Learning with $\ell ^{1}$-graph for image analysis
Bin Cheng, Jianchao Yang, Shuicheng Yan, Yun Fu, Thomas S. Huang · IEEE Transactions on Image Processing · 2010
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 l1-graph, in which the vertices involve all the samples and the ingoing edge weights to each vertex describe its l1-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 l1-graphs. Compared with the conventional k-nearest-neighbor graph and epsilon-ball graph, the l1-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 l1-graph over those classic graphs in data clustering, subspace learning, and semi-supervised learning tasks.