Alobaidan, K. (2014). Generalizing mutual clusters: A measure of cluster compactness. Retrieved from http://scholar.acadiau.ca/islandora/object/theses:329

Generalizing mutual clusters: A measure of cluster compactness

Author

Alobaidan, Khatoon

Call Number

LE3 .A278 2014

Date

2014

Supervisor

Chipman, Hugh

Degree Grantor

Acadia University

Degree Name

Master of Science

Degree Level

Masters

Discipline

Mathematics and Statistics

Affiliation

Mathematics & Statistics

Abstract

Previous work (Chipman & Tibshirani, 2006) introduced the idea of a mutual cluster (MC) as a group of points that are closer to each other than to any other outside points. An MC can be characterized in terms of its diameter (the maximum distance within a group) and the nearest outside distance (distance to points outside the group). In this thesis, we study the properties of a mutual cluster and generalize the original de nition of an MC. New computational methods are developed. We start by relaxing the de nition of an MC, using the \decision ratio" ( ), the ratio of the nearest outside distance to the diameter. The decision ratio will give information about the separation between clusters. A simpli cation of the mutual cluster algorithm, classic.MC, is developed to work with a particular group of points, rather than as part of a bottom-up hierarchical clustering. We then propose a new technique to de ne a mutual cluster. This technique is based on quantiles and data depth. It checks whether a given group of points is an MC, and calculates a modi ed decision ratio ( ). This method was introduced to be less sensitive to sample size and outliers. Illustrative examples are used to compare both methods. Lastly, we conduct a designed experiment to study the e ects of: sample size (n), dimension (p) and the separation between cluster means ( ), and to evaluate the performance of the decision ratios & .

Rights

The author grants permission to the University Librarian at Acadia University to reproduce, loan or distribute copies of my thesis in microform, paper or electronic formats on a non-profit basis. The author retains the copyright of the thesis.