T-mixture Models And Extended Locality Preserving Projections For Clustering And Dimensionality Reduction

Pattern recognition, as an interdisciplinary subject, has got great development in the past few decades. It has become not only the pursuit of researchers but also the interests of governments and organizations. The National Defenses, departments of public safety and industrial communities of many countries/ regions have invested a large amount of money on the research of pattern recognition techniques. The development of pattern recognition will greatly influence the progress of science and technology, national defence, public safety, industrial manufacture and the life of people.Based on the statistics theory and graph spectrum methods, this disserta,-tion mainly investigates these two aspects in pattern recognition — clustering and dimensionality reduction: (i) the in-depth study of estimation techniques of parameters of t-mixture models in clustering, where we take image segmentation into account; and (ii) the research on locality preserving projections and its extension of two-dimensional methods and that of linear mixtures in dimensionality reduction, during which we take image recognition into account. The main contributions of this dissertation are outlined as follows.Firstly, we investigate the estimation techniques of parameters of multivari-ate t-density mixtures and construct SMEM algorithm for them, t-density has heavier tail with good property of anti-noising. Modeling mixtures of multivariate t-densities is usually adopted as a standard and robust alternative to Gaussian mixtures. Expectation-maximization (EM) algorithm is a standard algorithm for solving the parameters of mixture models. However, EM often converges to local optimum rather than global one. We take the idea of allowing the parameters to jump out of local optimum and looking for global one by means of splitting...