Possibilistic and fuzzy clustering methods for robust analysis of non-precise data

This work focuses on robust clustering of data affected by imprecision. The imprecision is managed in terms of fuzzy sets. The clustering process is based on the fuzzy and possibilistic approaches. In both approaches the observations are assigned to the clusters by means of membership degrees. In fuzzy clustering the membership degrees express the degrees of sharing of the observations to the clusters. In contrast, in possibilistic clustering the membership degrees are degrees of typicality. These two sources of information are complementary because the former helps to discover the best fuzzy partition of the observations while the latter reflects how well the observations are described by the centroids and, therefore, is helpful to identify outliers. First, a fully possibilistic k-means clustering procedure is suggested. Then, in order to exploit the benefits of both the approaches, a joint possibilistic and fuzzy clustering method for fuzzy data is proposed. A selection procedure for choosing the parameters of the new clustering method is introduced. The effectiveness of the proposal is investigated by means of simulated and real-life data

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

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

Clustering algorithms for fuzzy rules decomposition

This paper presents the development, testing and evaluation of generalized Possibilistic fuzzy c-means (FCM) algorithms applied to fuzzy sets. Clustering is formulated as a constrained minimization problem, whose solution depends on the constraints imposed on the membership function of the cluster and on the relevance measure of the fuzzy rules. This fuzzy clustering of fuzzy rules leads to a fuzzy partition of the fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. When applied to the clustering of a flat fuzzy system results a set of decomposed sub-systems that will be conveniently linked into a Hierarchical Prioritized Structures

Possibilistic Clustering for Crisis Prediction: Systemic Risk States and Membership Degrees

Research on understanding and predicting systemic financial \ risk has been of increasing importance in the recent \ years. A common approach is to build predictive models \ based on macro-financial vulnerability indicators to \ identify systemic risk at an early stage. In this article, we \ outline an approach for identifying different systemic risk \ states through possibilistic fuzzy clustering. Instead of directly \ using a supervised classification method, we aim at \ identifying coherent groups of vulnerability with macrofinancial \ indicators for pre-crisis data, and determine the \ level of risk for a new observation based on its similarity \ to the identified groups. The approach allows for differentiating \ among different possible pre-crisis states, and \ using this information for estimating the possibility of systemic \ risk. In this work, we compare different fuzzy clustering \ methods, as well as conduct an empirical exercise \ for European systemic banking crises