Research On Sparse Principal Component Analysis

Nowadays, the world has entered the age of the internet. In every area, people can collect a large number of various data. The processed data can be used to describe the objective entity abundantly and specifically, find the essential laws, make right judgments and take measures to improve the utilization of social resources. However, there are a lot of redundancies in the practical application. Therefore, people pay close attention to the problems of processing these data and finding the intrinsic link among them. Traditional principal component analysis method is a popular tool to reduce the dimension of data, but most of the principal components are not sparse, that is, most of the data are non-zero. Thus it is difficult to explain the specific characteristic of each principal components. Sparse principal component analysis is an extracting sparse principal components algorithm which is based on principal component analysis. However, sparse principal component analysis is a linear classification tool and cannot deal with the nonlinear problems. Hence, this paper presents sparse kernel principal component analysis method. The paper is organized as follows.1.This paper first introduces some related norm, principal component analysis, kernel principal component analysis method, alternating direction method, and the deflation methods. In addition, this article also summarizes the 7 kinds of sparse principal component analysis algorithm.2.Sparse principal component analysis wants to extract several linear combinations of the original data variables and the combinations should retain the original information as much as possible while sparse. In this paper, we consider the measured variance norms（L₂,L₁）, two sparsity-inducing norms（L₀,L₁） and different ways（constraint, penalty）, finally two kinds of SPCA optimal models are obtained. Two new sparse principal component analysis methods are obtained by combining these two models with the alternating direction method. Experiments are done on the simulation data and real data, and the validity of the algorithm is proved.3.Because the data in the life are mostly nonlinear, so this paper is based on the idea of promoting principal component analysis to kernel principal component analysis. Then sparse principal components and kernel functions are combined to obtain a sparse kernel principal component analysis algorithm. The experimental results conducted on the consumption status data of rural households and the data of two dimensional synthetic samples show that our method can effectively extract the sparse principal components of nonlinear data.