The performance of machine learning (ML) algorithms is impacted due to the class imbalance issue. Although there are several techniques developed to take care of this issue, research on handling categorical or mixed imbalanced data has not been explored much. Moreover, the existing class imbalance handling techniques may not preserve the original characteristics of the data. To address these issues, a new technique, namely, the rough-allowance borderlineK-mode clustering-based weighted oversampling technique (RBKWOT), is developed. It consists of four steps: 1) extraction of rough-allowance borderline minority samples; 2) generation of optimumK-mode clusters; 3) assignment of sampling weights to these clusters; and 4) generation of rules for resampling instances corresponding to each cluster based on its sampling weight. The RBKWOT is capable of reducing the imbalance ratio without incurring any loss of information. It also handles the uncertainty in decision-making for the samples belonging to the boundary region. The efficacy of RBKWOT over some state-of-the-art techniques is demonstrated using 21 categorical, continuous, and mixed data that are acquired from the UCI Machine Learning Repository. Experimental results reveal the superiority of RBKWOT.

Convolutional neural networks (CNNs) are highly effective deep learning architectures for remote sensing (RS) image classification. However, the interpretability of CNN architecture remains challenging for further performance improvement. To address this issue, we propose an end-to-end interpretable CNN architecture called granulated interpretable CNN (GrI-CNN) within the granular computing (GrC) framework. The GrI-CNN uses fuzzy and rough sets to make each architecture component functionally interpretable. Fuzzy sets perform class-dependent granulation of the input feature space, while rough sets granulate the information with operations such as reduct for dimension reduction, functional dependency (FD) of samples for the optimal selection of filters, and weighted membership of granules. The decision layer of GrI-CNN measures the roughness of overlapping granules, encodes the domain knowledge, and initializes the weights using weighted membership and roughness measures. We combined two classification networks at the decision layer to achieve the best possible performance: FD-based interpretable-extreme learning machine (I-ELM) and knowledge-encoded evolving granular neural network (e-GNN). E-GNN is a kind of GNN in which the shape and size of granules evolve based on the user’s needs. Thus, GrI-CNN uses only the required weight parameters and reduces computational time. We have demonstrated the superiority of GrI-CNN over similar state-of-the-art models for classifying multispectral and hyperspectral RS images.

In this article, a new systematic approach to sensor fusion and state estimation is proposed for extended target tracking in human–robot coexisting environments. The developed method, calledhuman feature-based extended target tracking via multisensor information fusion(HFBETT-MSIF), can assimilate information from the onboard camera and sonar sensor of a mobile robot in a unified way, during tracking of a pair of human shoes. A novel generalized measurement model containing the complete information of the human target is formulated for both sensors, thus rendering the tracking system potentially robust to the failure of any one sensor. The study illustrates howheteroscedastic Gaussian process(HGP) regression can be used to derive the measurement model. It also develops an advanced HGP model, calledbias-minimized most likely HGP, to interpret the real-world shoe-contour data subjected to heteroscedastic noise. Performance evaluations conducted for real-life shoe tracking demonstrate the supremacy of the HFBETT-MSIF.

In this article, we present a study on the development in the theory and application of the Z-numbers since its inception in 2011. The review covers the formalization of Z-number-based mathematical operators, the role of Z-numbers in computing with words, decision-making, and trust modeling, application of Z-numbers in real-world problems such as multisensor data fusion, dynamic controller design, safety analytics, and natural language understanding, a brief comparison with conceptually similar paradigms, and some potential areas of future investigation. The paradigm currently has at least four extensions to its definition: multidimensional Z-numbers, parametric Z-numbers, hesitant-uncertain linguistic Z-numbers, and Z*-numbers. The Z-numbers have also been used in conjunction with rough sets and granular computing for enhanced uncertainty handling. While this decade has seen a plethora of theoretical initiatives toward its growth, there remains a major work scope in the direction of practical realization of the paradigm. Some challenges yet unresolved are automated translation of (imprecise, sarcastic, and metaphorical) linguistic expressions to their Z-number forms, discernment of probability–possibility distributions to map real-world situations under consideration, analysis of linguistic equivalents of Z-operator results to intuitive human responses, the endogenous arousal of belief in intelligent agents, and analysis of biases embedded in expert-belief values that are primary inputs to Z-number-based expert systems. After a decade of the Z-numbers, the paradigm has proved to be of use in expert-input-based decision-making systems and initial value problems. Its applicability in high-risk, high-precision areas, such as deep-sea exploration and space science, remains unexplored.

In this article, we have developed an improved failure mode and effect analysis (FMEA) model by leveraging the concepts of Z-number, rough number (RN), and probabilistic distance measure. Two new concepts, namely, double upper approximated rough number (DUARN) and granulized Z-number (gZN), a new scheme for measuring distance between two gZNs using weighted similarity and average linkage method, a new risk prioritization model, named, granulized Z-VIKOR, and a scheme for uncertainty assessment using box-plot are proposed. DUARN embodies the notion of double sided upper approximation of an ordinal decision class. gZN is developed using Z-number and DUARN. The distance between two gZNs is computed using the maximum entropy principle that captures the relationship between the A (opinion) and B (reliability of A) parts of gZN. The granulized Z-VIKOR involves synergistic integration of gZN and VIKOR. Both objective and subjective risk measures are computed and a combined risk measure is defined, which considers the interactions among the risk criteria using λ-Shapley index. Two case studies are conducted. Sensitivity and comparative analysis is carried out to demonstrate the applicability, effectiveness, and robustness of the proposed model, as well as its superiority to existing models.

Existing traffic video summarization algorithms are capable of detecting one-class (i.e., collision) anomaly and cannot handle uncertainty issues arising between two-class anomalies, such as collision and near-miss. To address the issues, a new video summarization algorithm, namely Z-number s-based spatio-temporal rough fuzzy granulation (Z-STRFG) is developed. In Z-STRFG, various spatio-temporal features are computed over the video frames and used for obtaining the approximate anomaly-prone regions in terms of granules. In these regions, uncertainty (i.e., fuzziness) may arise among three scenarios, namely collision, near-miss, and normal traffic. Therefore, two types of rough fuzzy granules (RFGs) along with their roughness scores are computed to distinguish the aforesaid three scenarios. For each RFG, Z-number is computed based on the membership value of its roughness score to ensure a higher degree of reliability in the detection of anomaly class. Aforesaid characteristics of Z-STRFG improve its speed and accuracy for traffic anomaly detection. The efficacy of Z-STRFG has been demonstrated over 130 real-time traffic videos containing collisions, near-misses, and normal traffics. The superiority of Z-STRFG over some state-of-the-art is also proved through extensive experiments.

In this paper, the problem of ensuring reliable energy distribution in smart grid is studied, while considering that each customer is connected with multiple micro-grids. In the traditional smart grid, each customer is connected with a single micro-grid. Additionally, in the existing literature, some researchers proposed energy distribution schemes considering the presence of multiple micro-grids. However, none of these existing schemes consider that the customers can consume energy from multiple micro-grids simultaneously, which can essentially enhance the quality of service (QoS) in energy distribution, as it aids in reducing the transmission loss and increasing the profit of the micro-grids, while the customers pay less. To address the aforementioned problem, we design a sustainable energy distribution scheme, named SEED, to decide the distributed energy request vector, while ensuring high QoS in terms of energy availability and the price charged by the micro-grids in smart grid. We use an evolutionary game to ensure that the energy load is optimally distributed among the micro-grids and each micro-grid gets an equal opportunity to earn a profit. Through simulation, we observe that using SEED, renewable energy consumption per customer improves by 14.05 percent while reducing the cost by 29.87 percent. In other words, SEED ensures a sustainable environment by reducing the CO$_2$2emission by 14.05 percent, while reducing non-renewable energy consumption from the main grid. Additionally, the profit of each micro-grid increases by 58.32 percent.

MicroRNAs play an important role in controlling drug sensitivity and resistance in cancer. Identification of responsible miRNAs for drug resistance can enhance the effectiveness of treatment. A new set theoretic entropy measure (SPEM) is defined to determine the relevance and level of confidence of miRNAs in deciding their drug resistant nature. Here, a pattern is represented by a pair of values. One of them implies the degree of its belongingness (fuzzy membership) to a class and the other represents the actual class of origin (crisp membership). A measure, called granular probability, is defined that determines the confidence level of having a particular pair of membership values. The granules used to compute the said probability are formed by a histogram based method where each bin of a histogram is considered as one granule. The width and number of the bins are automatically determined by the algorithm. The set thus defined, comprising a pair of membership values and the confidence level for having them, is used for the computation of SPEM and thereby identifying the drug resistant miRNAs. The efficiency of SPEM is demonstrated extensively on six data sets. While the achieved F-score in classifying sensitive and resistant samples ranges between 0.31 & 0.50 using all the miRNAs by SVM classifier, the same score varies from 0.67 to 0.94 using only the top 1 percent drug resistant miRNAs. Superiority of the proposed method as compared to some existing ones is established in terms of F-score. The significance of the top 1 percent miRNAs in corresponding cancer is also verified by the different articles based on biological investigations. Source code of SPEM is available at http://www.jayanta.droppages.com/SPEM.html.

