  Inspired by biological vision systems, the over-complete local features with
huge cardinality are increasingly used for face recognition during the last
decades. Accordingly, feature selection has become more and more important and
plays a critical role for face data description and recognition. In this paper,
we propose a trainable feature selection algorithm based on the regularized
frame for face recognition. By enforcing a sparsity penalty term on the minimum
squared error (MSE) criterion, we cast the feature selection problem into a
combinatorial sparse approximation problem, which can be solved by greedy
methods or convex relaxation methods. Moreover, based on the same frame, we
propose a sparse Ho-Kashyap (HK) procedure to obtain simultaneously the optimal
sparse solution and the corresponding margin vector of the MSE criterion. The
proposed methods are used for selecting the most informative Gabor features of
face images for recognition and the experimental results on benchmark face
databases demonstrate the effectiveness of the proposed methods.
