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Research On Variational Learning Algorithm For Non-Gaussian Mixture Models

Posted on:2015-07-26Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y P LaiFull Text:PDF
GTID:1228330467963691Subject:Information security
Abstract/Summary:PDF Full Text Request
Finite probability mixture models are commonly used tools for modeling and analyzing data. Since their forms are flexible, they have been one of the most efficient tools for estimating probability density functions and commonly used tools for clustering. Finite Gaussian mixture models (GMM) are one most popular tool for estimating probability density functions, and used widely in variety of domains. However, GMM are unable to fit the nonlinear, non-Gaussian data exactly. Therefore, non-Gussian mixture models have recently attracted considerable attention. This dissertation mainly focuses on the variational learning algorithms of non-Gaussian mixture models. The main contributions of the research presented in this dissertation are summarized as follows:1. The problem of learning algorithm of finite Beta-Liouville mixture models is investigated. A variational algorithm for learning this model is proposed, which can estimate the model parameters and mixture components simultaneously. Finally, Both artificial and real-world data sets, generated from scenes classification, are experimented to verify the effectiveness of the proposed approach.2. The problem of variational learning algorithm of finite inverted Dirichlet mixture models is investigated. First, a novel extended variational approximation inference algorithm is proposed. This variational learning framework can be used to deal with the problem of variational learning difficultly of the probability mixture model. Second, a theorem with respect to the lower bound of the multivariate Log-Inverse-Beta (MLIB) function is proposed, and proved true in detail. Third, this algorithm is used to carry out the Bayesian inference of the model. Finally, both artificial and real-world data sets, generated from scenes classification, are experimented to verify the effectiveness of the proposed approach.3. The problem of learning algorithms of finite mixture models based on the Dirichlet, Beta-Liouville and generalized Dirichlet distributions are investigated, respectively. First, two different approaches are used to calculate the lower bound of the variational objective function. Second, the extended variational approximation inference algorithm is applied to carry out the Bayesian inference for these models, respectively. Third, a completely variational Bayesian expectation maximum algorithm is presented. Finally, artificial, pattern recognition and real-world data sets, generated from scenes categorization, are experimented to verify the effectiveness of the proposed approaches.
Keywords/Search Tags:non-Gaussian data, non-Gaussian mixture models, variational Bayesian learning, secnes classification
PDF Full Text Request
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