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Multivariate normal finite mixture clustering : an approach to distributive computing and overcoming local optimum solutions using stratified datasets / Eric W. Taylor

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Identifier	Thesis 1792
Author	Taylor, Eric W., 1949-
Title	Multivariate normal finite mixture clustering : an approach to distributive computing and overcoming local optimum solutions using stratified datasets / Eric W. Taylor
Publisher	Central Connecticut State University
Date	2005
Resource Type	Master's Thesis
Notes	Data mining, at times, involves applying cluster analysis to large databases containing multivariate normal parameters. Most finite mixture clustering methods use the expectation-maximum (EM) algorithm to find solutions to the unknown parameters, p and. The EM algorithm, depending on the amount of data and number of parameters, requires considerable computing resources in terms of memory and time - both of which may be unattainable and/or unacceptable. The EM algorithm also reaches a local optimum with each pass through the database. A recommended practice to assure complete analysis of an EM solution is to provide different starting points within the data and/or alter the stopping criteria within the algorithm itself. In essence, the analyst should try several iterations over the complete database to observe the sensitivity (robustness) of the derived solutions. Given the size of the original database, this practice might also be unattainable or unacceptable to the analyst. This paper looks at overcoming the challenges of large databases and/or local optimum solutions by partitioning the large database into several stratified datasets, performing the finite mixture clustering methods within each dataset and consolidating the results between datasets. This consolidation is accomplished by identifying redundant clusters between datasets using Hotelling's T2 statistic and merging those identified using Bayes' Theorem. Using a recursive application of Bayes' Theorem across the stratified datasets, a posterior estimate for the multivariate normal parameters can be obtained. This methodology provides an alternative way to analyze large databases and provide the EM algorithm with several starting points (each stratified dataset accomplishes this). This strategy was applied to 3 databases with known clusters/groupings. Each database was subjected to the following steps: 1. Partition the database into K stratified datasets - usually with an equal number of observations per dataset and limiting the number of observations per dataset to 900. 2. Perform finite mixture clustering analysis within each of the K datasets and determine the covariance structure and number of clusters, C, that best describe all of the K datasets. 3. Obtain the maximum likelihood estimates for the MVN parameters for each cluster within each dataset. 4. Identify redundant clusters between datasets by comparing the difference between the mean vectors using Hotelling's T2. 5. Combine redundant clusters using a recursive application of Bayes' Theorem. 6. Obtain the posterior statistics - and - for each cluster C where n represents the number of observations within cluster C and represents the probability of an observation belonging to cluster C. 7. Perform the finite mixture cluster analysis on the database proper (i.e., no stratified subsets) in one step. 8. Compare the results of 6 and 7 to determine equivalency. The results obtained by analyzing the stratified datasets of the original database proved to be as good as those obtained by processing the original database in one step. The stratified datasets can represent performing the analysis via distributive computing. The stratified datasets also provide different starts for the EM algorithm and provide several opportunities to evaluate the local optimums between datasets. How do you eat an elephant? One bite at a time.
Subject	Multivariate analysis Stratified sets Bayesian statistical decision theory
Department	Department of Mathematical Sciences
Advisor	Larose, Daniel T.
Type	Text
Digital Format	application/pdf
Language	eng
OCLC number	61679300
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Multivariate normal finite mixture clustering : an approach to distributive computing and overcoming local optimum solutions using stratified datasets / Eric W. Taylor

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