Subspace learning in minimax detection

We consider the problem where a large known library of L alternatives is available and we wish to maximize the detection power in a worst case scenario. The considered minimax detection approach relies on a GLR test allied to a sparsity constraint. This approach conditions the optimization of the target subspaces, in number r ≪ L. While the exact solution of the minimax optimization problem can be found for r = 1, the problem for r > 1 is more intricate and we propose two algorithms aimed at finding an approximate solution. The proposed algorithms are illustrated on a face database and on hyperspectral data and are shown to improve on the r = 1 case.