Automatic Sparse PCA for High-Dimensional Data
Kazuyoshi Yata, Makoto Aoshima · Statistica Sinica · 2023
Sparse principal component analysis (SPCA) methods have proven to efficiently analyze high-dimensional data.Among them, threshold-based SPCA (TSPCA) is computationally more cost-effective than regularized SPCA, based on L1 penalties.We herein present an investigation of the efficacy of TSPCA for high-dimensional data settings and illustrate that, for a suitable threshold value, TSPCA achieves satisfactory performance for high-dimensional data.Thus, the performance of the TSPCA depends heavily on the selected threshold value.To this end, we propose a novel thresholding estimator to obtain the principal component (PC) directions using a customized noise-reduction methodology.The proposed technique is consistent under mild conditions, unaffected by threshold values, and therefore yields more accurate results quickly at a lower computational cost.Furthermore, we explore the shrinkage PC directions and their application in clustering high-dimensional data.Finally, we evaluate the performance of the estimated shrinkage PC directions in actual data analyses.