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Non-Elliptical and Fractionally-Supervised Classification

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Title: Non-Elliptical and Fractionally-Supervised Classification
Author: Vrbik, Irene
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: McNicholas, Paul
Abstract: Model-based classification uses finite mixture models to infer a group structure in data. Three species of classification include unsupervised classification (cluster- ing), semi-supervised classification (or simply classification), and supervised classification (discriminant analysis). We expound on these classical methods and present several flexible extensions. The first area we explore is finite mixtures of skewed distributions; namely, model-based clustering via skew-normal and skew- t mixture models. The algorithms used to fit these models are established and some approximations that were used in the computationally intractable E-steps are also presented. The second area of investigation involves two new ‘families’ of parsimonious mixture models. These families are constructed by imposing constraints on the decomposed component scale matrices of skew-normal and skew-t mixtures, thereby reducing the number of free parameters to be estimated. These models are tailored for skewed data but have the added capability of reverting to the symmetric Gaussian (or multivariate t) counterparts when appropriate. Finally, we introduce a generalized classification procedure, wherein any level of supervision — ranging from unsupervised to supervised — can be attained. We develop this novel approach, termed fractionally-supervised classification, using a weighted likelihood. This new method is tested on some benchmark data sets and the optimal choice of relevance weight is explored.
Date: 2014-03
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