Data Dimension Reduction Method Study Based On Manifold Learning

With the rapid development of modern science and technology, more data with high dimension and complex structure occurs very quickly. High dimension not only makes the data hard to understand, and makes traditional machine learning and data mining techniques less effective. Dimension reduction which is an important means of feature extraction and plays an important role in the pattern recognition system, is one of the important techniques to deal with high-dimensional data. Even though there have been many research work done in this field, there are still challenging problems to uncover the linear and nonlinear structure information in data. In 2000, three articles published on Science magazine studied the dimension reduction issue from 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.This thesis is developed from manifold learning algorithm and its application, studies the problem from the both the unsupervised, supervised and tensor representation perspectives. The main contributions of this dissertation can besummarized as follows:Firstly, Since locality preserving projections is designed for preserving local structure, it is likely that a nearest neighbor search in the low dimensional space will yield similar results to that in the high dimensional space. This makes for clustering. Two dimensional locality preserving projections algorithm have no need to transform images into 1D image vectors, so the structural information residing in original images is preserved. In this paper, we took small target detection of infrared images as a kind of anomaly detection. A infrared target detection method based on two dimensional locality preserving projections was designed, and the experimental results show that this method is fast and has low false alarm rate. Furthermore, the locality preserving projections, Laplacianface and two dimensional locality preserving projections were compared,and some useful results have been obtained.Secondly, as far as matrix data, such as images, are concerned, they are often vectorized for locality sensitive discriminant analysis algorithm to find the intrinsic manifold structure. While the dimension of matrix data is usually very high, locality sensitive discriminant analysis cannot be implemented because of the singularity of matrix. A method called two dimensional locality sensitive discriminant analysis is proposed, which is based directly on 2D image matrices, can overcome the singularity problem and can utilize the spatial information among pixels more effectively. It is a supervised linear dimension reduction with tensor representation. The experimental results show that the two dimensional locality sensitive discriminant analysis has higher recognition rate than that of locality sensitive discriminant analysis in the face recognition.