  Sparse coding has been popularly used as an effective data representation
method in various applications, such as computer vision, medical imaging and
bioinformatics, etc. However, the conventional sparse coding algorithms and its
manifold regularized variants (graph sparse coding and Laplacian sparse
coding), learn the codebook and codes in a unsupervised manner and neglect the
class information available in the training set. To address this problem, in
this paper we propose a novel discriminative sparse coding method based on
multi-manifold, by learning discriminative class-conditional codebooks and
sparse codes from both data feature space and class labels. First, the entire
training set is partitioned into multiple manifolds according to the class
labels. Then, we formulate the sparse coding as a manifold-manifold matching
problem and learn class-conditional codebooks and codes to maximize the
manifold margins of different classes. Lastly, we present a data point-manifold
matching error based strategy to classify the unlabeled data point.
Experimental results on somatic mutations identification and breast tumors
classification in ultrasonic images tasks demonstrate the efficacy of the
proposed data representation-classification approach.
