Research On Dimensionality Reduction Algorithms And Applications

With the rapid development of modern science and technology, data with high-dimensional have been emerging in many kinds of fields, such as computer vision, machine learning, bioinformatics and astronomy. The high-dimensional data not only makes people understand hardly, but also makes traditional machine learning and data mining techniques less effective. Dimensionality reduction has become an important means of dealing with the problem of high dimensional data. Although there have been a great deal of work done in this filed, there are still some challenging problems on the field of linear and nonlinear manifold learning, such as small sample size problem, out of sample problem and classification problem. In2000, three papers that studied the dimension reduction issue based on the perspectives of neuroscience and computer science respectively, which further accelerate the research of this field, and promote the manifold learning methods for dimension reduction become one of the hot problems in machine learning.In this paper, we developed from dimensionality reduction algorithm and its ap-plication, study the linear dimensionality reduction algorithm and manifold learning algorithms. In our work, a new unsupervised dimensionality reduction algorithm is proposed. The main work of this thesis can be summarized as follows:(1) We are discussed the traditional linear dimensionality reduction algorithms and the manifold learning algorithm, and both of the merits and the disadvantages are compared in this thesis.(2) Experiments on simulation data sets further demonstrated the differences among all kinds of dimensionality reduction algorithms, and we compare computational rate and memory requirement of different algorithms, respectively.(3) A new unsupervised dimensionality reduction algorithms is proposed, i.e. Ro-bust Dimensionality Reduction with Local and Global Structure (RLGS), RLGS can exploit the manifold structure of high-dimensional data adaptively, and being robust to the choice of parameters. Different from the traditional manifold learn-ing algorithms, the recognition performance of RLGS is free of the choice of the nearest neighbors. Face recognition experiments on three public face databases demonstrated the effectiveness of RLGS.