstrate how learning diagrams allow practitioners to build complicated models as compositions of smaller components, identify relationships between workflows, and manipulate models during or after training. Leveraging a category theoretic framework, we introduce a rigorous semantics for learning diagrams that puts such operations on a firm mathematical foundation.

Fine-scale pixel-level annotation of minirhizotron root images is a less common and challenging task. We present an interactive segmentation framework to accelerate root annotation. We leverage the concept of few-shot segmentation so that the pretrained model can be effectively fine-tuned and transferred to an unseen category. To provide immediate feedback for real-time interaction, we adapted a UNet architecture by attaching lightweight embedding layers which leveraged a prototype learning (PL) approach to efficiently learn the data metric in the embedding space. The prototypes optimized by the prototype loss preserve the within-class data variation, enabling effective fine-tuning. Furthermore, we designed a system with our interactive annotation framework and experimented with real users to validate the approach.

Understanding and quantifying ecosystem services are crucial for sustainable environmental management, conservation efforts, and policy-making. The advancement of remote sensing technology and machine learning techniques has greatly facilitated this process. Yet, ground truth labels, such as biodiversity, are very difficult and expensive to measure. In addition, more easily obtainable proxy labels, such as land use, often fail to capture the complex heterogeneity of the ecosystem. In this paper, we demonstrate how land use proxy labels can be implemented with a soft, multi-label classifier to predict ecosystem services with complex heterogeneity.

Artificial Intelligence (AI) has been enhancing data analysis efficiency and accuracy during plant phenotyping, which is vital for tackling global agricultural and environmental challenges. Designing a reliable AI system to assist precise plant phenotyping begins with high-quality phenotypic feature annotation, which usually involves collaboration between plant scientists and AI specialists. However, due to the high level of diversity in these researchers’ backgrounds, it is likely that they have differing user needs from a fine-grained plant feature annotation system. We conducted semi-structured interviews with eight experienced annotators from diverse backgrounds, and observed how they interact with their preferred annotation system, to elucidate the challenges faced when annotating plant features and identify user needs. We collected qualitative responses to the interview questions, and conducted a quantitative evaluation of the agreement of their annotations on the given images. By analyzing the participants’ behaviors and the collected data, we identified common user needs and derived implications for the design of an AI-assisted annotation system, including providing a range of annotation options, the flexibility to adapt annotations, and functions to help addressing uncertainty. Our research contributes to the design of systems that make annotations efficient and reliable, not only benefiting plant phenotyping, but also other interdisciplinary fields that rely on user-driven annotations.

Weakly supervised target detection and semantic segmentation (WSSS) approaches aim at learning object or pixel-level classification labels from imprecise, uncertain, or ambiguous data annotations. A crucial step in WSSS is to produce pseudolabels, which can be used to train a fully supervised semantic classifier. Post hoc attention mechanisms, such as class activation mapping (CAM), are commonly used to produce these pseudolabels. While traditional CAM methods derive feature importance from heuristics on gradient information, this work alternatively investigates whether a subset of discriminative activation feature maps can be down-selected and fused to improve pseudolabel accuracy. More specifically, the multiple instance Choquet integral (MICI) [1] was explored as a method for discriminative feature selection and fusion. Experimental results on both synthetic and real-world datasets indicate the utility of the MICI in down-selecting class-discriminative activation feature maps. Fusion of the MICI-selected sources was competitive to CAM methods for generating pseudolabels.

