This paper proposes exact and approximation algorithms for Sparse PCA, improving interpretability and scalability.
problem Selecting a prespecified-size principal submatrix from a covariance matrix to maximize its largest eigenvalue.
method Proposes two exact mixed-integer SDPs and a mixed-integer linear program (MILP) for SPCA, analyzes theoretical optimality gaps, and develops approximation algorithms.
result The proposed algorithms achieve strong theoretical optimality and effective scalability, with continuous relaxations close to optimality and MILP solving small to medium-size instances.