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 NeuralNetworks, 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.

Learning Machine Based on Optimized Dimensionality Reduction Algorithm for Fault Diagnosis of Rotor Broken Bars in Induction Machine

“…Suppose that observations for 𝑚 features form an n×m matrix, signe as X=(xij) i=1, 2, .., n, j= 1, 2…, m. The PCA is processed as follows [30].…”

“…where, X'=[x1, x2, …, xk] T is the reconstruction of the observed data and the dimensions of the data are reduced from m to k(k<m), the principle of PCA is illustrated in Figure 14. The method of determining the number (k) of the principal components is the key to the application of the PCA [30].…”