  In this paper, a novel semi-supervised dictionary learning and sparse
representation (SS-DLSR) is proposed. The proposed method benefits from the
supervisory information by learning the dictionary in a space where the
dependency between the data and class labels is maximized. This maximization is
performed using Hilbert-Schmidt independence criterion (HSIC). On the other
hand, the global distribution of the underlying manifolds were learned from the
unlabeled data by minimizing the distances between the unlabeled data and the
corresponding nearest labeled data in the space of the dictionary learned. The
proposed SS-DLSR algorithm has closed-form solutions for both the dictionary
and sparse coefficients, and therefore does not have to learn the two
iteratively and alternately as is common in the literature of the DLSR. This
makes the solution for the proposed algorithm very fast. The experiments
confirm the improvement in classification performance on benchmark datasets by
including the information from both labeled and unlabeled data, particularly
when there are many unlabeled data.
