Many functionals have been proposed for validation of partitions object data produced by the fuzzy c-means (FCM) clustering algorithm. We examine role a subtle but important parameter-the weighting exponent m FCM model-plays in determining validity partitions. The considered are partition coefficient and entropy indexes Bezdek, Xie-Beni (1991), extended indexes, Fukuyama-Sugeno index (1989). Limit analysis indicates, numerical experiments confirm, that is sensitive to both high low values...

In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership typicality values when clustering unlabeled data. FPCM constrains so sum over all data points of typicalities to a cluster is one. The row constraint produces unrealistic for large sets. this paper, propose new called possibilistic-fuzzy (PFCM) model. PFCM memberships possibilities simultaneously, along with usual point prototypes or centers each cluster. hybridization possibilistic...

Abstract Given a finite, unlabelled set of real vectors X, one often presumes the existence (c) subsets (clusters) in members which somehow bear more similarity to each other than adjoining clusters. In this paper, we use membership function matrices associated with fuzzy c-partitions together their values Euclidean (matrix) norm, formulate an posteriori method for evaluating algorithmically suggested clusterings X. Several numerical examples are offered support proposed technique.

We review two clustering algorithms (hard c-means and single linkage) three indexes of crisp cluster validity (Hubert's statistics, the Davies-Bouldin index, Dunn's index). illustrate deficiencies index which make it overly sensitive to noisy clusters propose several generalizations that are not as brittle outliers in clusters. Our numerical examples show standard measure interset distance (the minimum between points a pair sets) is worst (least reliable) upon base validation when expected...

In this paper the convergence of a class clustering procedures, popularly known as fuzzy ISODATA algorithms, is established. The theory Zangwill used to prove that arbitrary sequences generated by these (Picard iteration) procedures always terminates at local minimum, or worst, contains subsequence which converges minimum generalized least squares objective functional defines problem.

This paper reports the results of a numerical comparison two versions fuzzy c-means (FCM) clustering algorithms. In particular, we propose and exemplify an approximate (AFCM) implementation based upon replacing necessary ``exact'' variates in FCM equation with integer-valued or real-valued estimates. approximation enables AFCM to exploit lookup table approach for computing Euclidean distances exponentiation. The net effect proposed is that CPU time during each iteration reduced approximately...

Magnetic resonance (MR) brain section images are segmented and then synthetically colored to give visual representations of the original data with three approaches: literal approximate fuzzy c-means unsupervised clustering algorithms, a supervised computational neural network. Initial clinical results presented on normal volunteers selected patients tumors surrounded by edema. Supervised segmentation techniques provide broadly similar results. Unsupervised algorithms were visually observed...

A family of objective functions called fuzzy c-regression models, which can be used too fit switching regression models to certain types mixed data, is presented. Minimization particular in the yields simultaneous estimates for parameters c together with a c-partitioning data. general optimization approach given and corresponding theoretical convergence results are discussed. The illustrated by two numerical examples that show how it data coupled linear nonlinear models.< <ETX...

The problem of clustering a real s-dimensional data set X={x(1 ),,,,,x(n)} subset R(s) is considered. Usually, each observation (or datum) consists numerical values for all s features (such as height, length, etc.), but sometimes sets can contain vectors that are missing one or more the feature values. For example, particular datum x(k) might be incomplete, having form x(k)=(254.3, ?, 333.2, 47.45, ?)(T), where second and fifth missing. fuzzy c-means (FCM) algorithm useful tool data, it not...

Very large (VL) data or big are any that you cannot load into your computer's working memory. This is not an objective definition, but a definition easy to understand and one practical, because there dataset too for computer might use; hence, this VL you. Clustering of the primary tasks used in pattern recognition mining communities search databases (including images) various applications, so, clustering algorithms scale well important useful. paper compares efficacy three different...

A counterexample to the original incorrect convergence theorem for fuzzy <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -means (FCM) clustering algorithms (see J.C. Bezdak, IEEE Trans. Pattern Anal. and Math. Intell., vol.PAMI-2, no.1, pp.1-8, 1980) is provided. This establishes existence of saddle points FCM objective function at locations other than geometric centroid -partition space. Counterexamples previously discussed by W.T. Tucker...

When clustering algorithms are applied to image segmentation, the goal is solve a classification problem. However, these do not directly optimize duality. As result, they susceptible two problems: 1) criterion may be good estimator of "true" quality, and 2) often admit many (suboptimal) solutions. This paper introduces an algorithm that uses cluster validity mitigate problems 1 2. The validity-guided (re)clustering (VGC) cluster-validity information guide fuzzy process toward better It...

Describes a genetically guided approach to optimizing the hard (J/sub 1/) and fuzzy m/) c-means functionals used in cluster analysis. Our experiments show that genetic algorithm (GA) can ameliorate difficulty of choosing an initialization for clustering algorithms. Experiments use six data sets, including Iris data, magnetic resonance, color images. The is generally able find lowest known J/sub m/ value or associated with partition very similar value. On sets several local extrema, GA always...

Let f : Rs → R be a real-valued function, and let x = (x1,...,xs)T ∈ partitioned into t subsets of non-overlapping variables as (X1,...,Xt)T, with Xi Rpi for i 1,...,t, Σi=1tpi s. Alternating optimization (AO) is an iterative procedure minimizing f(x) f(X1, X2,..., Xt) jointly over all by alternating restricted minimizations the individual X1,...., Xt. has been (more or less) studied used in wide variety areas. Here self-contained general convergence theory presented that applicable to...

IT is my great pleasure to welcome you the inaugural issue of IEEE TRANSACTIONOSN FUZZY SYSTEMS. Many are probably quite familiar with basic ideas underlying fuzzy sets and systems that utilize models. However, there will also be readers who looking at contents this issue, wondering what it's all about. For latter group, papers in first may seem bewildering, for they technical, none tutorial nature. Consequently, preface divided into two parts. Section I contains a brief introduction our...

The relationship between the sequential hard c-means (SHCM) and learning vector quantization (LVQ) clustering algorithms is discussed. impact interaction of these two families methods with Kohonen's self-organizing feature mapping (SOFM), which not a method but often lends ideas to algorithms, are considered. A generalization LVQ that updates all nodes for given input proposed. network attempts find minimum well-defined objective function. rules depend on degree distance match winner node;...