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Robust Subspace Clustering via Latent Smooth Representation Clustering

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Abstract

Subspace clustering aims to group high-dimensional data samples into several subspaces which they were generated. Among the existing subspace clustering methods, spectral clustering-based algorithms have attracted considerable attentions because of their predominant performances shown in many subspace clustering applications. In this paper, we proposed to apply smooth representation clustering (SMR) to the reconstruction coefficient vectors which were obtained by sparse subspace clustering (SSC). Because the reconstruction coefficient vectors could be regarded as a kind of good representations of original data samples, the proposed method could be considered as a SMR performed in a latent subspace found by SSC and hoped to achieve better performances. For solving the proposed latent smooth representation algorithm (LSMR), we presented an optimization method and also discussed the relationships between LSMR with some related algorithms. Finally, experiments conducted on several famous databases demonstrate that the proposed algorithm dominates the related algorithms.

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Notes

  1. Namely, if \({\Vert{\mathbf{x}}_{i} - {\mathbf{x}}_{j}\Vert}_{2}^{2}\to 0\), we have \({\Vert{\mathbf{c}}_{i} - {\mathbf{c}}_{j}\Vert}_{2}^{2}\to 0.\)

  2. In our experiments, \(\varepsilon =0.01.\)

  3. It also contains a sequence of 5 motions which is called “dancing”. We neglect this sub-database in our experiments.

  4. The choices of PCA dimension is followed the suggestion in [5].

  5. Segmentation error = 1 − segmentation accuracy.

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Authors and Affiliations

  1. Department of Computer Science, Shanghai Maritime University, Haigang Avenue 1550, Shanghai, 201306, China

    Xiaobo Xiao & Lai Wei

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  1. Xiaobo Xiao
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Correspondence to Lai Wei.

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Xiao, X., Wei, L. Robust Subspace Clustering via Latent Smooth Representation Clustering. Neural Process Lett 52, 1317–1337 (2020). https://doi.org/10.1007/s11063-020-10306-8

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