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https://hdl.handle.net/2142/82057
Description
Title
Local Optima in K-Means Clustering
Author(s)
Steinley, Douglas Lee
Issue Date
2004
Doctoral Committee Chair(s)
Hubert, Lawrence J.
Department of Study
Psychology
Discipline
Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Psychology, Psychometrics
Language
eng
Abstract
"The study of the properties of local optimality in K-means clustering is pursued. In doing so, it is shown that several of the commercial software packages prove to be inadequate in their treatment of the K-means algorithm, resulting in the proposal of an alternative method based on several thousand initializations, which is imbedded in a MATLAB m-file. The further developments of this dissertation are four-fold: (a) a comprehensive cluster generation method based on distributional theory and probability is developed; (b) the properties of local optimality are related to a cluster recovery criterion to develop a test that is able to distinguish between ""good"" and ""bad"" cluster solutions; (c) a method of consensus analysis for K-means clustering is proposed and extended to within-cluster standardization; and (d) a lower bound for the K -means criterion function is derived, and based on the lower bound, another (more powerful) test is developed to determine the quality of a given cluster solution."
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