Exploratory Study of Fuzzy Clustering and Set-Distance Based Validation Indexes

This thesis is concerned with issues related to clustering. In particular, it addresses the con-vergence speed of fuzzy c-means family of algorithms and cluster validation. The fuzzy c-meansclustering algorithm and its objective function is studied along with a literature review of thespeed of clustering algorithms. After careful examination, several objective functions are derivedby modifying the fuzzy c-means’ objective function.In addition, cluster validation is examined and new set distance based cluster validation indexes(CVI) are proposed which are the ratio of separation between clusters to compactness within acluster. To this end, a new measure of compactness, compactness of a fuzzy partition is presentedand fuzzy derivative of Pompeiu-Hausdorff distance is used as separation.The convergence of fuzzy c-means clustering algorithm is tested on real classification and clus-tering datasets. Under classification datasets, Iris, Breast Cancer Wisconsin and Wine Recognitiondatasets are used. Water Treatment Plant and Libras Movement datasets are used as clusteringdatasets. In classification datasets, the class labels in the data set are used to measure the per-formance. For clustering datasets, Rand index and Jaccard index are used to evaluate clusteringresults.The new set distance based validation indexes are tested on both synthetic and real datasets.Datasets with three, four, five and six clusters are generated by using Gaussian distributions. Theabove mentioned real datasets, Iris, Breast Cancer Wisconsin and Wine Recognition are also used toevaluate the performance of set distance based validation indexes. The result (number of clusters)obtained from the set distance based validation indexes are compared with those obtained from [50]to demonstrate efficiency of set distance based validation indexes and how it considers the structureof underlying data unlike others, [50] in particular.

Name thesis:degree_name

MS

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Engineering and Applied Science: Computer Science

Grantor dc:publisher

University of Cincinnati

Year dc:date

2012

Author dc:creator

• Pangaonkar, Manali

Contributors dc:contributor

• Ralescu, Anca

• Computer Science
• Fuzzy Clustering
• Cluster Validation
• Compactness
• Separation
• Set Distance
• Cluster Comparison

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=ucin1353342433

OAI identifier oai:identifier

oai:etd.ohiolink.edu:ucin1353342433