Synthetic aperture sonar (SAS) intensity statistics are dependent upon the sensing geometry at the time of capture. Estimating bathymetry from acoustic surveys is challenging. While several methods have been proposed to estimate seabed relief via intensity, we develop the first large-scale study that relies on deep learning models. In this work, we pose bathymetric estimation from SAS surveys as a domain translation problem of translating intensity to height. Since no dataset of coregistered seabed relief maps and sonar imagery previously existed to learn this domain translation, we produce the first large simulated dataset containing coregistered pairs of seabed relief and intensity maps from two unique sonar data simulation techniques. We apply four types of models, with varying complexity, to translate intensity imagery to seabed relief: a shape-from-shading (SFS) approach, a Gaussian Markov random field (GMRF) approach, a conditional Generative Adversarial Network (cGAN), and UNet architectures. Each model is applied to datasets containing sand ripples, rocky, mixed, and flat sea bottoms. Methods are compared in reference to the coregistered simulated datasets using L1 error. Additionally, we provide results on simulated and real SAS imagery. Our results indicate that the proposed UNet architectures outperform an SFS, a GMRF, and a pix2pix cGAN model.

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.

In this work, we propose a new loss to improve feature discriminability and classification performance. Motivated by the adaptive cosine/coherence estimator [43] (ACE), our proposed method incorporates angular information that is inherently learned by artificial neural networks. Our learnable ACE (LACE) transforms the data into a new "whitened" space that improves the inter-class separability and intra-class compactness. We compare our LACE to alternative state-of-the art softmax-based and feature regularization approaches. Our results show that the proposed method can serve as a viable alternative to cross entropy and angular softmax approaches. Our code is publicly available.1

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.

Automated individual tree crown (ITC) delineation plays an important role in forest remote sensing. Accurate ITC delineation benefits biomass estimation, allometry estimation, and species classification among other forest related tasks, all of which are used to monitor forest health and make important decisions in forest management. In this paper, we introduce Neuro-Symbolic DeepForest, a convolutional neural network (CNN) based ITC delineation algorithm that uses a neuro-symbolic framework to inject domain knowledge (represented as rules written in probabilistic soft logic) into a CNN. We create rules that encode concepts for competition, allometry, constrained growth, mean ITC area, and crown color. Our results show that the delineation model learns from the annotated training data as well as the rules and that under some conditions, the injection of rules improves model performance and affects model bias. We then analyze the effects of each rule on its related aspects of model performance. We find that the addition of domain data can improve F1 by as much as 4 F1-points, reduce the KL-divergence between ground-truth and predicted area distributions, and reduce the aggregate error in area between ground-truth and predicted delineations.

In remote sensing, it is often challenging to acquire or collect a large data set that is accurately labeled. This difficulty is usually due to several issues, including but not limited to the study site’s spatial area and accessibility, errors in the global positioning system (GPS), and mixed pixels caused by an image’s spatial resolution. We propose an approach, with two variations, that estimates multiple-target signatures from training samples with imprecise labels: multitarget multiple-instance adaptive cosine estimator (MTMI-ACE) and multitarget multiple-instance spectral match filter (MTMI-SMF). The proposed methods address the abovementioned problems by directly considering the multiple-instance, imprecisely labeled data set. They learn a dictionary of target signatures that optimizes detection against a background using the adaptive cosine estimator (ACE) and spectral match filter (SMF). Experiments were conducted to test the proposed algorithms using a simulated hyperspectral data set, the MUUFL Gulfport hyperspectral data set collected over the University of Southern Mississippi–Gulfpark Campus, and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral data set collected over Santa Barbara County, CA, USA. Both simulated and real hyperspectral target detection experiments show that the proposed algorithms are effective at learning target signatures and performing target detection.

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.

Broad scale remote sensing promises to build forest inventories at unprecedented scales. A crucial step in this process is to associate sensor data into individual crowns. While dozens of crown detection algorithms have been proposed, their performance is typically not compared based on standard data or evaluation metrics. There is a need for a benchmark dataset to minimize differences in reported results as well as support evaluation of algorithms across a broad range of forest types. Combining RGB, LiDAR and hyperspectral sensor data from the USA National Ecological Observatory Network's Airborne Observation Platform with multiple types of evaluation data, we created a benchmark dataset to assess crown detection and delineation methods for canopy trees covering dominant forest types in the United States. This benchmark dataset includes an R package to standardize evaluation metrics and simplify comparisons between methods. The benchmark dataset contains over 6,000 image-annotated crowns, 400 field-annotated crowns, and 3,000 canopy stem points from a wide range of forest types. In addition, we include over 10,000 training crowns for optional use. We discuss the different evaluation data sources and assess the accuracy of the image-annotated crowns by comparing annotations among multiple annotators as well as overlapping field-annotated crowns. We provide an example submission and score for an open-source algorithm that can serve as a baseline for future methods.