In this article, we propose a new weighted Z-similarity measure between two Z-numbers, which is able to retain the original information provided by experts in linguistic terms. This measure takes care of the directional aspect of reliability of information by leveraging the Hausdorff distance. Probabilistic-approach-based statistical distance measure is used to characterize the internal relationship between two parts of a Z-number. Some properties of the Z-similarity measure are proved. The measure is capable of quantifying the probability of basic events in bow-tie analysis. It is experimentally shown that the Z-similarity measure is able to overcome the lacuna of the available techniques. Sensitivity analysis is done to verify its feasibility and applicability. We further propose another measure, called Z-similarity-based basic event contribution (Z-BEC), to quantify the contribution of basic events to the occurrence of different accidents. The performance of the Z-BEC measure is compared with that of Fussell-Vesely index and Birnbaum's structural index.

MicroRNAs (miRNAs) are known as an important indicator of cancers. The presence of cancer can be detected by identifying the responsible miRNAs. A fuzzy-rough entropy measure (FREM) is developed which can rank the miRNAs and thereby identify the relevant ones. FREM is used to determine the relevance of a miRNA in terms of separability between normal and cancer classes. While computing the FREM for a miRNA, fuzziness takes care of the overlapping between normal and cancer expressions, whereas rough lower approximation determines their class sizes. MiRNAs are sorted according to the highest relevance (i.e., the capability of class separation) and a percentage among them is selected from the top ranked ones. FREM is also used to determine the redundancy between two miRNAs and the redundant ones are removed from the selected set, as per the necessity. A histogram based patient selection method is also developed which can help to reduce the number of patients to be dealt during the computation of FREM, while compromising very little with the performance of the selected miRNAs for most of the data sets. The superiority of the FREM as compared to some existing methods is demonstrated extensively on six data sets in terms of sensitivity, specificity, and score. While for these data sets the score of the miRNAs selected by our method varies from 0.70 to 0.91 using SVM, those results vary from 0.37 to 0.90 for some other methods. Moreover, all the selected miRNAs corroborate with the findings of biological investigations or pathway analysis tools. The source code of FREM is available at http://www.jayanta.droppages.com/FREM.html.

This paper describes a new approach of viewing a social relation as a string with various forces acting on it. Accordingly, a tension measure for a relation is defined. Various component forces of the tension measure are identified based on the structural information of the network. A new variant of rough set, namely, double bounded rough set, is developed in order to define these forces mathematically. It is revealed experimentally with synthetic and real-world data that positive and negative tension characterizes, relatively, the presence and absence of a physical link between two nodes. An algorithm based on tension measure is proposed for link prediction. Superiority of the algorithm is demonstrated on nine real-world networks, which include four temporal networks. The source code for calculating tension measure and link prediction algorithm is publicly available at https://gitlab.com/suman5/social-tension-measure.

This paper aims at developing a novel methodology for unsupervised video tracking by exploring the merits of neighborhood rough sets. A neighborhood rough filter is designed in this process for initial labeling of continuous moving object(s) even in the presence of several variations in different feature spaces. The locations and color models of the object(s) are estimated using their lower-upper approximations in spatio-color neighborhood granular space. Velocity neighborhood granules and acceleration neighborhood granules are then defined over this estimation to predict the object location in the next frame and to speed up the tracking process. A novel concept, namely, intuitionsistic entropy is introduced here, which consists of two new measures: neighborhood rough entropy and neighborhood probabilistic entropy to deal with the ambiguities that arise due to occurrence of overlapping/ occlusion in a video sequence. The unsupervised method of tracking is equally good even when compared with some of the state-of-the art partially supervised methods while showing superior performance during total occlusion.

A new method of adaptive rule generation in granular computing framework is described based on rough rule base and granular flow graph, and applied for video tracking. In the process, several new concepts and operations are introduced, and methodologies formulated with superior performance. The flow graph enables in defining an intelligent technique for rule base adaptation where its characteristics in mapping the relevance of attributes and rules in decision-making system are exploited. Two new features, namely, expected flow graph and mutual dependency between flow graphs are defined to make the flow graph applicable in the tasks of both training and validation. All these techniques are performed in neighborhood granular level. A way of forming spatio-temporal 3-D granules of arbitrary shape and size is introduced. The rough flow graph-based adaptive granular rule-based system, thus produced for unsupervised video tracking, is capable of handling the uncertainties and incompleteness in frames, able to overcome the incompleteness in information that arises without initial manual interactions and in providing superior performance and gaining in computation time. The cases of partial overlapping and detecting the unpredictable changes are handled efficiently. It is shown that the neighborhood granulation provides a balanced tradeoff between speed and accuracy as compared to pixel level computation. The quantitative indices used for evaluating the performance of tracking do not require any information on ground truth as in the other methods. Superiority of the algorithm to nonadaptive and other recent ones is demonstrated extensively.

A new granular self-organizing map (GSOM) is developed by integrating the concept of a fuzzy rough set with the SOM. While training the GSOM, the weights of a winning neuron and the neighborhood neurons are updated through a modified learning procedure. The neighborhood is newly defined using the fuzzy rough sets. The clusters (granules) evolved by the GSOM are presented to a decision table as its decision classes. Based on the decision table, a method of gene selection is developed. The effectiveness of the GSOM is shown in both clustering samples and developing an unsupervised fuzzy rough feature selection (UFRFS) method for gene selection in microarray data. While the superior results of the GSOM, as compared with the related clustering methods, are provided in terms of β -index, DB-index, Dunn-index, and fuzzy rough entropy, the genes selected by the UFRFS are not only better in terms of classification accuracy and a feature evaluation index, but also statistically more significant than the related unsupervised methods. The C-codes of the GSOM and UFRFS are available online at http://avatharamg.webs.com/software-code.

The present issue enlists a series of six articles describing some novel contributions in image processing in the framework of machine learning. Image processing has been the subject of increasing interest to researchers for about five decades. Image information processing has seen a lot of changes with time in terms of methodology development and application. The maturity of the field can be characterised by the significant growth of active applications in the related domains. For example, remote sensing, technical diagnostics, autonomous vehicle guidance, medical (2D and 3D) imaging and automatic surveillance are the most rapidly developing areas. Machine learning is a rapidly evolving field dedicated to developing and improving algorithms that allow computers to learn from data and recognise patterns. In recent years, machine learning has experienced a surge in popularity due to the growing need for more powerful and efficient means of analysing complex data. In several cases the use of machine learning methods has demonstrated merits over other approaches in image processing. For example, the edges or boundaries detected by machine learning methods from an image have been shown to be more consistent with those perceived by human visual system and more semantically meaningful. The problem of classification is one aspect of machine learning that is of particular importance to researchers in several fields. As the scale of datasets grows larger and the need for greater classification accuracy increases, new techniques for classifying data are more highly sought after. Examples of growing data volumes can be found in image categorisation and automatic image retrieval tasks, as well as in automated person recognition. Pattern classification methods have proven to be eminently successful in many such real-life applications. Machine learning has changed the various fields of computer science and the image processing community has become a user of the machine learning paradigm. The Big Data challenge of handling large volumes of visual information has become an integral part of the digital universe. Today, like voice and text data, the volume and size of images to be processed for various applications are becoming very large. Application areas such as medical imaging, remote sensing using multispectral and hyper-spectral images, image archival and retrievals, biometrics, video processing and surveillance deal with advanced machine learning and pattern recognition technologies for their efficient processing and analysis. Various data mining schemes have been developed to process images in order to enable enhanced decision-making and knowledge discovery. Granular computing and soft computing technologies are being used to provide speedy, approximate and effective solutions. Recently the Big Data issues characterised by "3Vs", namely, volume, variety and velocity have begun to demand a revolutionary change in approaches, research methodologies and tools to meet the new challenges in all levels of image processing and mining. As a result, novel machine learning and computational intelligence techniques may need to be developed. The objective of this Special Issue is to present novel research contributions in this interdisciplinary research area as it enters maturity and a new phase of its development. It consists of six articles related to certain tasks and applications of image (including video) processing and analysis. These are described as follows: The issue starts with the article of Suranjana Samanta and Sukhendu Das, where a method of unsupervised domain adaptation is proposed using eigen-analysis in kernel space for categorisation tasks. Eigenvectors and eigenvalues of both the source and target domains are used in the analysis. The method involves optimal linear transformation of data in source domain such that the transformed source and target domains have similar eigenvectors and eigenvalues. Moreover, for non-linear projection of the data they used the concept of reproducing kernel Hilbert space and estimated a suitable transformation in the (reduced) sub-space. The method is fast, as eigen-decomposition in lower dimensional subspace and the use of kernel Gram matrix help in reducing the time complexity in the case of very large dimensional datasets. These features have been demonstrated on real-world datasets for tasks like object, video and text categorisation. Meiyu Liang et al., describe in their article a super-resolution reconstruction method using Pseudo-Zernike moments and nonlocal similarity matching. By learning the nonlocal similarity between dynamic images, similarity weights are computed to estimate the high resolution image. Due to trans-scale fusion of nonlocal similarity information between dynamic images, the technique can adapted to complex motion patterns and it is robust to noise and rotation. Here, the luminance compensation is implemented based on multisource bidirectional similarity, which can eliminate the influences of multi-exposure factors on registration accuracy. The next contribution is on multi-step radiographic image enhancement, where the authors, Changying Dang et al., explain an algorithm that provides very high accuracy for weld defect segmentation. A linear combination is taken adaptively between the original image and the contrast-limited adaptive histogram enhanced image, and then an anisotropic diffusion filter is applied. Finally, the method uses an iterative fuzzy enhancement which is adaptive based on improved Otsu's relation. By taking the inverse transformation of the fuzzy image the enhanced image is obtained for segmentation. Conflicting issues of noise amplification, image blur, edge loss, over-enhancement – which often exist in conventional enhancement algorithms – have been dealt with, and greater accuracy in segmentation is achieved. The paper of Seba Susan et al., proposes a new fuzzy set theoretic classifier for scale invariant feature transform (SIFT) features that involve all the key-points required for decision making. As an application, the problem of face recognition using a single training template is considered where uncropped images of frontal faces in the presence of high background clutter are used. Facial features are given more importance using feature entropy as weight in the classifier. The product of cumulative fuzzy measure, corresponding to fuzzy classifier with SIFT features and entropy weighted fuzzy SIFT classifier, is seen to be a good criterion for face recognition under weak supervision. Comparative results with state-of-the-art methods on benchmark facial databases confirm the efficiency of proposed method. The next two articles deal with video tracking and gait recognition. In the article of Shinfeng D. Lin et al., a patch-based appearance model is presented for handling occlusion in object tracking. The model contains two main features: colour and motion vector. In case of failure in tracking, the speeded up robust features (SURF) are used for error recovery. The use of particle filter makes the tracking against occlusions robust. A gait recognition system using Kinect depth stream, captured in the frontal view, is used in the article of Pratik Chattopadhyay et al., for person re-identification. The method involves information fusion for multi Kinect cameras to combine partial gait features. The effectiveness of the system is demonstrated experimentally. These papers provide various applications including a wide range of techniques applied to different image processing tasks. We believe, they will enhance the knowledge in the field and encourage further research activities in the interface between image processing, machine learning and their applications. The guest editors would like to thank all the authors who submitted their research papers to be considered for publications in this Special Issue. The reviewers who spent their valuable time for reviewing the manuscripts and providing constructive suggestions are gratefully acknowledged. Special thanks are due to the Editor-in-chief of the journal Dr. Farzin Deravi for his support. We would also like to thank the IET Editorial Office for their help and support that made this Special Issue possible. One of the guest editors, Prof. S. K. Pal, acknowledges the J.C. Bose Fellowship of the Govt. of India, and Chair Professorship of Indian National Academy of Engineering (INAE). Date: 2015 1 September

