An Improvement Algorithm of Principal Component Analysis

Abstract

The conventional method of principal component analysis (PCA) is reducing data dimensions directly from m to k (k<m) by one step. The lost information of PCA is holistically determined by the k. To reduce the lost information in the case of k is determined, we decrease the dimensions of the data from m to k by n(1≤n≤(m-k))steps. This new PCA method is called multi-step PCA (MPCA). The algorithm of MPCA is shown in the article. Two linear Neural Networks based on the PCA or MPCA is analyzed. Compared the PCA with MPCA and compared the numeric algorithm with Neural Networks, we find that the correct classification capability of MPCA is some better than the PCA and the correct classification capability o f Neural Networks is some better than the numeric algorithm.