Internal Structure Identification of Random Process Using Principal Component Analysis

Abstract

Principal component analysis (PCA) is known to be a powerful linear technique for data set dimensionality reduction. This paper focuses on revealing the essence of PCA to interpret the data, which is to identify the internal structure of the random process from a large experimental data set. We give an explanation of the PCA procedure performed on a generated data set to demonstrate the exact meaning of the dimensionality reduction. Especially, a method is proposed to precisely determine the number of significant principal components for a random process. Then, the internal structure of the random process can be modeled by analyzing the relation between the PCA results and the original data set. This is vital in the efficient random process modeling, which is finally applied to an application in HRTF Modeling.