Year: 2025
Type: article
Abstract: This paper establishes the theoretical foundations of an alternating optimization scheme for penalized sparse principal component analysis (PCA) focusing on variance maximization. We provide a theoretical foundation for the optimality of solutions derived from this widely used algorithm, addressing a gap in the current literature where empirical results often lack theoretical support. We show the algorithm’s success when the dataset’s covariance matrix is positive definite. Additionally, we characterize sparsity-inducing penalties and examine the use of various ones, including the $$ \ell _1$$ ℓ 1 -norm, SCAD, and $$\ell _0$$ ℓ 0 -norm. We conduct numerical experiments to evaluate standard metrics, such as explained variance, number of iterations, and computational time.
Source: Optimization and Engineering
Institutions: Radboud University Nijmegen, Tilburg University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4414345790