Learning With $\ell ^{1}$ -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 ??¹-graph, in which the vertices involve all the samples and the ingoing edge weights to each vertex describe its ??¹-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 ??¹-graphs. Compared with the conventional k -nearest-neighbor graph and ??-ball graph, the ??¹-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 ??¹-graph over those classic graphs in data clustering, subspace learning, and semi-supervised learning tasks.