Term of Award

Spring 2012

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Yingkang Hu

Committee Member 1

James Bergin

Committee Member 2

James J. Burnham

Committee Member 3

Abebayehu Tekleselassie

Abstract

The visual assessment of clustering tendency (VAT) method, which was developed by J. C. Bezdek, R. J. Hathaway and J. M. Huband uses a reordering of the rows and columns of a dissimilarity matrix; it then displays the ordered dissimilarity matrix (ODM) as a 2D gray-level image called an ordered dissimilarity image (ODI). Al- though successful in determining potential clustering structure of various data sets, the technique offers room for improvement. In this thesis, we propose a new proximity measure called the diver's distance which is defined based on concepts in graph theory. We then theoretically study the diver's distance and its properties. From the theoretical results, we develop an algorithm (ddVAT) to efficiently compute an ODM of diver's distances; its corresponding ODI proves to be more informative than the ODI obtained from VAT. Moreover, ddVAT turns out to be very efficient with linear clusters and very useful in cases where there is difficulty to satisfactorily represent cluster point representatives.

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