Semi-supervised Learning by Sparse Representation

Shuicheng YAN, Huan Wang

Abstract: In this paper, we present a novel semi-supervised learning framework based on ℓ1 graph. The ℓ1 graph is motivated by that each datum can be reconstructed by the sparse linear superposition of the training data. The sparse reconstruction coefficients, used to deduce the weights of the directed ℓ1 graph, are derived by solving an ℓ1 optimization problem on sparse representation. Different from conventional graph construction processes which are generally divided into two independent steps, i.e., adjacency searching and weight selection, the graph adjacency structure as well as the graph weights of the ℓ1 graph is derived simultaneously and in a parameter-free manner. Illuminated by the validated discriminating power of sparse representation in [16], we propose a semi-supervised learning framework based on ℓ1 graph to utilize both labeled and unlabeled data for inference on a graph. Extensive experiments on semi-supervised face recognition and image classification demonstrate the superiority of our proposed semi-supervised learning framework based on ℓ1 graph over the counterparts based on traditional graphs.