Grouped variable selection for generalized eigenvalue problems

Many problems require the selection of a subset variables from full set optimization variables. The computational complexity an exhaustive search over all possible subsets is, however, prohibitively expensive, necessitating more efficient but potentially suboptimal strategies. We focus on sparse variable for generalized Rayleigh quotient and eigenvalue problems. Such often arise in signal processing field, e.g., design optimal data-driven filters. extend generalize existing work convex optimization-based using semidefinite relaxations toward group-sparse ℓ1,∞-norm. This group-sparsity allows, instance, to perform sensor spatio-temporal (instead purely spatial) filters, select based multiple eigenvectors instead only dominant one. Furthermore, we extensively compare our method state-of-the-art methods filter simulated network setting. results show both proposed algorithm backward greedy best approximate solution. However, has specific failure cases, particular ill-conditioned covariance matrices. As such, is most robust currently available