The paper addresses the problem of finding top k influential nodes in large scale directed social networks. We propose two new centrality measures, Diffusion Degree for independent cascade model of information diffusion and Maximum Influence Degree. Unlike other existing centrality measures, diffusion degree considers neighbors' contributions in addition to the degree of a node. The measure also works flawlessly with non uniform propagation probability distributions. On the other hand, Maximum Influence Degree provides the maximum theoretically possible influence (Upper Bound) for a node. Extensive experiments are performed with five different real life large scale directed social networks. With independent cascade model, we perform experiments for both uniform and non uniform propagation probabilities. We use Diffusion Degree Heuristic (DiDH) and Maximum Influence Degree Heuristic (MIDH), to find the top k influential individuals. k seeds obtained through these for both the setups show superior influence compared to the seeds obtained by high degree heuristics, degree discount heuristics, different variants of set covering greedy algorithms and Prefix excluding Maximum Influence Arborescence (PMIA) algorithm. The superiority of the proposed method is also found to be statistically significant as per T-test.

Nowadays, the high availability of data gathered from wireless sensor networks and telecommunication systems has drawn the attention of researchers on the problem of extracting knowledge from spatiotemporal data. Detecting outliers which are grossly different from or inconsistent with the remaining spatiotemporal data set is a major challenge in real-world knowledge discovery and data mining applications. In this paper, we deal with the outlier detection problem in spatiotemporal data and describe a rough set approach that finds the top outliers in an unlabeled spatiotemporal data set. The proposed method, called Rough Outlier Set Extraction (ROSE), relies on a rough set theoretic representation of the outlier set using the rough set approximations, i.e., lower and upper approximations. We have also introduced a new set, named Kernel Set, that is a subset of the original data set, which is able to describe the original data set both in terms of data structure and of obtained results. Experimental results on real-world data sets demonstrate the superiority of ROSE, both in terms of some quantitative indices and outliers detected, over those obtained by various rough fuzzy clustering algorithms and by the state-of-the-art outlier detection methods. It is also demonstrated that the kernel set is able to detect the same outliers set but with less computational time.

Granular information processing is one of the human-inspired problem-solving aspects of natural computing, as information abstraction is inherent in human thinking and reasoning processes, and plays an essential role in human cognition. Among the different facets of natural computing fuzzy sets, rough sets and their hybridization are well accepted paradigms that are based on the construction, representation and interpretation of granules, as well as the utilization of granules for problem solving. These tools are also known as primary constituents of soft computing whose objective is to provide flexible information processing capability for handling real-life ambiguous situations. They have been successfully employed in various image processing tasks, including image segmentation, enhancement and classification, both individually or in combination with other computing techniques. The reason of such success is rooted to the fact that they provide powerful tools to describe uncertainty, naturally embedded in images, which can be exploited in various image processing tasks.

This special issue of Fundamenta Informaticae focuses on the foundations and applications of Cognitive Informatics and Computational Intelligence (briefly, CI2).CI2 focuses on studies of human information processing as well as the byproducts of perception and cognition.Cognitive Informatics (CI) is a multidisciplinary study of cognition, computing and information sciences which investigates the information processing mechanisms and processes of the brain and natural intelligence, as well as their engineering applications in cognitive computing.Specifically, CI2 provides a coherent set of fundamental theories and contemporary mathematics that form the foundation for most science and engineering disciplines such as applied mathematics (e.g., perceptual forms of fuzzy sets, near sets and rough sets), computer science, cognitive science, computer engineering (e.g., computer vision), cybernetics (e.g., machine behavior), neuropsychology and pure mathematics (e.g., proximity spaces, topological spaces via near and far).This special issue presents some of the latest advances in cognitive informatics and cognitive computing.A total of 11 papers were accepted for publication.Each accepted paper has undergone a thorough review (at least two reviewers for each paper) and a second round of review and revision cycle.The paper by M.H-Herrero, P. Rabanal, I. Rodríguez, and F. Rubio on Comparing Problem Solving Strategies for NP-hard Optimization Problems, present analysis of performance of humans when solving NP-complete problems.These analyses are supported by experiments which include the human capability to compute good suboptimal solutions to these problems, and the authors try to identify the kind of problem instances which make humans compute the best and worst solutions (including the dependance of their performance on the size of problem instances).Finally, their performance with computational heuristics typically used to approximately solve these problems are compared, and participants in these experiments are also interviewed in order to infer the most typical strategies used by them, as well as how these strategies depend on the form and size of problem instances.The paper by G. Virginia and H.S. Nguyen on Lexicon-based Document Representation, is based on tolerance rough sets model(TRSM) to model document-term relations in text mining.Specifically, this representation maps the terms occurring in TRSM-representation to terms in the lexicon, hence the final representation of a document is a weight vector consisting only of terms that occurred in the lexicon (lexicon-representation).The lexicon-representation can be viewed as a compact form of TRSM-v-viii v

The Z-number is a new fuzzy-theoretic concept, proposed by Zadeh in 2011. It extends the basic philosophy of Computing With Words (CWW) to include the perception of uncertainty of the information conveyed by a natural language statement. The Z-number

This paper presents a novel methodology for tracking a single moving object in a video sequence applying the concept of rough set theory. The novelty of this technique is that it does not consider any prior information about the video sequence unlike

MicroRNAs (miRNA) are one kind of non-coding RNA which play many important roles in eukaryotic cell. Investigations on miRNAs show that miRNAs are involved in cancer development in animal body. In this article, a threshold based method to check the condition (normal or cancer) of miRNAs of a given sample/patient, using weighted average distance between the normal and cancer miRNA expressions, is proposed. For each miRNA, the city block distance between two representatives, corresponding to scaled normal and cancer expressions, is obtained. The average of all such distances for different miRNAs is weighted by a factor, to generate the threshold. The weight factor, which is cancer dependent, is determined through an exhaustive search by maximizing the F score during training. In a part of the investigation, a ranking algorithm for cancer specific miRNAs is also discussed. The performance of the proposed method is evaluated in terms of Matthews Correlation Coefficient (MCC) and by plotting points (1 – Specificity vs: Sensitivity) in Receiver Operating Characteristic (ROC) space, besides the F score. Its efficiency is demonstrated on breast, colorectal, melanoma lung, prostate and renal cancer data sets and it is observed to be superior to some of the existing classifiers in terms of the said indices.

