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

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

Abstract Details

2012, MS, University of Cincinnati, Engineering and Applied Science: Computer Science.
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-means clustering algorithm and its objective function is studied along with a literature review of the speed of clustering algorithms. After careful examination, several objective functions are derived by 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 a cluster. To this end, a new measure of compactness, compactness of a fuzzy partition is presented and 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 Recognition datasets are used. Water Treatment Plant and Libras Movement datasets are used as clustering datasets. 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 clustering results. 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. The above mentioned real datasets, Iris, Breast Cancer Wisconsin and Wine Recognition are also used to evaluate 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 structure of underlying data unlike others, [50] in particular.
Anca Ralescu, Ph.D. (Committee Chair)
Kenneth Berman, Ph.D. (Committee Member)
Dan Ralescu, Ph.D. (Committee Member)
73 p.
Computer Science
Fuzzy Clustering; Cluster Validation; Compactness; Separation; Set Distance; Cluster Comparison;

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Citations

  • Pangaonkar, M. (2012). Exploratory Study of Fuzzy Clustering and Set-Distance Based Validation Indexes [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1353342433

    APA Style (7th edition)

  • Pangaonkar, Manali. Exploratory Study of Fuzzy Clustering and Set-Distance Based Validation Indexes. 2012. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1353342433.

    MLA Style (8th edition)

  • Pangaonkar, Manali. "Exploratory Study of Fuzzy Clustering and Set-Distance Based Validation Indexes." Master's thesis, University of Cincinnati, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1353342433

    Chicago Manual of Style (17th edition)

ucin1353342433
559
© 2012, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.