Sparse Principal Component Analysis via Fractional Function Regularity

Abstract

In this paper, we describe a novel approach to sparse principal component analysis (SPCA) via a nonconvex sparsity-inducing fraction penalty function SPCA (FP-SPCA). Firstly, SPCA is reformulated as a fraction penalty regression problem model. Secondly, an algorithm corresponding to the model is proposed and the convergence of the algorithm is guaranteed. Finally, numerical experiments were carried out on a synthetic data set, and the experimental results show that the FP-SPCA method is more adaptable and has a better performance in the tradeoff between sparsity and explainable variance than SPCA.