Histogram equalisation has been a much sought‐after technique for improving the contrast of an image, which however leads to an over enhancement of the image, giving it an unnatural and degraded appearance. In this framework, a generalised contrast enhancement algorithm is proposed which is independent of parameter setting for a given dynamic range of the input image. The algorithm uses the modified histogram for spatial transformation on grey scale to render a better quality image irrespective of the image type. Added to this, two variants of the proposed methodology are presented, one of which preserves the brightness of original image while the other variant increases the image brightness adaptively, giving it a better look. Qualitative and quantitative assessments like degree of entropy un‐preservation, edge‐based contrast measure and structure similarity index measures are then applied to the 500 image data set for comparing the proposed algorithm with several existing state‐of‐the‐art algorithms. Experimental results show that the proposed algorithm produces better or comparable enhanced images than several algorithms.

Prediction of RNA structure is invaluable in creating new drugs and understanding genetic diseases. Several deterministic algorithms and soft computing-based techniques have been developed for more than a decade to determine the structure from a known RNA sequence. Soft computing gained importance with the need to get approximate solutions for RNA sequences by considering the issues related with kinetic effects, cotranscriptional folding, and estimation of certain energy parameters. A brief description of some of the soft computing-based techniques, developed for RNA secondary structure prediction, is presented along with their relevance. The basic concepts of RNA and its different structural elements like helix, bulge, hairpin loop, internal loop, and multiloop are described. These are followed by different methodologies, employing genetic algorithms, artificial neural networks, and fuzzy logic. The role of various metaheuristics, like simulated annealing, particle swarm optimization, ant colony optimization, and tabu search is also discussed. A relative comparison among different techniques, in predicting 12 known RNA secondary structures, is presented, as an example. Future challenging issues are then mentioned.

Genetic Algorithm (GA) has now become one of the leading mechanisms in providing solution to complex optimization problems. Although widely used, there are very few theoretical guidelines for determining when to stop the algorithm. This article establishes theoretically that the variance of the best fitness values obtained in the iterations can be considered as a measure to decide the termination criterion of a GA with elitist model (EGA). The criterion automatically takes into account the inherent characteristics of the objective function. Implementation issues of the proposed stopping criterion are explained. Its difference with some other stopping criteria is also critically analyzed.

Histogram equalization, which aims at information maximization, is widely used in different ways to perform contrast enhancement in images. In this paper, an automatic exact histogram specification technique is proposed and used for global and local contrast enhancement of images. The desired histogram is obtained by first subjecting the image histogram to a modification process and then by maximizing a measure that represents increase in information and decrease in ambiguity. A new method of measuring image contrast based upon local band-limited approach and center-surround retinal receptive field model is also devised in this paper. This method works at multiple scales (frequency bands) and combines the contrast measures obtained at different scales using L(p)-norm. In comparison to a few existing methods, the effectiveness of the proposed automatic exact histogram specification technique in enhancing contrasts of images is demonstrated through qualitative analysis and the proposed image contrast measure based quantitative analysis.

The selection of nonredundant and relevant features of real-valued data sets is a highly challenging problem. A novel feature selection method is presented here based on fuzzy-rough sets by maximizing the relevance and minimizing the redundancy of the selected features. By introducing the fuzzy equivalence partition matrix, a novel representation of Shannon's entropy for fuzzy approximation spaces is proposed to measure the relevance and redundancy of features suitable for real-valued data sets. The fuzzy equivalence partition matrix also offers an efficient way to calculate many more information measures, termed as f-information measures. Several f-information measures are shown to be effective for selecting nonredundant and relevant features of real-valued data sets. This paper compares the performance of different f-information measures for feature selection in fuzzy approximation spaces. Some quantitative indexes are introduced based on fuzzy-rough sets for evaluating the performance of proposed method. The effectiveness of the proposed method, along with a comparison with other methods, is demonstrated on a set of real-life data sets.

The excitatory-inhibitory visual receptive-field model may be looked upon as a classical structuralist approach to vision that relies upon brightness-contrast information of the image as a preliminary step toward visual representation. The corresponding mathematical operator (Laplacian) was first proposed by the empiricist Ernst Mach on the basis of the Mach band illusion. The Helmholtz's constructivist approach, on the other hand, argues that perception is the product of unconscious inference. Propagating a sort of intermediate stance between these two viewpoints led to the emergence of the Gestalt school for whom perception follows a minimum principle and is at the same time holistic, based on certain coherence criteria. In this paper, we have modeled the extraclassical receptive field through an eigenfunction-based generalization of the Gaussian derivative approach that resulted in a modification of Mach's equation, introducing a higher order isotropic derivative (Bi-Laplacian) of Gaussian and a fourth-moment operator. The proposed computational model draws its inspiration from the structuralist approach, performs figure-ground segregation in Gestalt sense, and also provides cues toward brightness perception in tune with the constructivist notion of unconscious inference.

Several information measures such as entropy, mutual information, and f-information have been shown to be successful for selecting a set of relevant and nonredundant genes from a high-dimensional microarray data set. However, for continuous gene expression values, it is very difficult to find the true density functions and to perform the integrations required to compute different information measures. In this regard, the concept of the fuzzy equivalence partition matrix is presented to approximate the true marginal and joint distributions of continuous gene expression values. The fuzzy equivalence partition matrix is based on the theory of fuzzy-rough sets, where each row of the matrix represents a fuzzy equivalence partition that can automatically be derived from the given expression values. The performance of the proposed approach is compared with that of existing approaches using the class separability index and the predictive accuracy of the support vector machine. An important finding, however, is that the proposed approach is shown to be effective for selecting relevant and nonredundant continuous-valued genes from microarray data.

This paper discusses the applications of rough ensemble classifier [27] in two emerging problems of web mining, the categorization of web services and the topic specific web crawling. Both applications, discussed here, consist of two major steps: (1)

Feature space based approaches have been the most popular ones among those used to perform image segmentation. In this paper, a density modification framework is proposed in order to aid feature space based segmentation in images. The framework embeds a position-dependent property associated with each sample in the feature space of an image into the corresponding density map and hence modifies it. The property association and embedding operations in the framework is implemented using a fuzzy set theory based system devised with cue from beam theory of solid mechanics and the appropriateness of this approach is established. Experimental results of segmentation in images are given to demonstrate the effectiveness of the proposed framework.

We have made a case here for utilizing tensor framework for hypertext mining. Tensor is a generalization of vector and tensor framework discussed here is a generalization of vector space model which is widely used in the information retrieval and web mining literature. Most hypertext documents have an inherent internal tag structure and external link structure that render the desirable use of multidimensional representations such as those offered by tensor objects. We have focused on the advantages of Tensor Space Model, in which documents are represented using sixth-order tensors. We have exploited the local-structure and neighborhood recommendation encapsulated by the proposed representation. We have defined a similarity measure for tensor objects corresponding to hypertext documents, and evaluated the proposed measure for mining tasks. The superior performance of the proposed methodology for clustering and classification tasks of hypertext documents have been demonstrated here. The experiment using different types of similarity measure in the different components of hypertext documents provides the main advantage of the proposed model. It has been shown theoretically that, the computational complexity of an algorithm performing on tensor framework using tensor similarity measure as distance is at most the computational complexity of the same algorithmperforming on vector space model using vector similarity measure as distance.

This paper presents a novel histogram thresholding methodology using fuzzy and rough set theories. The strength of the proposed methodology lies in the fact that it does not make any prior assumptions about the histogram unlike many existing techniques. For bilevel thresholding, every element of the histogram is associated with one of the two regions by comparing the corresponding errors of association. The regions are considered ambiguous in nature, and, hence, the error measures are based on the fuzziness or roughness of the regions. Multilevel thresholding is carried out using the proposed bilevel thresholding method in a tree structured algorithm. Segmentation, object/background separation, and edge extraction are performed using the proposed methodology. A quantitative index to evaluate image segmentation performance is also proposed using the median of absolute deviation from median measure, which is a robust estimator of scale. Extensive experimental results are given to demonstrate the effectiveness of the proposed methods in terms of both qualitative and quantitative measures.

Often, ranking is performed on the the basis of some scores available for each item. The existing practice for comparing scoring functions is to compare the induced rankings by one of the multitude of rank comparison methods available in the literature. We suggest that it may be better to compare the underlying scores themselves. To this end, a generalized Kendall distance is defined, which takes into consideration not only the final ordering that the two schemes produce, but also at the spacing between pairs of scores. This is shown to be equivalent to comparing the scores after fusing with another set of scores, making it theoretically interesting. A top k version of the score comparison methodology is also provided. Experimental results clearly show the advantages score comparison has over rank comparison.

