Face recognition is a very important topic in data science and biometric security research areas. It has multiple applications in military, finance, and retail, to name a few. In this paper, the sparse PCA will be implemented by using the Proximal Gradient method (or ISTA method) and the Runge Kutta numerical method(s). Then, the combination of the sparse PCA with the k nearest-neighbor method or with the kernel ridge regression method will be employed to solve the face recognition problem. Experimental results illustrate that the accuracy of the combination of the sparse PCA method (using the Proximal Gradient Method and the Runge Kutta numerical method(s)) and one specific classification system is better than the accuracy of the combination of the PCA method and one specific classification system. Moreover, we recognize that the process computing the sparse PCA algorithm using the Runge Kutta numerical method(s) is always faster than the process computing the sparse PCA algorithm using the Proximal Gradient method (or ISTA method).