Research On Data Dimensionality Reduction Algorithms Based On Matrix Decomposition Learning

With the information age's arrival, we always encounter massive high-dimensional data inevitably when doing researches, including image/video retrieved, pattern recognition, human gene distribution,feature cluster and so on. In normal case, we use the way of dimensionality reduction for analyzing data and making an investigation on the internal structure of data. The goal of dimensionality reduction is to find the low-dimensional manifold structure embedded in the high-dimensional data set. To investigate the vary of the internal structure of data precisely, it is essential to use mathematical method for matrix can reflect all information of the data. Two-dimensional matrix decomposition and tensor decomposition of matrix decomposition theory is an important method of artificial intelligence learning rose in recent years, it has archived remarkable success in data dimensionality reduction.In recent years, there has already developed many effectively data dimensionality reduction methods which are based on manifold learning, mainly including Principal Component Analysis (PCA), Locally Linear Embedding (LLE), Neighborhood Preserving Embedding (NPE) and so on. These typical one-dimensional reduction methods have many applications in data dimensional reduction, pattern recognition and feature extraction. The one-dimensional reduction method can only work with vectorized data which may not capture well some useful information in the original data. Moreover, high-dimensional victorized representations also suffer from the curse of dimensionality and the high computational demand. These are all problems the one-dimensional reduction method has. At the present time, scientific research workers have summarized the data dimensionality reduction theory which utilizing two-dimensional matrix decomposition and tensor decomposition based on matrix decomposition theory to solve those problems. Many effectively data dimensionality reduction methods which are based on matrix decomposition theory learning have already been proposed, mainly including Two-Dimensional Principal Component Analysis (2D-PCA), Two-Dimensional Linear Discriminant Analysis (2D-LDA), Tensor Local Discriminant Embedding (TLDE), Tensor Subspace Analysis (TSA) and so on.This paper is based on matrix decomposition theory, analyzes the existing data dimensionality reduction algorithms comprehensively and summarizes the important theory of data dimensionality reduction algorithms. It puts emphasis on NPE algorithm and proposes its improved algorithm. The following innovative works in this paper includes: (1) Combined with two algorithms of Tensor Subspace Analysis and Tensor Neighborhood Preserving Embedding, we discuss the theory of applications for dimensionality reduction based on the singular value decomposition of matrix and higher-order singular value decomposition of tensor.(2) Traditional algorithm of neighborhood preserving embedding (NPE) which has been used for dimensionality reduction need transform the original data into vectors. But the dimension of the original data are usually high, and the vectorized data also lost some useful information so that the intrinsic local geometric and topological properties of the original data could not be estimated. Then, a new two-dimensional neighborhood preserving embedding (2D-NPE) is proposed for solve the this problem, which is based directly on matrix decomposition theory learning for dimensionality reduction.