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.

翻译：稀疏主成分分析（SPCA）方法已被证明能有效分析高维数据。其中，基于阈值的稀疏主成分分析（TSPCA）在计算上比基于L1惩罚的正则化SPCA更具成本效益。本文研究了TSPCA在高维数据场景中的有效性，并证明在合适的阈值下，TSPCA对高维数据能达到令人满意的性能。因此，TSPCA的性能严重依赖于所选阈值。为此，我们提出了一种新的阈值估计器，通过定制化的降噪方法获取主成分（PC）方向。所提出的技术在温和条件下具有一致性，不受阈值取值影响，从而能以更低计算成本快速获得更准确的结果。此外，我们探究了收缩PC方向及其在高维数据聚类中的应用。最后，我们在实际数据分析中评估了所估计的收缩PC方向的性能。