Learning With l1-Graph for Image Analysis

The graph construction procedure essentially determines the potentials of those graph-oriented learning algorithms for image analysis. In this paper, we propose a process to build the so-called directed graph, in which the vertices involve all the samples and the ingoing edge weights to each vertex describe its norm driven reconstruction from the remaining samples and the noise. Then, a series of new algorithms for various machine learning tasks, e. g., data clustering, subspace learning, and semi-supervised learning, are derived upon the graphs. Compared with the conventional-nearest-neighbor graph and epsilon-ball graph, the graph possesses the advantages: 1) greater robustness to data noise, 2) automatic sparsity, and 3) adaptive neighborhood for individual datum. Extensive experiments on three real-world datasets show the consistent superiority of graph over those classic graphs in data clustering, subspace learning, and semi-supervised learning tasks.