Sparse principal component analysis using bootstrap method

Abstract

Sparse principal component analysis (SPCA) gives a sparse description of the loading matrix. In order to determine the “0” values in the loading matrix, often artificial thresholds are set on the loading values. To resolve these issues, two methods are proposed in this article to calculate the confidence intervals of the loading values. The first method is based on a resampling technique, while the second method estimates the error variance of data to calculate confidence intervals of the loadings. The position and number of non-zero loadings (NNZL) for the PCs are chosen based on a hypothesis test for “0”. Both methods lead to sparse structures of PCs. The fault detection and diagnosis performance of the proposed SPCA techniques are compared with the traditional PCA and three widely used SPCA methods for the benchmark continuous stirred tank heater (CSTH) process. The outcomes indicate that the proposed approaches perform better than the traditional PCA and benchmark SPCA (i.e., AV) method in fault detection and diagnosis.