Discriminative Sparse Coding on Multi-Manifold for Data Representation and Classification

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.