Abstract
In recent years, graph based subspace clustering has attracted considerable attentions in computer vision, as its capability of clustering data efficiently. However, the graph weights built by using representation coefficients are not the exact ones as the traditional definition. That is, the two steps are conducted in independent manner such that an overall optimal result cannot be guaranteed. To this end, in this paper, a novel subspace clustering via learning an adaptive graph affinity matrix is proposed, where the soft label and the representation coefficients of data are learned in an unified framework. First, the proposed method learns a robust representation for the data through least square regression, which reveals the subspace structure within data and captures various noises inside. Second, the segmentation is sought by conducting spectral clustering simultaneously. Most importantly, during the optimization process, the segmentation is utilized to iteratively enhance the block-diagonal structure of the learned representation to further assist the clustering process. Experimental results on several famous databases demonstrate that the proposed method performs better against the state-of-the-art approaches, in clustering.
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Notes
c is the number of cluster.
The entropy \(\text {H}(K)\) is defined as \(\text {H}(K)= \sum \nolimits _{y \in {K}}{- p(y)\cdot \log _2(p(y))}\) where p(y) is the probability that a sample belongs to a cluster.
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This work was supported by the National Natural Science Foundation of China Grants (61473253, 11301427, 61773130), in part by the Fundamental Research Funds for the Central Universities under No. XDJK2014B021. Ming Yin’s work was supported in part by the Guangdong Natural Science Foundation under Grant (No. 2014A030313511), in part by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China, in part by Science and Technology Planning Project of Guangdong Province (No. 2017A010101024), China, in part by Science and Technology Program of Guangzhou, China (No. 201604016086).
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Wu, Z., Yin, M., Zhou, Y. et al. Robust Spectral Subspace Clustering Based on Least Square Regression. Neural Process Lett 48, 1359–1372 (2018). https://doi.org/10.1007/s11063-017-9726-z
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DOI: https://doi.org/10.1007/s11063-017-9726-z