Quantifying ambiguities in images using fuzzy set theory has been of utmost interest to researchers in the field of image processing. In this paper, we present the use of rough set theory and its certain generalizations for quantifying ambiguities in images and compare it to the use of fuzzy set theory. We propose classes of entropy measures based on rough set theory and its certain generalizations, and perform rigorous theoretical analysis to provide some properties which they satisfy. Grayness and spatial ambiguities in images are then quantified using the proposed entropy measures. We demonstrate the utility and effectiveness of the proposed entropy measures by considering some elementary image processing applications. We also propose a new measure called average image ambiguity in this context.

In this article we describe a novel Particle Swarm Optimization (PSO) approach to Multi-objective Optimization (MOO) called Adaptive Multi-objective Particle Swarm Optimization (AMOPSO). AMOPSO algorithm's novelty lies in its adaptive nature, that is attained by incorporating inertia and the acceleration coefficient as control variables with usual optimization variables, and evolving these through the swarming procedure. A new diversity parameter has been used to ensure sufficient diversity amongst the solutions of the non dominated front. AMOPSO has been compared with some recently developed multi-objective PSO techniques and evolutionary algorithms for nine function optimization problems, using different performance measures.

In most pattern recognition algorithms, amino acids cannot be used directly as inputs since they are nonnumerical variables. They, therefore, need encoding prior to input. In this regard, bio-basis function maps a nonnumerical sequence space to a numerical feature space. It is designed using an amino acid mutation matrix. One of the important issues for the bio-basis function is how to select the minimum set of bio-bases with maximum information. In this paper, we describe an algorithm, termed as rough-fuzzy c{\hbox{-}}{\rm{medoids}} (RFCMdd) algorithm, to select the most informative bio-bases. It is comprised of a judicious integration of the principles of rough sets, fuzzy sets, the c{\hbox{-}}{\rm{medoids}} algorithm, and the amino acid mutation matrix. While the membership function of fuzzy sets enables efficient handling of overlapping partitions, the concept of lower and upper bounds of rough sets deals with uncertainty, vagueness, and incompleteness in class definition. The concept of crisp lower bound and fuzzy boundary of a class, introduced in RFCMdd, enables efficient selection of the minimum set of the most informative bio-bases. Some new indices are introduced for evaluating quantitatively the quality of selected bio-bases. The effectiveness of the proposed algorithm, along with a comparison with other algorithms, has been demonstrated on different types of protein data sets.

A novel corpus-based method for stemmer refinement, which can provide improvement in both classification and retrieval, is described. The method models the given words as generated from a multinomial distribution over the topics available in the corpus and includes a procedurelike sequential hypothesis testing that enables grouping together distributionally similar words. The system can refine any stemmer, and its strength can be controlled with parameters that reflect the amount of tolerance to be allowed in computing the similarity between the distributions of two words. Although obtaining the morphological roots of the given words is not the primary objective, the algorithm automatically does that to some extent. Despite a huge reduction in dictionary size, classification accuracies are seen to improve significantly when the proposed system is applied on some existing stemmers for classifying 20 Newsgroups and WebKB data. The refinements obtained are also suitable for cross-corpus stemming. Regarding retrieval, its superiority is extensively demonstrated with respect to four existing methods.

A generalized hybrid unsupervised learning algorithm, which is termed as rough-fuzzy possibilistic c-means (RFPCM), is proposed in this paper. It comprises a judicious integration of the principles of rough and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy sets enables efficient handling of overlapping partitions. It incorporates both probabilistic and possibilistic memberships simultaneously to avoid the problems of noise sensitivity of fuzzy c-means and the coincident clusters of PCM. The concept of crisp lower bound and fuzzy boundary of a class, which is introduced in the RFPCM, enables efficient selection of cluster prototypes. The algorithm is generalized in the sense that all existing variants of c-means algorithms can be derived from the proposed algorithm as a special case. Several quantitative indices are introduced based on rough sets for the evaluation of performance of the proposed c-means algorithm. The effectiveness of the algorithm, along with a comparison with other algorithms, has been demonstrated both qualitatively and quantitatively on a set of real-life data sets.

This investigation deals with a new distance measure for genes using their microarray expressions and a new algorithm for fast gene ordering without clustering. This distance measure is called "Maxrange distance," where the distance between two genes corresponding to a particular type of experiment is computed using a normalization factor, which is dependent on the dynamic range of the gene expression values of that experiment. The new gene-ordering method called "Minimal Neighbor" is based on the concept of nearest neighbor heuristic involving O(n2) time complexity. The superiority of this distance measure and the comparability of the ordering algorithm have been extensively established on widely studied microarray data sets by performing statistical tests. An interesting application of this ordering algorithm is also demonstrated for finding useful groups of genes within clusters obtained from a nonhierarchical clustering method like the self-organizing map.

CBR systems that are built for the classification problems are called CBR classifiers. This paper presents a novel and fast approach to building efficient and competent CBR classifiers that combines both feature reduction (FR) and case selection (CS). It has three central contributions: 1) it develops a fast rough-set method based on relative attribute dependency among features to compute the approximate reduct, 2) it constructs and compares different case selection methods based on the similarity measure and the concepts of case coverage and case reachability, and 3) CBR classifiers built using a combination of the FR and CS processes can reduce the training burden as well as the need to acquire domain knowledge. The overall experimental results demonstrating on four real-life data sets show that the combined FR and CS method can preserve, and may also improve, the solution accuracy while at the same time substantially reducing the storage space. The case retrieval time is also greatly reduced because the use of CBR classifier contains a smaller amount of cases with fewer features. The developed FR and CS combination method is also compared with the kernel PCA and SVMs techniques. Their storage requirement, classification accuracy, and classification speed are presented and discussed.

This paper provides an overview of the application of evolutionary algorithms in certain bioinformatics tasks. Different tasks such as gene sequence analysis, gene mapping, deoxyribonucleic acid (DNA) fragment assembly, gene finding, microarray analysis, gene regulatory network analysis, phylogenetic trees, structure prediction and analysis of DNA, ribonucleic acid and protein, and molecular docking with ligand design are, first of all, described along with their basic features. The relevance of using evolutionary algorithms to these problems is then mentioned. These are followed by different approaches, along with their merits, for addressing some of the aforesaid tasks. Finally, some limitations of the current research activity are provided. An extensive bibliography is included

Cycle detection in graphs and digraphs has received wide attention and several algorithms are available for this purpose. While the Web may be modeled as a digraph, such algorithms would not be of much use due to both the scale of the Web and the number of uninteresting cycles and sequences in it. We propose a novel sequence detection algorithm for Web pages, and highlight its importance for search related systems. Here, the sequence found is such that its consecutive elements have the same relation among them. This relation is measured in terms of the positional properties of navigational links, for which we provide a method for identifying navigational links. The proposed methodology does not detect all possible sequences and cycles in the Web graph, but just those that were intended by the creators of those Web pages. Experimental results confirm the accuracy of the proposed algorithm.

A novel Web surfer model, where the transitions between Web pages are fuzzy quantities, is proposed in this article. Such a model is appropriate when the links between pages are imprecise. The theoretical aspects of modeling the uncertainty associated with links are discussed. The advantages and limitations of the proposed methodology, which is based on the theory of fuzzy Markov chains, are described. Situations where fuzzy Web surfer models are appropriate compared to existing models are highlighted.

This paper describes a surfer model which incorporates information about topic continuity derived from the surfer's history. Therefore, unlike earlier models, it captures the interrelationship between categorization (context) and ranking of Web documents simultaneously. The model is mathematically formulated. A scalable and convergent iterative procedure is provided for its implementation. Its different characteristic features, as obtained from the joint probability matrix, and their significance in Web intelligence are mentioned. Experiments performed on Web pages obtained from WebBase confirm the superiority of the model.

The research activities of the WIC-India Research Center include topics like improving the performance of search engines, link and neighborhood analysis, as well as, surfer modeling for ranking and categorization of web pages, and query answering. In solving several web mining tasks, both statistical and soft computing tools are employed. Besides, some international collaborations and establishing a center of excellence are going on.

The paper describes a probabilistic active learning strategy for support vector machine (SVM) design in large data applications. The learning strategy is motivated by the statistical query model. While most existing methods of active SVM learning query for points based on their proximity to the current separating hyperplane, the proposed method queries for a set of points according to a distribution as determined by the current separating hyperplane and a newly defined concept of an adaptive confidence factor. This enables the algorithm to have more robust and efficient learning capabilities. The confidence factor is estimated from local information using the k nearest neighbor principle. The effectiveness of the method is demonstrated on real-life data sets both in terms of generalization performance, query complexity, and training time.

We propose a rough-fuzzy hybridization scheme for case generation. Fuzzy set theory is used for linguistic representation of patterns, thereby producing a fuzzy granulation of the feature space. Rough set theory is used to obtain dependency rules which model informative regions in the granulated feature space. The fuzzy membership functions corresponding to the informative regions are stored as cases along with the strength values. Case retrieval is made using a similarity measure based on these membership functions. Unlike the existing case selection methods, the cases here are cluster granules and not sample points. Also, each case involves a reduced number of relevant features. These makes the algorithm suitable for mining data sets, large both in dimension and size, due to its low-time requirement in case generation as well as retrieval. Superiority of the algorithm in terms of classification accuracy and case generation and retrieval times is demonstrated on some real-life data sets.

