A DC Programming Approach for Sparse Eigenvalue Problem

We investigate the sparse eigenvalue problem which arises in various fields such as machine learning and statistics. Unlike standard approaches relying on approximation of the l0norm, we work with an equivalent reformulation of the problem at hand as a DC program. Our starting point is the eigenvalue problem to which a constraint for sparsity requirement is added. The obtained problem is first formulated as a mixed integer program, and exact penalty techniques are used to equivalently transform the resulting problem into a DC program, whose solution is assumed by a customized DCA. Computational results for sparse principal component analysis are reported, which show the usefulness of our approach that compares favourably with some related standard methods using approximation of the l0-norm.