Global Optimization of Finite Mixture Models

The Expectation-Maximization (EM) algorithm is a popular and convenient tool for the estimation of Gaussian mixture models and its natural extension, model-based clustering. However, while the algorithm is convenient to implement and numerically very stable, it only produces solutions that are locally optimal…


1 Introduction
1.1 Background
1.2 Contributions of this Dissertation
2 Mathematical Background
2.1 Choosing the Optimal Number of Mixture Components
2.2 Finite Mixture Models
2.3 Model-Based Clustering
2.4 The Expectation-Maximization Algorithm
3 New Global Optimization Algorithms for Model-Based Clustering
3.1 Motivation
3.2 Global Optimization Methods
3.2.1 The Cross-Entropy Method Original CE Mixture Model Algorithm
3.2.2 Challenges of the CE Mixture Model Algorithm
3.2.3 Two New CE Mixture Model Algorithms CE-EM algorithm CE-CD Algorithm
3.2.4 Model Reference Adaptive Search
3.2.5 Two New MRAS mixture model algorithms MRAS-EM Algorithm MRAS-CD Algorithm
3.3 Numerical Experiments
3.3.1 Preventing Degenerate Clusters
3.3.2 Initial Parameters
3.3.3 Numerical Experiment 1
3.3.4 Numerical Experiment 2
3.3.5 Clustering of Survey Responses
3.3.6 A Fair Comparison
3.3.7 Does the Global Optimum “Matter”?
3.4 Discussion
4 Global Convergence of Gaussian Mixture Models with MRAS
4.1 Motivation
4.2 Model Reference Adaptive Search
4.2.1 Global Convergence of MRAS
4.3 MRAS algorithm for Gaussian Mixture Models
4.3.1 Preventing Degenerate Solutions
4.3.2 Proving Global Convergence of the MRAS Mixture Model Al-gorithm
4.4 Discussion
5 Landscape Analysis of Finite Mixture Models…..

Author: Heath, Jeffrey Wells

Source: University of Maryland

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