基于仿射子空间稀疏表示的半监督分类

Abstract

Graph-based semi-supervised classification is one of the hottest research areas in machine learning and data mining. These methods usually model an entire dataset as a graph, then utilize the structure information extracted by the graph to help with the classification of unlabeled data. Generally speaking, the performance of graph-based semi-supervised classification methods highly depends on the constructed graphs. In this paper, we propose a new kind of graph construction method based on affine subspace sparse representation. The proposed sparse coding method minimizes the construction error of the input signal, considering three constraints: (1) the input signal being approximately reconstructed by the affine combination of the dictionary; (2) the nonnegativity constraint of the reconstruction coefficients; (3) the sparsity constraint of the reconstruction coefficients. Based on the constraints, we present the ι 0-norm constrained optimization problem for sparse coding; then, we propose the algorithm to solve the problem and further construct the ι 0-graph of data. Finally, under the manifold regularization framework, we propose a new kind of semi-supervised classification method by introducing the regularization term that measures the structure preserving error of the ι 0-graph. The proposed semi-supervised classification method has an explicit multiclass classification function and inherits the strong discriminative information from sparse representation. As a result, it has efficient and effective classification ability. Experimental results on artificial and real-world datasets are provided to show the effectiveness of the proposed method.