标题： 基于龙格-库塔数值方法的新型稀疏PCA方法在人脸识别中的应用 显示英文标题

标题： Novel sparse PCA method via Runge Kutta numerical method(s) for face recognition

摘要： 人脸识别是数据科学和生物特征安全领域的重要课题，其应用涵盖军事、金融和零售等行业。 本文探讨了使用近端梯度法（也称为ISTA）和龙格-库塔数值方法实现稀疏主成分分析（PCA）的方法。 为了解决人脸识别问题，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，通过近端梯度法或龙格-库塔数值方法求解的稀疏PCA与分类系统结合，其准确性高于标准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端梯度法。 显示英文摘要

摘要： 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.