Non-invasive heart rate estimation is of great importance in daily monitoring of cardiovascular diseases. In this paper, a bidirectional long short term memory (bi-LSTM) regression network is developed for non-invasive heart rate estimation from the ballistocardiograms (BCG) signals. The proposed deep regression model provides an effective solution to the existing challenges in BCG heart rate estimation, such as the mismatch between the BCG signals and ground-truth reference, multi-sensor fusion and effective time series feature learning. Allowing label uncertainty in the estimation can reduce the manual cost of data annotation while further improving the heart rate estimation performance. Compared with the state-of-the-art BCG heart rate estimation methods, the strong fitting and generalization ability of the proposed deep regression model maintains better robustness to noise (e.g., sensor noise) and perturbations (e.g., body movements) in the BCG signals and provides a more reliable solution for long term heart rate monitoring.

In remote sensing, each sensor can provide complementary or reinforcing information. It is valuable to fuse outputs from multiple sensors to boost overall performance. Previous supervised fusion methods often require accurate labels for each pixel in the training data. However, in many remote-sensing applications, pixel-level labels are difficult or infeasible to obtain. In addition, outputs from multiple sensors often have different resolutions or modalities. For example, rasterized hyperspectral imagery (HSI) presents data in a pixel grid while airborne light detection and ranging (LiDAR) generates dense 3-D point clouds. It is often difficult to directly fuse such multimodal, multiresolution data. To address these challenges, we present a novel multiple instance multiresolution fusion (MIMRF) framework that can fuse multiresolution and multimodal sensor outputs while learning from automatically generated, imprecisely labeled data. Experiments were conducted on the MUUFL Gulfport HSI and LiDAR data set and a remotely sensed soybean and weed data set. Results show improved, consistent performance on scene understanding and agricultural applications when compared to traditional fusion methods.

In classifier (or regression) fusion, the aim is to combine the outputs of several algorithms to boost overall performance. Standard supervised fusion algorithms often require accurate and precise training labels. However, accurate labels may be difficult to obtain in many remote sensing applications. This paper proposes novel classification and regression fusion models that can be trained given ambiguously and imprecisely labeled training data in which the training labels are associated with sets of data points (i.e., “bags”) instead of individual data points (i.e., “instances”) following a multiple-instance learning framework. Experiments were conducted based on the proposed algorithms on both synthetic data and applications such as target detection and crop yield prediction given remote sensing data. The proposed algorithms show effective classification and regression performance.

In this paper, two methods for discriminative multiple instance target characterization, MI-SMF and MI-ACE, are presented. MI-SMF and MI-ACE estimate a discriminative target signature from imprecisely-labeled and mixed training data. In many applications, such as sub-pixel target detection in remotely-sensed hyperspectral imagery, accurate pixel-level labels on training data is often unavailable and infeasible to obtain. Furthermore, since sub-pixel targets are smaller in size than the resolution of a single pixel, training data is comprised only of mixed data points (in which target training points are mixtures of responses from both target and non-target classes). Results show improved, consistent performance over existing multiple instance concept learning methods on several hyperspectral sub-pixel target detection problems.

While the Choquet integral (Chi) is a powerful parametric nonlinear aggregation function, it has limited scope and is not a universal function generator. Herein, we focus on a class of problems that are outside the scope of a single Chi. Namely, we are interested in tasks where different subsets of inputs require different Chls. Herein, a genetic program (GF) is used to extend the Chi, referred to as GpChI hereafter, specifically in terms of compositions of Chls and/or arithmetic combinations of Chls. An algorithm is put forth to leam the different GP Chls via genetic algorithm (GA) optimization. Synthetic experiments demonstrate GpChI in a controlled fashion, i.e., we know the answer and can compare what is learned to the truth. Real-world experiments are also provided for the mult-sensor fusion of electromagnetic induction (EMI) and ground penetrating radar (GPR) for explosive hazard detection. Our mutli-sensor fusion experiments show that there is utility in changing aggregation strategy per different subsets of inputs (sensors or algorithms) and fusing those results.

