Robust sparse smooth principal component analysis for face reconstruction and recognition

Existing Robust Sparse Principal Component Analysis (RSPCA) does not incorporate the two-dimensional spatial structure information of images. To address this issue, we introduce a smooth constraint that characterizes the spatial structure information of images into conventional RSPCA, generating a novel algorithm called Robust Sparse Smooth Principal Component Analysis (RSSPCA). The proposed RSSPCA achieves three key objectives simultaneously: robustness through L1-norm optimization, sparsity for feature selection, and smoothness for preserving spatial relationships. Within the Minorization-Maximization (MM) framework, an iterative process is designed to solve the RSSPCA optimization problem, ensuring that a locally optimal solution is achieved. To evaluate the face reconstruction and recognition performance of the proposed algorithm, we conducted comprehensive experiments on six benchmark face databases. Experimental results demonstrate that incorporating robustness and smoothness improves reconstruction performance, while incorporating sparsity and smoothness improves classification performance. Consequently, the proposed RSSPCA algorithm generally outperforms existing algorithms in face reconstruction and recognition. Additionally, visualization of the generalized eigenfaces provides intuitive insights into how sparse and smooth constraints influence the feature extraction process. The data and source code from this study have been made publicly available on the GitHub repository: https://github.com/yuzhounh/RSSPCA.