The concept of multiobjective optimization (MOO) has been integrated with variable length chromosomes for the development of a nonparametric genetic classifier which can overcome the problems, like overfitting/overlearning and ignoring smaller classes, as faced by single objective classifiers. The classifier can efficiently approximate any kind of linear and/or nonlinear class boundaries of a data set using an appropriate number of hyperplanes. While designing the classifier the aim is to simultaneously minimize the number of misclassified training points and the number of hyperplanes, and to maximize the product of class wise recognition scores. The concepts of validation set (in addition to training and test sets) and validation functional are introduced in the multiobjective classifier for selecting a solution from a set of nondominated solutions provided by the MOO algorithm. This genetic classifier incorporates elitism and some domain specific constraints in the search process, and is called the CEMOGA-Classifier (constrained elitist multiobjective genetic algorithm based classifier). Two new quantitative indices, namely, the purity and minimal spacing, are developed for evaluating the performance of different MOO techniques. These are used, along with classification accuracy, required number of hyperplanes and the computation time, to compare the CEMOGA-Classifier with other related ones.

PageRank is primarily based on link structure analysis. Recently, it has been shown that content information can be utilized to improve link analysis. We propose a novel algorithm that harnesses the information contained in the history of a surfer to determine the topic of interest on a given page. As the history is unavailable until query time, we guess it probabilistically so that the operations can be performed offline. This leads to a better Web page categorization and, thereby, to a better ranking of Web pages.

A methodology is described for evolving a Rough-fuzzy multi layer perceptron with modular concept using a genetic algorithm to obtain a structured network suitable for both classification and rule extraction. The modular concept, based on "divide and conquer" strategy, provides accelerated training and a compact network suitable for generating a minimum number of rules with high certainty values. The concept of variable mutation operator is introduced for preserving the localized structure of the constituting knowledge-based subnetworks, while they are integrated and evolved. Rough set dependency rules are generated directly from the real valued attribute table containing fuzzy membership values. Two new indices viz., "certainty" and "confusion" in a decision are defined for evaluating quantitatively the quality of rules. The effectiveness of the model and the rule extraction algorithm is extensively demonstrated through experiments alongwith comparisons.

In this article, we describe an unsupervised feature selection algorithm suitable for data sets, large in both dimension and size. The method is based on measuring similarity between features whereby redundancy therein is removed. This does not need any search and, therefore, is fast. A new feature similarity measure, called maximum information compression index, is introduced. The algorithm is generic in nature and has the capability of multiscale representation of data sets. The superiority of the algorithm, in terms of speed and performance, is established extensively over various real-life data sets of different sizes and dimensions. It is also demonstrated how redundancy and information loss in feature selection can be quantified with an entropy measure.

A problem gaining interest in pattern recognition applied to data mining is that of selecting a small representative subset from a very large data set. In this article, a nonparametric data reduction scheme is suggested. It attempts to represent the density underlying the data. The algorithm selects representative points in a multiscale fashion which is novel from existing density-based approaches. The accuracy of representation by the condensed set is measured in terms of the error in density estimates of the original and reduced sets. Experimental studies on several real life data sets show that the multiscale approach is superior to several related condensation methods both in terms of condensation ratio and estimation error. The condensed set obtained was also experimentally shown to be effective for some important data mining tasks like classification, clustering, and rule generation on large data sets. Moreover, it is empirically found that the algorithm is efficient in terms of sample complexity.

The problem of segmentation of multispectral satellite images is addressed. An integration of rough-set-theoretic knowledge extraction, the Expectation Maximization (EM) algorithm, and minimal spanning tree (MST) clustering is described. EM provides the statistical model of the data and handles the associated measurement and representation uncertainties. Rough-set theory helps in faster convergence and in avoiding the local minima problem, thereby enhancing the performance of EM. For rough-set-theoretic rule generation, each band is discretized using fuzzy-correlation-based gray-level thresholding. MST enables determination of nonconvex clusters. Since this is applied on Gaussians, determined by granules, rather than on the original data points, time required is very low. These features are demonstrated on two IRS-1A four-band images. Comparison with related methods is made in terms of computation time and a cluster quality measure.

The present article provides a survey of the available literature on data mining using soft computing. A categorization has been provided based on the different soft computing tools and their hybridizations used, the data mining function implemented, and the preference criterion selected by the model. The utility of the different soft computing methodologies is highlighted. Generally fuzzy sets are suitable for handling the issues related to understandability of patterns, incomplete/noisy data, mixed media information and human interaction, and can provide approximate solutions faster. Neural networks are nonparametric, robust, and exhibit good learning and generalization capabilities in data-rich environments. Genetic algorithms provide efficient search algorithms to select a model, from mixed media data, based on some preference criterion/objective function. Rough sets are suitable for handling different types of uncertainty in data. Some challenges to data mining and the application of soft computing methodologies are indicated. An extensive bibliography is also included.

The paper summarizes the different characteristics of Web data, the basic components of Web mining and its different types, and the current state of the art. The reason for considering Web mining, a separate field from data mining, is explained. The limitations of some of the existing Web mining methods and tools are enunciated, and the significance of soft computing (comprising fuzzy logic (FL), artificial neural networks (ANNs), genetic algorithms (GAs), and rough sets (RSs) are highlighted. A survey of the existing literature on "soft Web mining" is provided along with the commercially available systems. The prospective areas of Web mining where the application of soft computing needs immediate attention are outlined with justification. Scope for future research in developing "soft Web mining" systems is explained. An extensive bibliography is also provided.

A fuzzy knowledge-based network is developed based on the linguistic rules extracted from a fuzzy decision tree. A scheme for automatic linguistic discretization of continuous attributes, based on quantiles, is formulated. A novel concept for measuring the goodness of a decision tree, in terms of its compactness (size) and efficient performance, is introduced. Linguistic rules are quantitatively evaluated using new indices. The rules are mapped to a fuzzy knowledge-based network, incorporating the frequency of samples and depth of the attributes in the decision tree. New fuzziness measures, in terms of class memberships, are used at the node level of the tree to take care of overlapping classes. The effectiveness of the system, in terms of recognition scores, structure of decision tree, performance of rules, and network size, is extensively demonstrated on three sets of real-life data.

In this paper, we present an automated face recognition (AFR) system that contains two components: eye detection and face recognition. Based on invariant radial basis function (IRBF) networks and knowledge rules of facial topology, a hybrid neural method is proposed to localize human eyes and segment the face region from a scene. A dual eigenspaces method (DEM) is then developed to extract algebraic features of the face and perform the recognition task with a two-layer minimum distance classifier. Experimental results illustrate that the proposed system is effective and robust.

The concept of chromosome differentiation, commonly witnessed in nature as male and female sexes, is incorporated in genetic algorithms with variable length strings for designing a nonparametric classification methodology. Its significance in partitioning different landcover regions from satellite images, having complex/overlapping class boundaries, is demonstrated. The classifier is able to evolve automatically the appropriate number of hyperplanes efficiently for modeling any kind of class boundaries optimally. Merits of the system over the related ones are established through the use of several quantitative measure.

An algorithm for data condensation using support vector machines (SVM) is presented. The algorithm extracts data points lying close to the class boundaries, which form a much reduced but critical set for classification. The problem of large memory requirements for training SVM in batch mode is circumvented by adopting an active incremental learning algorithm. The learning strategy is motivated from the condensed nearest neighbor classification technique. Experimental results presented show that such active incremental learning enjoy superiority in terms of computation time and condensation ratio, over related methods.

The present article demonstrates a way of formulating neuro-fuzzy approaches for both feature selection and extraction under unsupervised learning. A fuzzy feature evaluation index for a set of features is defined in terms of degree of similarity between two patterns in both the original and transformed feature spaces. A concept of flexible membership function incorporating weighted distance is introduced for computing membership values in the transformed space. Two new layered networks are designed. The tasks of membership computation and minimization of the evaluation index, through unsupervised learning process, are embedded into them without requiring the information on the number of clusters in the feature space. The network for feature selection results in an optimal order of individual importance of the features. The other one extracts a set of optimum transformed features, by projecting -dimensional original space directly to n'-dimensional (n' < n) transformed space, along with their relative importance. The superiority of the networks to some related ones is established experimentally.

A system design methodology for fuzzy clustering neural networks (FCNs) is presented. This methodology emphasizes coordination between FCN model definition, architectural description, and systolic implementation. Two mapping strategies both from FCN model to system architecture and from the given architecture to systolic arrays are described. The effectiveness of the methodology is illustrated by: 1) applying the design to an effective FCN model; 2) developing the corresponding parallel architecture with special feedforward and feedback paths; and 3) building the systolic array (SA) suitable for very large scale integration (VLSI) implementation.

