The Discriminate Analysis and Dimension Reduction Methods of High Dimension

Lan Fu^1,2

¹Statistics School, Jiangxi University of Finance of Economics, Nanchang, China.
²Research Center of Applied Statistics, Jiangxi University of Finance of Economics, Nanchang, China.

DOI: 10.4236/jss.2015.33002                

Abstract

Statistical methods have been getting constant development since 1970s. However, the statistical methods of the big data are no longer restricted with these methods which are listed in the textbook. This paper mainly demonstrates the Discrimination Analysis of Multivariate Statistical Analysis, Linear Dimensionality Reduction and Nonlinear Dimensionality Reduction Method under the circumstances of the wide range of applications of high-dimensional data. This paper includes three parts. To begin with, the paper illustrates a developing trend from the data to the high-dimensional. Meanwhile, it analyzes the impacts of the high-dimensional data on discriminate analysis methods. The second part represents the necessity of the dimensionality reduction studies in the era of the high-dimensional data overflowing. Then, the paper focuses on introducing the main methods of the linear dimensionality reduction. In addition, this paper covers the basic idea of the nonlinear dimensionality reduction. Moreover, it systematically analyzes the breakthrough of the traditional methods. Furthermore, it chronologically demonstrates the developing trend of the dimensionality reduction method. The final part shows a comprehensive and systematic conclusion to the whole essay and describes a developing prospect of the dimension reduction methods in the future. The purpose of this essay is to design a framework of a performance system which is subject to the characteristics of China High-tech enterprises. It based on the analysing the principles and significance of the performance system of High-tech enterprises. The framework will promote the standardize management of High-tech enterprises of China.

Keywords

High-Dimensional Data, Method of Dimensionality Reduction, Discriminant Analysis, Linear Dimensionality Reduction, Manifold Structure

Conflicts of Interest

The authors declare no conflicts of interest.

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