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Abstract: Cognitive maps and fuzzy cognitive maps offer interesting and transparent modeling capabilities by functioning at a level of conceptual entities (nodes) and their relationships expressed either at the qualitative level of excitatory/inhibitory relationships or being further numerically quantified as encountered in fuzzy cognitive maps. While there has been a vast array of conceptual enhancements, a relatively less attention has been paid to the design of the maps especially when dealing with an algorithmic way of forming the map. The objective of this study is to offer a design strategy in which starting with experimental evidence in the form of numeric data, those data are transformed into a finite and small number of concepts (nodes) of the map and afterwards the connections of the map are estimated. We show that techniques of Granular Computing, especially fuzzy clustering are effectively used to form concepts (nodes) of well-articulated semantics. In the sequel, we show the use of global optimization in the form of Particle Swarm Optimization (PSO) to carry out calibration of the connections of the interrelationships between the nodes of the map. Numeric examples are concerned with the representation of time series and their visualization in the form of fuzzy cognitive maps. Further interpretation of the maps is also discussed. [Copyright &y& Elsevier]

Abstract: In this study, we present a comprehensive comparative analysis of kernel-based fuzzy clustering and fuzzy clustering. Kernel based clustering has emerged as an interesting and quite visible alternative in fuzzy clustering, however, the effectiveness of this extension vis-à-vis some generic methods of fuzzy clustering has neither been discussed in a complete manner nor the performance of clustering quantified through a convincing comparative analysis. Our focal objective is to understand the performance gains and the importance of parameter selection for kernelized fuzzy clustering. Generic Fuzzy C-Means (FCM) and Gustafson–Kessel (GK) FCM are compared with two typical generalizations of kernel-based fuzzy clustering: one with prototypes located in the feature space (KFCM-F) and the other where the prototypes are distributed in the kernel space (KFCM-K). Both generalizations are studied when dealing with the Gaussian kernel while KFCM-K is also studied with the polynomial kernel. Two criteria are used in evaluating the performance of the clustering method and the resulting clusters, namely classification rate and reconstruction error. Through carefully selected experiments involving synthetic and Machine Learning repository (http://archive.ics.uci.edu/beta/) data sets, we demonstrate that the kernel-based FCM algorithms produce a marginal improvement over standard FCM and GK for most of the analyzed data sets. It has been observed that the kernel-based FCM algorithms are in a number of cases highly sensitive to the selection of specific values of the kernel parameters. [Copyright &y& Elsevier]

Fuzzy clustering forms a cornerstone of fuzzy (granular) modeling. The clusters (prototypes) are viewed as a blueprint of the model that is further refined through a number of detailed estimation techniques. In this study, we claim that while clustering is indisputable essential to fuzzy modeling, the essence of clustering mechanisms supporting this process of information granulation is not compatible with the character of the task at hand. In modeling, the required constructs are inherently direction-sensitive (that is we clearly distinguish between input and output variables). On the other hand, fuzzy clustering is direction neutral and during the formation of the clusters does not take this into consideration. We re-formulate the clustering so that the directionality aspect can be addressed in the optimization process. This leads to a new, augmented objective function to be minimized. A detailed algorithm is derived. As the directional sensitivity of the clustering method gives rise to different numbers of clusters in the input and output space, it becomes necessary to identify a mapping between these clusters which in turn gives rise to some allocation problem. Because of its inherently combinatorial character, the proposed solution is obtained through some genetic optimization. Comprehensive experiments demonstrate the performance of the approach and compare it with some of the generic version of the FCM clustering. [ABSTRACT FROM AUTHOR]

This study is concerned with clustering carried out in presence of labeled patterns. An objective of this optimization is to reconcile between the structure residing in data (and being primarily discovered by the underlying clustering mechanism) and the labels of the patterns forming such structure. In this sense, one can consider the supervised fuzzy clustering to be a framework of preliminary data analysis providing with a thorough insight into the structure of the data and supporting the ensuing design of detailed classifiers. The proposed method augments the standard fuzzy C-means algorithm by extending the original objective function by the supervision component (labeled patterns). Experimental results illustrate the approach and discuss the use of this type of clustering in vector quantization. [Copyright &y& Elsevier]

Abstract: Several fuzzy c-means based clustering techniques have been developed to tackle many problems in a number of areas such as pattern recognition, image analysis, communication, data mining. Among all, a common use of such a class of clustering algorithms is in the training of radial basis function neural networks (RBFNNs). In this paper, we describe a novel approach to fuzzy clustering, which organizes the data in clusters on the basis of the input data and a ‘prototype’ regression function built, in the output space, as a summation of a number of linear local regression models. This methodology is shown to be effective in the training of RBFNNs leading to improved performance with respect to other clustering algorithms. [Copyright &y& Elsevier]