The application of Partial Membership Latent Dirichlet Allocation (PM-LDA) for hyperspectral endmember estimation and spectral unmixing is presented. PM-LDA provides a model for a hyperspectral image analysis that accounts for spectral variability and incorporates spatial information through the use of superpixel-based “documents.” In our application of PM-LDA, we employ the Normal Compositional Model in which endmembers are represented as Normal distributions to account for spectral variability and proportion vectors are modeled as random variables governed by a Dirichlet distribution. The use of the Dirichlet distribution enforces positivity and sum-to-one constraints on the proportion values. Algorithm results on real hyperspectral data indicate that PM-LDA produces endmember distributions that represent the ground truth classes and their associated variability.

Signature-based detectors for hyperspectral target detection rely on knowing the specific target signature in advance. However, target signatures are often difficult or impossible to obtain. Furthermore, common methods for obtaining target signatures, such as from laboratory measurements or manual selection from an image scene, usually do not capture the discriminative features of target class. In this paper, an approach for estimating a discriminative target signature from imprecise labels is presented. The proposed approach maximizes the response of the hybrid sub-pixel detector within a multiple instance learning framework and estimates a set of discriminative target signatures. After learning target signatures, any signature based detector can then be applied on test data. Both simulated and real hyperspectral target detection experiments are shown to illustrate the effectiveness of the method.

A map-guided superpixel segmentation method for hyperspectral imagery is developed and introduced. The proposed approach develops a hyperspectral version of the SLIC superpixel algorithm, leverages map information to guide segmentation, and incorporates the semi-supervised Partial Membership Latent Dirichlet Allocation (sPM-LDA) to obtain a final segmentation. The proposed method is applied to two hyperspectral data sets and quantitative cluster validity metrics indicate that the proposed approach outperforms existing hyperspectral superpixel segmentation methods.

Topic models [e.g., probabilistic latent semantic analysis, latent Dirichlet allocation (LDA), and supervised LDA] have been widely used for segmenting imagery. However, these models are confined to crisp segmentation, forcing a visual word (i.e., an image patch) to belong to one and only one topic. Yet, there are many images in which some regions cannot be assigned a crisp categorical label (e.g., transition regions between a foggy sky and the ground or between sand and water at a beach). In these cases, a visual word is best represented with partial memberships across multiple topics. To address this, we present a partial membership LDA (PM-LDA) model and an associated parameter estimation algorithm. This model can be useful for imagery, where a visual word may be a mixture of multiple topics. Experimental results on visual and sonar imagery show that PM-LDA can produce both crisp and soft semantic image segmentations; a capability previous topic modeling methods do not have.

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.

Topic models (e.g., pLSA, LDA, SLDA) have been widely used for segmenting imagery. These models are confined to crisp segmentation. Yet, there are many images in which some regions cannot be assigned a crisp label (e.g., transition regions between a foggy sky and the ground or between sand and water at a beach). In these cases, a visual word is best represented with partial memberships across multiple topics. To address this, we present a partial membership latent Dirichlet allocation (PM-LDA) model and associated parameter estimation algorithms. Experimental results on two natural image datasets and one SONAR image dataset show that PM-LDA can produce both crisp and soft semantic image segmentations; a capability existing methods do not have.

Dictionary Learning Functions of Multiple Instances (DL-FUMI) is proposed to address target detection problems with inaccurate training labels. DL-FUMI is a multiple instance dictionary learning method that estimates target atoms that describe distinctive and representative features of the target class and background atoms that account for the shared features found across both target and non-target data points. Experimental results show that the target atoms estimated by DL-FUMI are more discriminative and representative of the target class than comparison methods. DL-FUMI is shown to have improved performance on several detection problems as compared to other multiple instance dictionary learning algorithms.

