A Heuristic Approach to Possibilistic Clustering for Fuzzy Data

The paper deals with the problem of the fuzzy data clustering. In other words, objects attributes can be represented by fuzzy numbers or fuzzy intervals. A direct algorithm of possibilistic clustering is the basis of an approach to the fuzzy data clustering. The paper provides the basic ideas of the method of clustering and a plan of the direct possibilistic clustering algorithm. Definitions of fuzzy intervals and fuzzy numbers are presented and distances for fuzzy numbers are considered. A concept of a vector of fuzzy numbers is introduced and the fuzzy data preprocessing methodology for constructing of a fuzzy tolerance matrix is described. A numerical example is given and results of application of the direct possibilistic clustering algorithm to a set of vectors of triangular fuzzy numbers are considered in the example. Some preliminary conclusions are stated

Designing Gaussian Membership Functions for Fuzzy Classifier Generated by Heuristic Possibilistic Clustering

The paper deals with the problem of constructing Gaussian membership functions of fuzzy sets for fuzzy rules derived from the data by using heuristic algorithms of possibilistic clustering. Basic concepts of the heuristic approach to possibilistic clustering are reminded and the extended technique of constructing membership functions of fuzzy sets is proposed. An illustrative example is given and preliminary conclusions are made

An Efficient Fuzzy Possibilistic C-Means with Penalized and Compensated Constraints

Improvement in sensing and storage devices and impressive growth in applications such as Internet search, digital imaging, and video surveillance have generated many high-volume, high-dimensional data. The raise in both the quantity and the kind of data requires improvement in techniques to understand, process and summarize the data. Categorizing data into reasonable groupings is one of the most essential techniques for understanding and learning. This is performed with the help of technique called clustering. This clustering technique is widely helpful in fields such as pattern recognition, image processing, and data analysis. The commonly used clustering technique is K-Means clustering. But this clustering results in misclassification when large data are involved in clustering. To overcome this disadvantage, Fuzzy- Possibilistic C-Means (FPCM) algorithm can be used for clustering. FPCM combines the advantages of Possibilistic C-Means (PCM) algorithm and fuzzy logic. For further improving the performance of clustering, penalized and compensated constraints are used in this paper. Penalized and compensated terms are embedded with the modified fuzzy possibilistic clustering method2019;s objective function to construct the clustering with enhanced performance. The experimental result illustrates the enhanced performance of the proposed clustering technique when compared to the fuzzy possibilistic c-means clustering algorithm

A Heuristic Approach to Possibilistic Clustering for Fuzzy Data

The paper deals with the problem of the fuzzy data clustering. In other words, objects attributes can be represented by fuzzy numbers or fuzzy intervals. A direct algorithm of possibilistic clustering is the basis of an approach to the fuzzy data clustering. The paper provides the basic ideas of the method of clustering and a plan of the direct possibilistic clustering algorithm. Definitions of fuzzy intervals and fuzzy numbers are presented and distances for fuzzy numbers are considered. A concept of a vector of fuzzy numbers is introduced and the fuzzy data preprocessing methodology for constructing of a fuzzy tolerance matrix is described. A numerical example is given and results of application of the direct possibilistic clustering algorithm to a set of vectors of triangular fuzzy numbers are considered in the example. Some preliminary conclusions are stated

A survey of kernel and spectral methods for clustering

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved