This paper presents a multistage random sampling fuzzy c-means based clustering algorithm, which signi cantly reduces the computation time required to partition a data set into c classes. A series of subsets of the full data set are used for classi cation in order to provide an approximation to the nal cluster centers. The quality of the nal partitions is equivalent to that of fuzzy c-means. Th...

By a Ruspini partition we mean a finite family of fuzzy sets {f1, . . . , fn}, fi : [0, 1] → [0, 1], such that ∑n i=1 fi(x) = 1 for all x ∈ [0, 1], where [0, 1] denotes the real unit interval. We analyze such partitions in the language of Gödel logic. Our first main result identifies the precise degree to which the Ruspini condition is expressible in this language, and yields inter alia a const...

Many functionals have been proposed for validation of partitions of object data produced by the fuzzy c-means (FCM) clustering algorithm. We examine the role a subtle but important parameter-the weighting exponent m of the FCM model-plays in determining the validity of FCM partitions. The functionals considered are the partition coefficient and entropy indexes of Bezdek, the Xie-Beni, and exten...

In this paper we introduce a methodology for the segmentation of colour images by means of a nested hierarchy of fuzzy partitions. Colour image segmentation attempts to divide the pixels of an image in several homogeneously-coloured and topologically connected groups, called regions. Our methodology deals with the different (but related) aspects of imprecision that are present in this process. ...

This work presents the use of local fuzzy prototypes as a new idea to obtain accurate local semantics-based Takagi–Sugeno–Kang ~TSK! rules. This allow us to start from prototypes considering the interaction between input and output variables and taking into account the fuzzy nature of the TSK rules. To do so, a two-stage evolutionary algorithm based on MOGUL ~a methodology to obtain Genetic Fuz...

Recent advances in technology has led to huge growth in generating high dimensional data sets by capturing millions of facts in various fields, time phases, localities and brands. Microarray data contains gene expression from thousands of genes (features) from only tens of hundreds of samples. The rich source of information generated from microarray experiments often consist of incomplete and/o...

We present a novel approach to visualize and explore unstructured text. The underlying technology, called TOPIC-O-GRAPHY, applies wavelet transforms to a custom digital signal constructed from words within a document. The resultant multiresolution wavelet energy is used to analyze the characteristics of the narrative flow in the frequency domain, such as theme changes, which is then related to ...

Two basic issues for data analysis and kernel-machines design are approached in this paper: determining the number of partitions of a clustering task and the parameters of kernels. A distance metric is presented to determine the similarity between kernels and FCM proximity matrices. It is shown that this measure is maximized, as a function of kernel and FCM parameters, when there is coherence w...

Cluster validity has been mainly used to evaluate the quality of individual clusters, and compare whole partitions resulting from different or same (using different parameters) clustering algorithms [13]. However, depending on the application, the demands for a validity measure may differ, inducing the necessity of introducing new measures which will suit to the problem under investigation. We ...

In this paper, we present a novel optimization-based method for the combination of cluster ensembles. The information among the ensemble is formulated in 0-1 bit strings. The suggested model de ̄nes a constrained nonlinear objective function, called fuzzy string objective function (FSOF), which maximizes the agreement between the ensemble members and minimizes the disagreement simultaneously. De...