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

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.