A possibilistic approach to latent structure analysis for symmetric fuzzy data.

In many situations the available amount of data is huge and can be intractable. When the data set is single valued, latent structure models are recognized techniques, which provide a useful compression of the information. This is done by considering a regression model between observed and unobserved (latent) fuzzy variables. In this paper, an extension of latent structure analysis to deal with fuzzy data is proposed. Our extension follows the possibilistic approach, widely used both in the cluster and regression frameworks. In this case, the possibilistic approach involves the formulation of a latent structure analysis for fuzzy data by optimization. Specifically, a non-linear programming problem in which the fuzziness of the model is minimized is introduced. In order to show how our model works, the results of two applications are given.Latent structure analysis, symmetric fuzzy data set, possibilistic approach.

An Algorithm for Detecting the Principal Allotment among Fuzzy Clusters and Its Application as a Technique of Reduction of Analyzed Features Space Dimensionality

This paper describes a modification of a possibilistic clustering method based on the concept of allotment among fuzzy clusters. Basic ideas of the method are considered and the concept of a principal allotment among fuzzy clusters is introduced. The paper provides the description of the plan of the algorithm for detection principal allotment. An analysis of experimental results of the proposed algorithm’s application to the Tamura’s portrait data in comparison with the basic version of the algorithm and with the NERFCM-algorithm is carried out. A methodology of the algorithm’s application to the dimensionality reduction problem is outlined and the application of the methodology is illustrated on the example of Anderson’s Iris data in comparison with the result of principal component analysis. Preliminary conclusions are formulated also

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

Review on Fuzzy Clustering Algorithms

Image segmentation especially fuzzy-based segmentation techniques are widely used due to effective segmentation performance. For this reason, a number of algorithms are proposed in the literature. This paper presents a survey report of different types of classical fuzzy clustering techniques which are available in the literature

Kernel-based modified fuzzy possibilistic c-means clustering

Classification and clustering algorithms are, without doubt, a useful tool to explore data structures, and have been widely employed in many domains such as pattern recognition, image processing, data mining, and data analysis. The focus of this paper is the partitioning problem with a special interest in kernel method. The aim of this paper is to extend this method to the modified fuzzy possibilistic c-means (MFPCM) algorithm. It is realized by substitution of a kernel-induced distance metric for the Euclidean distance, and the corresponding algorithm is called kernel MFPCM algorithm. Numerical simulations are given to illustrate the performances of the proposed method

Fuzzy Clustering for Image Segmentation Using Generic Shape Information

The performance of clustering algorithms for image segmentation are highly sensitive to the features used and types of objects in the image, which ultimately limits their generalization capability. This provides strong motivation to investigate integrating shape information into the clustering framework to improve the generality of these algorithms. Existing shape-based clustering techniques mainly focus on circular and elliptical clusters and so are unable to segment arbitrarily-shaped objects. To address this limitation, this paper presents a new shape-based algorithm called fuzzy clustering for image segmentation using generic shape information (FCGS), which exploits the B-spline representation of an object's shape in combination with the Gustafson-Kessel clustering algorithm. Qualitative and quantitative results for FCGS confirm its superior segmentation performance consistently compared to well-established shape-based clustering techniques, for a wide range of test images comprising various regular and arbitrary-shaped objects