Several techniques exist for dealing with spectral variability in hyperspectral unmixing, such as multiple endmember spectral mixture analysis (MESMA) or compositional models. These algorithms are computationally very involved, and often cannot be executed on problems of reasonable size. In this work, we present a new algorithm for solving the unmixing problem when spectral variability is present. The algorithm uses a library-based approach to describe the variability present in each class, and executes an alternating optimization with respect to these libraries. The optimization problem itself is constructed as an angle minimization problem by exploiting the geometrical interpretation of the unmixing problem. This results in an algorithm which yields almost identical results as MESMA, but is computationally much more favorable.

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.

In hyperspectral unmixing applications, one typically assumes that a single spectrum exists for every endmember. In many scenarios, this is not the case, and one requires a set or a distribution of spectra to represent an endmember or class. This inherent spectral variability can pose severe difficulties in classical unmixing approaches. In this paper, we present a new algorithm for dealing with endmember variability in spectral unmixing, based on the geometrical interpretation of the resulting unmixing problem, and an alternating optimization approach. This alternating-angle-minimization algorithm uses sets of spectra to represent the variability present in each class and attempts to identify the subset of endmembers which produce the smallest reconstruction error. The algorithm is analogous to the popular multiple endmember spectral mixture analysis technique but has a much more favorable computational complexity while producing similar results. We illustrate the algorithm on several artificial and real data sets and compare with several other recent techniques for dealing with endmember variability.

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.

We present a Bayesian probabilistic model and inference algorithm for fuzzy clustering that provides expanded capabilities over the traditional Fuzzy C-Means approach. Additionally, we extend the Bayesian Fuzzy Clustering model to handle a variable number of clusters and present a particle filter inference technique to estimate the model parameters including the number of clusters. We show results on synthetic and real data and compare with other approaches.

The aim of this work is to characterize the seafloor by estimating invariant sand ripple parameters from synthetic aperture sonar (SAS) imagery. Using a hierarchical Bayesian framework and a known sensing geometry, a method for estimating sand ripple frequency, amplitude, and orientation values from a single SAS image, as well as from sets of SAS imagery over an area, is presented. This is accomplished through the development of an extended model for sand ripple characterization and a Metropolis-within-Gibbs sampler to estimate sand ripple frequency, amplitude, and orientation characteristics for multiaspect high-frequency side-look sonar data. Results are presented on synthetic and measured SAS imagery that indicate the ability of the proposed method to estimate desired sand ripple characteristics.

A new algorithm for subpixel target detection in hyperspectral imagery is proposed which uses the PFCM-FLICM-PCE algorithm to model and estimate the parameters of the image background. This method uses the piece-wise convex mixing model with spatial-spectral constraints, and uses possibilistic and fuzzy clustering techniques to find the piece-wise convex regions and robustly estimate the parameters. A method for integrating the elevation measurements of a co-registered LiDAR sensor is also proposed. The performance of the proposed methods is demonstrated on a real-world dataset with emplaced detection targets.

In this paper, the SimUltaneous Band-weighting and Spectral Unmixing for Multiple Endmember Sets (SUBSUME) which performs endmember extraction for multiple sets of endmembers, estimates proportion values, and assigns partition-specific band weights is presented. By incorporating simultaneous band weighting, input hyperspectral data is partitioned while focusing on spectral information from the wavelengths that provide the smallest error. Results are shown on two measured hyperspectral images.

A number of noteworthy techniques have been put forth recently in different research fields for comparing clusterings. Herein, we introduce a new method for comparing soft (fuzzy, probabilistic, and possibilistic) partitions based on the earth mover's distance (EMD) and the ordered weighted average (OWA). The proposed method is a metric, depending on the ground distance, for all but possibilistic partitions. It is extremely flexible due to its EMD formulation, OWA aggregation, and abstract concept of ground distance. In theory, our method is agnostic to the type (uncertainty) of soft partition, clustering algorithm, and distance measure used in the clustering algorithm(s), and it is applicable to the clustering of both object and relational data. Validation is performed theoretically, experimentally, as well as in terms of computational complexity. Emphasis is placed on the set of possibilistic partitions, specifically noise and coincident clusters, which are important cases that have received little to no attention to date in the comparing clustering literature. Improvements are reported in terms of metric properties and computational complexity over existing extended concordance/discordance (e.g., soft Rand and Jaccard) approaches and improved design and robustness in comparison with existing transportation problem-based approaches.

A hyperspectral endmember detection and spectral unmixing algorithm that finds multiple sets of endmembers is presented. Hyperspectral data are often nonconvex. The Piecewise Convex Multiple-Model Endmember Detection algorithm accounts for this using a piecewise convex model. Multiple sets of endmembers and abundances are found using an iterative fuzzy clustering and spectral unmixing method. The results indicate that the piecewise convex representation estimates endmembers that better represent hyperspectral imagery composed of multiple regions where each region is represented with a distinct set of endmembers.

A Metropolis-within-Gibbs sampler for piecewise convex hyperspectral unmixing and endmember extraction is presented. The standard linear mixing model used for hyperspectral unmixing assumes that hyperspectral data reside in a single convex region. However, hyperspectral data are often nonconvex. Furthermore, in standard endmember extraction and unmixing methods, endmembers are generally represented as a single point in the high-dimensional space. However, the spectral signature for a material varies as a function of the inherent variability of the material and environmental conditions. Therefore, it is more appropriate to represent each endmember as a full distribution and use this information during spectral unmixing. The proposed method searches for several sets of endmember distributions. By using several sets of endmember distributions, a piecewise convex mixing model is applied, and given this model, the proposed method performs spectral unmixing and endmember estimation given this nonlinear representation of the data. Each set represents a random simplex. The vertices of the random simplex are modeled by the endmember distributions. The hyperspectral data are partitioned into sets associated with each of the extracted sets of endmember distributions using a Dirichlet process prior. The Dirichlet process prior also estimates the number of sets. Thus, the Metropolis-within-Gibbs sampler partitions the data into convex regions, estimates the required number of convex regions, and estimates endmember distributions and abundance values for all convex regions. Results are presented on real hyperspectral and simulated data that indicate the ability of the method to effectively estimate endmember distributions and the number of sets of endmember distributions.

A hyperspectral endmember detection and spectral unmixing algorithm that finds multiple sets of endmembers is presented. This algorithm, the Piece-wise Convex Multiple Model Endmember Detection (P-COMMEND) algorithm, models a hyperspectral image using a piece-wise convex representation. By using a piece-wise convex representation, non-convex hyperspectral data are more accurately characterized. For example, the well-known Indian Pines hyperspectral image is used as an example of a piece-wise convex collection of pixels. The convex regions, weights, endmembers and abundances are found using an iterative fuzzy clustering method. Results indicate that the piece-wise convex representation provides endmembers that better represent hyperspectral data sets over methods that use a single convex region.

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.

A compressive sensing framework is described for hyperspectral imaging. It is based on the widely used linear mixing model,LMM, which represents hyperspectral pixels as convex combinations of small numbers of endmember (material) spectra. The coefficients of the endmembers for each pixel are called proportions. The endmembers and proportions are often the sought-after quantities; the full image is an intermediate representation used to calculate them. Here, a method for estimating proportions and endmembers directly from compressively sensed hyperspectral data based onLMMis shown. Consequently, proportions and endmembers can be calculated directly from compressively sensed data with no need to reconstruct full hyperspectral images. If spectral information is required, endmembers can be reconstructed using compressive sensing reconstruction algorithms. Furthermore, given known endmembers, the proportions of the associated materials can be measured directly using a compressive sensing imaging device. This device would produce a multiband image; the bands would directly represent the material proportions.

