期刊
IEEE TRANSACTIONS ON IMAGE PROCESSING
卷 26, 期 6, 页码 2988-3001出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2017.2691557
关键词
Structured sparse subspace clustering; structured subspace clustering; constrained subspace clustering; subspace structured norm; cancer clustering
资金
- National Natural Science Foundation of China [61273217]
- Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China
- Key Laboratory of Machine Perception (MOE), Peking University
- National Science Foundation [1447822]
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1447822] Funding Source: National Science Foundation
Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-theart approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data using sparse or low-rank minimization techniques. In the second step, the segmentation is found by applying spectral clustering to this affinity. While this approach has led to the state-of-the-art results in many applications, it is suboptimal, because it does not exploit the fact that the affinity and the segmentation depend on each other. In this paper, we propose a joint optimization framework - Structured Sparse Subspace Clustering ((SC)-C-3) - for learning both the affinity and the segmentation. The proposed (SC)-C-3 framework is based on expressing each data point as a structured sparse linear combination of all other data points, where the structure is induced by a norm that depends on the unknown segmentation. Moreover, we extend the proposed (SC)-C-3 framework into Constrained (SC)-C-3 ((CSC)-C-3) in which available partial side-information is incorporated into the stage of learning the affinity. We show that both the structured sparse representation and the segmentation can be found via a combination of an alternating direction method of multipliers with spectral clustering. Experiments on a synthetic data set, the Extended Yale B face data set, the Hopkins 155 motion segmentation database, and three cancer data sets demonstrate the effectiveness of our approach.
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