Learning with l1-graph for image analysis

Authors:
Bin Cheng;Jianchao Yang;Shuicheng Yan;Yun Fu;Thomas S. Huang
Affiliations:
Department of Electrical and Computer Engineering, National University of Singapore, Singapore;Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL;Department of Electrical and Computer Engineering, National University of Singapore, Singapore;Department of Computer Science and Engineering, University at Buffalo, State University of New York, Buffalo, NY;Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL
Venue:
IEEE Transactions on Image Processing
Year:
2010

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Abstract

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 semisupervised learning, are derived upon the l1-graphs. Compared with the conventional -nearest-neighbor graph and -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.