Extended Fuzzy Clustering Algorithms

Fuzzy clustering is a widely applied method for obtaining fuzzy models from data. Ithas been applied successfully in various fields including finance and marketing. Despitethe successful applications, there are a number of issues that must be dealt with in practicalapplications of fuzzy clustering algorithms. This technical report proposes two extensionsto the objective function based fuzzy clustering for dealing with these issues. First, the(point) prototypes are extended to hypervolumes whose size is determined automaticallyfrom the data being clustered. These prototypes are shown to be less sensitive to a biasin the distribution of the data. Second, cluster merging by assessing the similarity amongthe clusters during optimization is introduced. Starting with an over-estimated number ofclusters in the data, similar clusters are merged during clustering in order to obtain a suitablepartitioning of the data. An adaptive threshold for merging is introduced. The proposedextensions are applied to Gustafson-Kessel and fuzzy c-means algorithms, and the resultingextended algorithms are given. The properties of the new algorithms are illustrated invarious examples.fuzzy clustering;cluster merging;similarity;volume prototypes

A new fuzzy set merging technique using inclusion-based fuzzy clustering

This paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space, taking into account the degree of inclusion of each fuzzy set in the cluster prototypes. The merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype. The feasibility and the performance of the proposed method are studied using an application in mobile robot navigation. The results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts. In this paper, we concentrate mainly on fuzzy systems with Gaussian membership functions, but the general approach can also be applied to other parameterized fuzzy sets

Analysis of FMRI Exams Through Unsupervised Learning and Evaluation Index

In the last few years, the clustering of time series has seen significant growth and has proven effective in providing useful information in various domains of use. This growing interest in time series clustering is the result of the effort made by the scientific community in the context of time data mining. For these reasons, the first phase of the thesis focused on the study of the data obtained from fMRI exams carried out in task-based and resting state mode, using and comparing different clustering algorithms: SelfOrganizing map (SOM), the Growing Neural Gas (GNG) and Neural Gas (NG) which are crisp-type algorithms, a fuzzy algorithm, the Fuzzy C algorithm, was also used (FCM). The evaluation of the results obtained by using clustering algorithms was carried out using the Davies Bouldin evaluation index (DBI or DB index). Clustering evaluation is the second topic of this thesis. To evaluate the validity of the clustering, there are specific techniques, but none of these is already consolidated for the study of fMRI exams. Furthermore, the evaluation of evaluation techniques is still an open research field. Eight clustering validation indexes (CVIs) applied to fMRI data clustering will be analysed. The validation indices that have been used are Pakhira Bandyopadhyay Maulik Index (crisp and fuzzy), Fukuyama Sugeno Index, Rezaee Lelieveldt Reider Index, Wang Sun Jiang Index, Xie Beni Index, Davies Bouldin Index, Soft Davies Bouldin Index. Furthermore, an evaluation of the evaluation indices will be carried out, which will take into account the sub-optimal performance obtained by the indices, through the introduction of new metrics. Finally, a new methodology for the evaluation of CVIs will be introduced, which will use an ANFIS model