A method for pattern classification using genetic algorithms (GAs) has been recently described in Pal, Bandyopadhyay and Murthy (1998), where the class boundaries of a data set are approximated by a fixed number H of hyperplanes. As a consequence of fixing H a priori, the classifier suffered from the limitation of overfitting (or underfitting) the training data with an associated loss of its generalization capability. In this paper, we propose a scheme for evolving the value of H automatically using the concept of variable length strings/chromosomes. The crossover and mutation operators are newly defined in order to handle variable string lengths. The fitness function ensures primarily the minimization of the number of misclassified samples, and also the reduction of the number of hyperplanes. Based on an analogy between the classification principles of the genetic classifier and multilayer perceptron (with hard limiting neurons), a method for automatically determining the architecture and the connection weights of the latter is described.

The authors develop a parallel structure for the time-delay neural network used in some speech recognition applications. The effectiveness of the design is illustrated by: (1) extracting a window computing model from the time-delay neural systems; (2) building its pipelined architecture with parallel or serial processing stages; and (3) applying this parallel window computing to some typical speech recognition systems. An analysis of the complexity of the proposed design shows a greatly reduced complexity while maintaining a high throughput rate.

An analogy between a genetic algorithm based pattern classification scheme (where hyperplanes are used to approximate the class boundaries through searching) and multilayer perceptron (MLP) based classifier is established. Based on this, a method for

In this article, the concept of e-optimal stopping time of a genetic algorithm with elitist model (EGA) has been introduced. The probability of performing mutation plays an important role in the computation of the ε-optimal stopping times. Two approa

A new scheme of knowledge encoding in a fuzzy multilayer perceptron (MLP) using rough set-theoretic concepts is described. Crude domain knowledge is extracted from the data set in the form of rules. The syntax of these rules automatically determines the appropriate number of hidden nodes while the dependency factors are used in the initial weight encoding. The network is then refined during training. Results on classification of speech and synthetic data demonstrate the superiority of the system over the fuzzy and conventional versions of the MLP (involving no initial knowledge).

A method is described for finding decision boundaries, approximated by piecewise linear segments, for classifying patterns in R(N),N>/=2, using an elitist model of genetic algorithms. It involves generation and placement of a set of hyperplanes (represented by strings) in the feature space that yields minimum misclassification. A scheme for the automatic deletion of redundant hyperplanes is also developed in case the algorithm starts with an initial conservative estimate of the number of hyperplanes required for modeling the decision boundary. The effectiveness of the classification methodology, along with the generalization ability of the decision boundary, is demonstrated for different parameter values on both artificial data and real life data sets having nonlinear/overlapping class boundaries. Results are compared extensively with those of the Bayes classifier, k-NN rule and multilayer perceptron.

An application of Genetic Algorithms (GAs) to evolve Hopfield type optimum neural network architectures for object extraction problem is demonstrated. Different optimizing functions involving minimization of energy value of the network, maximization of percentage of correct classification of pixels (pcc), minimization of number of connections of the network (noc), and a combination of pcc and noc have been considered. The noc value of the evolved (sub)optimal architectures is seen to be reduced to two-third of that required for the fully connected version. The performance of GA is seen to be better than that of Simulated Annealing for this problem.

A new scheme of knowledge-based classification and rule generation using a fuzzy multilayer perceptron (MLP) is proposed. Knowledge collected from a data set is initially encoded among the connection weights in terms of class a priori probabilities. This encoding also includes incorporation of hidden nodes corresponding to both the pattern classes and their complementary regions. The network architecture, in terms of both links and nodes, is then refined during training. Node growing and link pruning are also resorted to. Rules are generated from the trained network using the input, output, and connection weights in order to justify any decision(s) reached. Negative rules corresponding to a pattern not belonging to a class can also be obtained. These are useful for inferencing in ambiguous cases. Results on real life and synthetic data demonstrate that the speed of learning and classification performance of the proposed scheme are better than that obtained with the fuzzy and conventional versions of the MLP (involving no initial knowledge encoding). Both convex and concave decision regions are considered in the process.

Merits of genetic algorithms (GAs), an efficient evolutionary searching paradigm, are utilized for pattern classification in /spl Rfr//sup N/ by fitting hyperplanes to model the decision boundaries in the feature space. Theoretical analysis establishes that as the size of the training set (n) goes towards infinity, the error probability and the decision boundary of the GA based classifier will approach those of Bayes (optimum) classifier.

The present work describes a method of analyzing Indian Remote Sensing (IRS) satellite imagery for detecting various man-made objects, namely, roads, bridges, airports, seaports, city area and town-ship/industrial areas. A multivalued recognition system has initially been used to classify the image pixels into six land cover types by providing multiple choices of classes. In order to identify certain targets, some spatial knowledge about them and their inter-relationships have been incorporated on the clustered image using some heuristic rules. The use of multiple class choices makes the detection procedures effective.

A connectionist inferencing network, based on the fuzzy version of Kohonen's model already developed by the authors, is proposed. It is capable of handling uncertainty and/or impreciseness in the input representation provided in quantitative, linguistic and/or set forms. The output class membership value of an input pattern is inferred by the trained network. A measure of certainty expressing confidence m the decision is also defined. The model is capable of querying the user for the more important input feature information, if required, in case of partial inputs. Justification for an inferred decision may be produced in rule form, when so desired by the user. The connection weight magnitude of the trained neural network are utilized in every stage of the proposed inferencing procedure. The antecedent and consequent parts of the justificatory rules are provided in natural forms. The effectiveness of the algorithm is tested on the vowel recognition problem and on two sets of artificially generated nonconvex pattern classes.

A connectionist model for categorization (self-organization) even in the presence of multiple or mixed patterns has been presented. During self-organization, the network automatically adjusts the number of nodes in the hidden and output layers, depending on the complexity or nature of overlap between the patterns. An ambiguity measure is given based on how well the features are being interpreted by the network. From the ambiguity measure a certainty factor about the decision of the network is derived. The effect of noise on the certainty factor is investigated. A vigilance threshold is used to decide whether the network's decision is correct or not. Functionally the network consists of two parts, one of them categorizes the incoming patterns and the other monitors the performance of categorization. The characteristics of the model has also been demonstrated experimentally on both 1D binary strings and image patterns even when they are corrupted by additive, subtractive, and mixed noise.

A connectionist system has been designed for learning and simultaneous recognition of flat industrial objects (based an the concepts of conventional and structured connectionist computing) by integrating the psychological hypotheses with the generalized Hough transform technique. The psychological facts include the evidence of separation of two regions for identification ("what it is") and pose estimation ("where it is"). The system uses the mechanism of selective attention for initial hypotheses generation. A special two-stage training paradigm has been developed for learning the structural relationships between the features and objects and the importance values of the features with respect to the objects. The performance of the system has been demonstrated on real-life data both for single and mixed (overlapped) instances of object categories. The robustness of the system with respect to noise and false alarming has been theoretically investigated.

The robustness of neural network (NN) based information processing systems with respect to component failure (damaging of nodes/links) is studied. The damaging/component failure process has been modeled as a Poisson process. To choose the instants or moments of damaging, statistical sampling technique is used. The nodes/links to be damaged are determined randomly. As an illustration, the model is implemented and tested on different object extraction algorithms employing Hopfield's associative memory model, Gibbs random fields, and a self-organizing multilayer neural network. The performance of these algorithms is evaluated in terms of percentage of pixels correctly classified under different noisy environments and different degrees and sequences of damaging. The deterioration in the output is seen to be very small even when a large number of nodes/links are damaged.

A connectionist expert system model, based on a fuzzy version of the multilayer perceptron developed by the authors, is proposed. It infers the output class membership value(s) of an input pattern and also generates a measure of certainty expressing confidence in the decision. The model is capable of querying the user for the more important input feature information, if and when required, in case of partial inputs. Justification for an inferred decision may be produced in rule form, when so desired by the user. The magnitudes of the connection weights of the trained neural network are utilized in every stage of the proposed inferencing procedure. The antecedent and consequent parts of the justificatory rules are provided in natural forms. The effectiveness of the algorithm is tested on the speech recognition problem, on some medical data and on artificially generated intractable (linearly nonseparable) pattern classes.

A multivalued (fuzzy) recognition system was formulated by Mandal et. al. which is capable of handling various imprecise inputs and provides multiple class choices to any input. In the present article, an application of the recognition system for detecting road-like structures from Indian Remote Sensing satellite (IRS) imagery has been described. The concept of multiple choices of the recognition system is found to be quite useful here. The results are seen to agree well with the geographical maps when various image frames were considered as input.

