Application Of Principal Component Analysis In Complex Network Community Discovery

Complex network community detection is a hot research topic in recent years, has great research value in the research of computer network and social computing. The main process of complex network research in this article is through the original information analysis in complex network node and edge relationship, get the topological structure of the whole network, analyze the network characteristics by mathematical method,find the key characteristics that can reflect of network structure,accurate detected the community in the networks, and sort them according to the sizes.This article make a brief introduction to some important network model parameters and several basic complex network and the commonly used methods of complex community discovery, several mainstream community discovery algorithms were compared, and based spectual analysis method and eigenvalue analysis method provided a method based on principal component analysis to reveal community structure, and through the comparison of the experimental data prove the accuracy of result, explain the basic theory of this transformation, meanwhile illustrate the relationship between community and anticomunity structure and the eigenvalue.And introduce the relationship between covariance matrix and correlation matrix. Finally achieve purposes that discovered community from perspective of dimension reduction.This article also discussed and proved that the advantage of rescaled transformation in dealing with the heterogeneous network,and explained it with the experiment data.This paper focuses on the following several contents:(1) Analyse The principal component analysis method and its derived covariance matrix and the ordinary laplace matrix,did experiments on community discovery and analyzes their performance.(2) The relationship between the eigenvalue spectrum and community structure is described in detail.(3) showing good performance through analyse covariance matrix, eigengap in community detected, especially for the chosen of the important eigenvector, and affect in the accuracy of community detected.(4) proposed the rescaling transformation method, discuss the significant of it in solving the heterogeneous complex network community discovery.