Imaging spectroscopy refers to methods for identifying materials in a scene using cameras that digitize light into hundreds of spectral bands. Each pixel in these images consists of vectors representing the amount of light reflected in the different spectral bands from the physical location corresponding to the pixel. Images of this type are called hyperspectral images. Hyperspectral image analysis differs from traditional image analysis in that, in addition to the spatial information inherent in an image, there is abundant spectral information at the pixel or sub-pixel level that can be used to identify materials in the scene. Spectral unmixing techniques attempt to identify the material spectra in a scene down to the sub-pixel level. In this paper, a piece-wise convex hyperspectral unmixing algorithm using both spatial and spectral image information is presented. The proposed method incorporates possibilistic and fuzzy clustering methods. The typicality and membership estimates from those methods can be combined with traditional material proportion estimates to produce more meaningful proportion estimates than obtained with previous spectral unmixing algorithms. An analysis of the utility of using all three estimates produce a better estimate is given using real hyperspectral imagery.

Hyperspectral unmixing estimates the proportions of materials represented within a spectral signature. The over whelming majority of hyperspectral unmixing algorithms are based entirely on the spectral signatures of each individual pixel and do not incorporate the spatial information found in a hyperspectral data cube. In this work, a spectral unmixing algorithm, the Local Information Proportion estimation (LIP) algorithm, is presented. The proposed LIP algorithm incorporates spatial information while determining the proportions of materials found within a spectral signature. Spatial information is incorporated through the addition of a spatial term that regularizes proportion value estimates based on the weighted proportion values of neighboring pixels. Results are shown in the AVIRIS Indian Pines hyperspectral data set.

The Functions of Multiple Instances (FUMI) method for learning a target prototype from data points that are functions of target and non-target prototypes is introduced. In this paper, a specific case is considered where, given data points which are convex combinations of a target prototype and several non-target prototypes, the Convex-FUMI (C-FUMI) method learns the target and non-target patterns, the number of nontarget patterns, and determines the weights (or proportions) of all the prototypes for each data point. For this method, training data need only binary labels indicating whether the data contains or does not contain some proportion of the target prototype; the specific target weights for the training data are not needed. After learning the target prototype using the binary labeled training data, target detection is performed on test data. Results showing detection of the skin in hyper spectral imagery and sub-pixel target detection in simulated data are presented.

The results from L1-Endmembers display the algorithm's stability and accuracy with increasing levels of noise. The algorithm was extremely stable in the number of endmembers when compared to the SPICE algorithm and the Virtual Dimensionality methods for estimating the number of endmembers. Furthermore, the results shown for this algorithm were generated with the same parameter set for all of the data sets, from two-dimensional data to 51-dimensional real hyperspectral data. This indicates L1-Endmembers may lack of sensitivity to parameter value settings. The L1-Endmembers algorithm requires several quadratic programming steps per iteration. These can be completed directly in quadratic programming software packages such as CPLEX and take advantage of any running time reductions the software packages provide. Investigations will be conducted into whether the specific form of this algorithm, particularly with respect to the constraints on the abundance values, can be used to reduce the running time.

A new hyperspectral endmember detection method that represents endmembers as distributions, autonomously partitions the input data set into several convex regions, and simultaneously determines endmember distributions (EDs) and proportion values for each convex region is presented. Spectral unmixing methods that treat endmembers as distributions or hyperspectral images as piecewise convex data sets have not been previously developed. Piecewise convex endmember (PCE) detection can be viewed in two parts. The first part, the ED detection algorithm, estimates a distribution for each endmember rather than estimating a single spectrum. By using EDs, PCE can incorporate an endmember's inherent spectral variation and the variation due to changing environmental conditions. ED uses a new sparsity-promoting polynomial prior while estimating abundance values. The second part of PCE partitions the input hyperspectral data set into convex regions and estimates EDs and proportions for each of these regions. The number of convex regions is determined autonomously using the Dirichlet process. PCE is effective at handling highly mixed hyperspectral images where all of the pixels in the scene contain mixtures of multiple endmembers. Furthermore, each convex region found by PCE conforms to the convex geometry model for hyperspectral imagery. This model requires that the proportions associated with a pixel be nonnegative and sum to one. Algorithm results on hyperspectral data indicate that PCE produces endmembers that represent the true ground-truth classes of the input data set. The algorithm can also effectively represent endmembers as distributions, thus incorporating an endmember's spectral variability.

