Joint learning dictionary and discriminative features for high dimensional data

Recently, sparse representation (SR) over a redundant dictionary has become a popular way of representing the data. It has been verified as an efficient and useful tool to promote the discrimination between signals. This work develops a joint learning approach to find the low dimensional discriminative features for high dimensional data. To avoid the high computational cost of direct sparse coding on large scale input data, we first learn SR in an orthogonal projected space over a task-driven sparsifying dictionary. We then exploit the discriminative projection on SR. The whole learning process is treated as an optimization problem of trace quotient maximization, which involves an orthogonal projection on original data space, a dictionary and a discriminative projection on sparse codes. The related cost function is well defined on a product manifold of the Stiefel manifold, the Oblique manifold and the Grassmann manifold. Finally, we employ a stochastic gradient descent algorithm on the smooth product manifold to maximize the cost function. Our numerical experiments on visual recognition demonstrate the effectiveness of the proposed algorithm, in comparison with the state of the arts.