Robust Subspace Clustering via Latent Smooth Representation Clustering
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Robust Subspace Clustering via Latent Smooth Representation Clustering Xiaobo Xiao1 · Lai Wei1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Subspace clustering · Smooth representation · Sparse representation · Latent subspace
1 Introduction The high-dimensional data samples in computer vision and pattern recognition applications are usually viewed as lying in/near several low-dimensional subspaces [1, 2]. Subspace clustering algorithms attempt to partition the high-dimensional data samples into the corresponding subspaces where they are drawn from [3–8]. Among the existing subspace clustering methods, methods based on spectral clustering [3, 5, 9, 10] have attracted lots of interests due to their prominent performances in many machine learning and patter recognition tasks. * Lai Wei [email protected] Xiaobo Xiao [email protected] 1
Department of Computer Science, Shanghai Maritime University, Haigang Avenue 1550, Shanghai 201306, China
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X. Xiao, L. Wei
Typically, spectral clustering-based algorithms divide the subspace clustering processes into three steps: (1) using the given data samples to compute a reconstructive coefficient matrix 𝐙 , (2) applying the obtained coefficient matrix 𝐙 to construct an affinity graph 𝐖 , (3) adopting a kind of spectral clustering (e.g. Normalize cuts (N-cut) [11] to produce the clustering results. It is known that the performance of a spectral clustering-based method greatly depends on whether the computed reconstructive coefficient matrix 𝐙 could reveal the intrinsic structure of a data set.
1.1 Related Work As a result, the main efforts of spectral clustering-based methods concentrate on the construction of coefficient matrices [5, 6, 12, 13]. The two most representative algorithms of spectral clustering-based algorithms are sparse subspace clustering (SSC) [3, 4] and lowrank representation (LRR) [5, 6]. A large amount of subsequent res
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