Abstract
Face recognition is a crucial topic in data science and biometric security, with applications spanning military, finance, and retail industries. This paper explores the implementation of sparse Principal Component Analysis (PCA) using the Proximal Gradient method (also known as ISTA) and the Runge-Kutta numerical methods. To address the face recognition problem, we integrate sparse PCA with either the k-nearest neighbor method or the kernel ridge regression method. Experimental results demonstrate that combining sparse PCA-solved via the Proximal Gradient method or the Runge-Kutta numerical approach-with a classification system yields higher accuracy compared to standard PCA. Additionally, we observe that the Runge-Kutta-based sparse PCA computation consistently outperforms the Proximal Gradient method in terms of speed.
Abstract (translated)
人脸识别是数据科学和生物识别安全中的一个关键议题，其应用范围涵盖了军事、金融及零售等行业。本文探讨了使用近似梯度法（又称ISTA）和龙格-库塔数值方法实现稀疏主成分分析（PCA）。为解决人脸识别问题，我们将稀疏PCA与k最近邻方法或核岭回归方法相结合。 实验结果表明，通过近似梯度法或龙格-库塔数值方法求解的稀疏PCA结合分类系统，在精度上优于标准PCA。此外，我们观察到基于龙格-库塔的稀疏PCA计算在速度方面始终优于近似梯度法。
URL
https://arxiv.org/abs/2504.01035
