Sparse PCA via hard thresholding for blind source separation

Abstract

Principal Component Analysis (PCA) is adopted in diverse areas including signal processing and machine leaning. However, the derived principal components, the linear combinations of the original variables, are hard to be interpreted in many applications especially the blind source separation. Therefore, we propose regularized PCA via hard thresholding such that the derived loadings are sparse and easier to be interpreted. The proposed method has advantages due to the adoption of hard thresholding. First, the proposed method can be implemented by linear operators and thus computational efficient even in p ≫ n or large p scenarios. Second, the threshold can be objectively selected based on statistical decision theory without domain knowledge. Moreover, simulations show the superiority of our method compared to the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -penalized method. Therefore, our approach can be a strong competitor of the existing sparse PCA.