An endmember detection algorithm for hyperspectral imagery using the Dirichlet process to determine the number of endmembers in a hyperspectral image is described. This algorithm provides an estimate of endmember spectra, proportion maps, and the number of endmembers needed for a scene. Updates to the proportion vector for a pixel are sampled using the Dirichlet process. As opposed to previous methods that prune unnecessary endmembers, the proposed algorithm is initialized with one endmember and new endmembers are added through sampling as needed. Results are shown on a two-dimensional dataset and a simulated dataset using endmembers selected from an AVIRIS hyperspectral image.

This letter presents a simultaneous band selection and endmember detection algorithm for hyperspectral imagery. This algorithm is an extension of the sparsity promoting iterated constrained endmember (SPICE) algorithm. The extension adds spectral band weights and a sparsity promoting prior to the SPICE objective function to provide integrated band selection. In addition to solving for endmembers, the number of endmembers, and end- member fractional maps, this algorithm attempts to autonomously perform band selection and to determine the number of spectral bands required for a particular scene. Results are presented on a simulated data set and the AVIRIS Indian Pines data set. Experiments on the simulated data set show the ability to find the correct endmembers and abundance values. Experiments on the Indian Pines data set show strong classification accuracies in comparison to previously published results.

We develop a vegetation mapping method using long-wave hyperspectral imagery and apply it to landmine detection. The novel aspect of the method is that it makes use of emissivity skewness. The main purpose of vegetation detection for mine detection is to minimize false alarms. Vegetation, such as round bushes, may be mistaken as mines by mine detection algorithms, particularly in synthetic aperture radar (SAR) imagery. We employ an unsupervised vegetation detection algorithm that exploits statistics of emissivity spectra of vegetation in the long-wave infrared spectrum for identification. This information is incorporated into a Choquet integral-based fusion structure, which fuses detector outputs from hyperspectral imagery and SAR imagery. Vegetation mapping is shown to improve mine detection results over a variety of images and fusion models.

An extension of the Iterated Constrained Endmembers (ICE) that incorporates sparsity promoting priors to find the correct number of endmembers and simultaneously select informative spectral bands is presented. In addition to solving for endmembers and endmember fractional maps, this algorithm attempts to autonomously determine the number of endmembers required for a particular scene. The number of endmembers is found by adding a sparsity-promoting term to ICE’s objective function. Additionally, hyperspectral band selection is performed by incorporating weights associated with each hyperspectral band. A sparsity promoting term for the band weights is added to the objective function to perform band selection.

An extension of the iterated constrained endmember (ICE) algorithm that incorporates sparsity-promoting priors to find the correct number of endmembers is presented. In addition to solving for endmembers and endmember fractional maps, this algorithm attempts to autonomously determine the number of endmembers that are required for a particular scene. The number of endmembers is found by adding a sparsity-promoting term to ICE's objective function.

We discuss the application of Choquet integrals to multi-algorithm and multi-sensor fusion in landmine detection. Choquet integrals are defined. Specific classes of measures, the full and Sugeno measures, are described. Full measures are optimized via quadratic programming. A steepest descent algorithm for optimizing Sugeno measures is derived by applying implicit differentiation. Multiple detection algorithms are applied to hyper-spectral and synthetic aperture radar imagery. In addition, a LWIR vegetation index is computed using statistics of apparent emissivity. The detection algorithms are combined using an OR operator and Choquet integrals with respect to full and Sugeno measures. The Choquet integral with respect to the full measure achieves lower false alarm rates