A multivalued recognition system was formulated by the authors which has the ability of discriminating the nonoverlapping, and overlapping and no-class ( ambiguous/doubtful) regions and of analyzing the associated uncertainties by providing output decisions in four states, namely, single, first-second, combined, and null choices. The single choices correspond to the nonoverlapping regions, whereas the overlapping regions are reflected by the first-second and combined choices. The null choices reflect the portions outside the pattern classes and/or the portions of the pattern classes uncovered by the training samples. A theoretical analysis of these characteristics and of the performance of the recognition system is provided. It is shown theoretically that with the increase in the size of the training samples, the estimates of the overlapping, nonoverlapping, and no-class regions tend to their actual sizes. All analytical findings have been substantiated with experimental results various situations in one and two-dimensional feature spaces. Bayes decision boundaries are always found to lie within the combined choice region as provided by the multivalued recognition system. The present investigation, in turn, establishes analytically the justification of providing multivalued output decisions in four states for managing uncertainties arising from ambiguous regions.>

This paper describes a self-organizing artificial neural network, based on Kohonen's model of self-organization, which is capable of handling fuzzy input and of providing fuzzy classification. Unlike conventional neural net models, this algorithm incorporates fuzzy set-theoretic concepts at various stages. The input vector consists of membership values for linguistic properties along with some contextual class membership information which is used during self-organization to permit efficient modeling of fuzzy (ambiguous) patterns. A new definition of gain factor for weight updating is proposed. An index of disorder involving mean square distance between the input and weight vectors is used to determine a measure of the ordering of the output space. This controls the number of sweeps required in the process. Incorporation of the concept of fuzzy partitioning allows natural self-organization of the input data, especially when they have ill-defined boundaries. The output of unknown test patterns is generated in terms of class membership values. Incorporation of fuzziness in input and output is seen to provide better performance as compared to the original Kohonen model and the hard version. The effectiveness of this algorithm is demonstrated on the speech recognition problem for various network array sizes, training sets and gain factors.>

Structural description of objects comprised descriptions of the parts and spatial relations between the parts. This paper presents a Hopfield net based scheme for matching structural shape descriptions. The current formulation of the matching scheme is general enough to take care of partial mismatch between the individual parts and spatial constraints between these parts. In addition, a transformation of the shape descriptions has been suggested with which shape descriptions containing asymmetrical spatial constraints between the parts can be matched using symmetric interconnection weights for the Hopfield net. The Hopfield net based formulation has been extended to consider the problem of finding the best match of the test shape descriptions with one of the stored prototypes. The matching scheme has been experimentally applied for recognition of hand-tools and symbols. In both cases, the network produced encouraging recognition results.

Abstract-The feedforward multilayer perceptron (MLP) with back-propagation of error is described. Since use of this network requires a set of labeled input-output, as such it cannot be used for segmentation of images when only one image is available. (However, if images to be processed are of similar nature, one can use a set of known images for learning and then use the network for processing of other images.) A self-organizing multilayer neural network architecture suitable for image processing is proposed. The proposed architecture is also a feedforward one with back-propagation of errors; but like MLP it does not require any supervised learning. Each neuron is connected to the corresponding neuron in the previous layer and the set of neighbors of that neuron. The output status of neurons in the output layer is described as a fuzzy set. A fuzziness measure of this fuzzy set is used as a measure of error in the system (instability of the network). Learning rates for various measures of fuzziness have been theoretically and experimentally studied. An application of the proposed network in object extraction from noisy scenes is also demonstrated. Index Terms- Image processing, object extraction, fuzzy sets, neural networks, multilayer perceptron. I.

Object extraction algorithms with a Neural Network (NN) are described. The objective function to be minimized for object extraction from a scene is shown to be similar to the expression of energy of a neural network. A modified version of Hopfield's Neural Network model is used here. The weights and input biases are given in such a way that the network self-organizes to form compact clusters. Both the discrete and the continuous dynamics of the network have been used for this purpose. Performance of the proposed methods has been compared with that of the relaxation technique.

A fuzzy neural network model based on the multilayer perceptron, using the backpropagation algorithm, and capable of fuzzy classification of patterns is described. The input vector consists of membership values to linguistic properties while the output vector is defined in terms of fuzzy class membership values. This allows efficient modeling of fuzzy uncertain patterns with appropriate weights being assigned to the backpropagated errors depending upon the membership values at the corresponding outputs. During training, the learning rate is gradually decreased in discrete steps until the network converges to a minimum error solution. The effectiveness of the algorithm is demonstrated on a speech recognition problem. The results are compared with those of the conventional MLP, the Bayes classifier, and other related models.

A recognition system based on fuzzy set theory and approximate reasoning that is capable of handling various imprecise input patterns and providing a natural decision system is described. The input feature is considered to be of either quantitative form, linguistic form, mixed form, or set form. The entire feature space is decomposed into overlapping subdomains depending on the geometric structure and the relative position of the pattern classes found in the training samples. Uncertainty (ambiguity) in the input statement is managed by providing/modifying membership values to a great extent. A relational matrix corresponding to the subdomains and the pattern classes is used to recognize the samples. The system uses L.A. Zadeh's (1977) compositional rule of inference and gives a natural (linguistic) multivalued output decision associated with a confidence factor denoting the degree of certainty of a decision. The effectiveness of the algorithm is demonstrated for some artificially generated patterns and for real-life speech data.>

The theory of formation of an ideal image has been described which shows that the gray level in an image follows the Poisson distribution. Based on this concept, various algorithms for object background classification have been developed. Proposed algorithms involve either the maximum entropy principle or the minimum χ2 statistic. The appropriateness of the Poisson distribution is further strengthened by comparing the results with those of similar algorithms which use conventional normal distribution. A set of images with various types of histograms has been considered here as the test data.

Shannon's definition of entropy is critically examined and a new definition of classical entropy based on the exponential behavior of information gain is proposed along with its justification. The concept is extended to defining the global, local, and conditional entropy of a gray-level image. Based on these definitions four algorithms for object extraction are developed. One of these algorithms uses a Poisson distribution-based model of an ideal image. A concept of positional entropy giving any information regarding the location of an object in a scene is introduced.>

Two methods are proposed for coding the discrete contour of binary images. A set of key pixels (guiding pixels) on the contour is defined for this purpose. The decoding schemes approximate the contour through the key pixels using the quadratic Bezier approximation technique. The amount of deviation of the decoded image from the original image is studied using the objective measures of percentage error and shape compactness. The decoded images are found to be faithful reproductions of the original image. A set of cleaning operations is also introduced as an intermediate step before final reproduction. It was found that the bit requirements and the compression ratios are also improved significantly as compared to the contour run length coding and discrete line segment coding techniques.>

The terms index of fuzziness, entropy, and π-ness, which give measures of fuzziness in a set, are used to define an index of feature evaluation in pattern recognition problems in terms of their intraclass and interclass measures. The index value decreases as the reliability of a feature in characterizing and discriminating different classes increases. The algorithm developed has been implemented in cases of vowel and plosive identification problem using formant frequencies and different S and π membership functions.

A hierarchical three-stage syntactic recognition algorithm using six-tuple fuzzy and seven-tuple fractionally fuzzy grammars is described for identifying different stages of maturity of bones from X-rays of hand and wrist. The primitives considered are "dot," "straight line," and "arc" as obtained elsewhere. For each arc, its memberships in the sets of "sharp," "fair," and "gentle" arcs have been considered in order to describe and interpret the structural development of epiphysis and metaphysis with growth of a child. The two algorithms are illustrated with the help of the radiograph of a 10-12-year old boy along with some "noisy" versions of the radiograph, which was artificially generated by taking into account possible variations in shape of the relevent contours in the radiograph. Relative merits of the two algorithms with respect to each other and as well as the existing nonfuzzy approach are also discussed.

The effectiveness of the theory of fuzzy sets in detecting different regional boundaries of X-ray images is demonstrated. The algorithm includes a prior enhancement of the contrast among the regions (having small change in gray levels) using the contrast intensification (INT) operation along with smoothing in the fuzzy property plane before detecting its edges. The property plane is extracted from the spatial domain using S, ¿ and (1 ¿) functions and the fuzzifiers. Final edge detection is achieved using max or min operator. The system performance for different parameter conditions is illustrated by application to an image of a radiograph of the wrist.

An application of the theory of fuzzy sets in understanding an image is demonstrated. The task of understanding consists of three parts. A representation of image contours by their respective chains of octal codes, smoothing of the chain to remove spurious wiggles, and segmentation and assignment of degree of `arcness' to each segmented smoothed chain in order to extract their primitives for description. Octal code is provided to a two-pixel or, even more length contour by taking maximum of its grades of membership corresponding to `vertical', `horizontal' and `oblique' lines. Four different smoothers have been used to eliminate the spurious wiggles occurring in the contours. Segmentation of edges into different curves and lines is made on the basis of constant change in code values. The primitives for description and interpretation of images are extracted by assigning the appropriate membership value which provides a measure of curvature to the different arcs. The sense of curving is also determined. The effectiveness of the algorithm is demonstrated when a gray tone edge-detected X-ray image of wrist is considered as input.

The ``index of fuzziness'' and ``entropy'' of an image reflect a kind of quantitative measure of its enhancement quality. Their values are found to decrease with enhancement of an image when different sets of S-type membership functions with appropriate crossover points were considered for extracting the fuzzy property plane from the spatial domain of the image.

An algorithm for extracting different regional boundaries of x-ray images is described which includes three-stage enhancement of the image in the fuzzy property plane and a smoother before the detection of edges. The property plane is extracted from the spatial domain using S and π functions and fuzzifiers. The operator 'contrast intensifier' is used as an enhancement tool. The final edge detection is achieved using '\max' or '\min' operator.