On The Principal Component Analysis Methods Based On Subspace Identification

Principal Component Analysis(PCA)technology,as a high-dimensional data preprocessing method,has attracted much attention and has been widely applied.With the rapid development of Information,the ability of human to obtain information has been gradually improved.The data may be characterized with larger scales,more attributes,and more complex structures.These data are often generated continuously and automatically,which are called high-dimensional data streams.Due to the need of data analysis,at present,higher requirements of the accuracy and practicability of dimensional reduction methods for high-dimensional data have been put forward.This is the motivation of this paper to study the PCA method and the incremental PCA(Incremental Principal Component Analysis,IPCA)method.In this paper,the method of subspace identification is used as a basic tool.The PCA dimensionality reduction method for high dimensional data has been studied and proposed.On the basis,a new IPCA method is proposed.The main tasks are as follows:1.The PCA method is restudied for the problem of high dimensional data dimensionality reduction.With the aid of the subspace identification method,the principal components of high dimensional data can be computed.The main idea is that a low-order single input single output discrete time dynamic system is reconstructed for a high-order single input single output discrete time dynamic system,by using the impulse corresponding of the high-order system,in order to obtain the principal components information of the high dimensional data.First,a high-order system state space model is constructed with the covariance matrix of high-dimensional data,and the impulse response output of the system is calculated.Then,select the number of the principal components.Based on the input and output data,a low-order discrete system is obtained by using the subspace identification method.And the order is equal to the number of the principal components.Finally,the eigenvalues of the low-order system matrix are calculated.By using the orthogonal projection method,the principal component scores of the high-dimensional data are obtained.The dimensional reduction is thus completed.The simulation experiments show the effectiveness of the proposed method.2.For data streams,on the base of the previous algorithm,an IPCA method based on the subspace identification method is proposed.The covariance matrix of a data stream will change when a new data is obtained.The main idea here is to reconstruct the high-order time-varying dynamic system with a low-order dynamic system,by using the impulse response sequence,so as to the principal component information of the high-dimensional data stream can be obtained.The simulation experiments show that the proposed IPCA algorithm has better denoising and compression effects on data streams.