A Block Minorization-Maximization Algorithm for Row-Sparse Principal Component Analysis

We present a block minorization-maximization (MM) algorithm to solve the row-sparse principal component analysis (RSPCA) problem. The RSPCA problem consists of orthogonality and row-sparsity constraints. We model the decision variable as a product of a selection matrix and the matrix of principal components. This problem is solved by updating the two blocks in a cyclic manner. As the problem with respect to the selection matrix does not admit a closed-form solution, we propose to utilize the MM technique to solve this subproblem. Numerical simulations are provided to show the efficacy of the proposed algorithm.