Dimensionality Reduced $\ell^{0}$-Sparse Subspace Clustering


Yingzhen Yang ;
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:2065-2074, 2018.


Subspace clustering partitions the data that lie on a union of subspaces. $\ell^{0}$-Sparse Subspace Clustering ($\ell^{0}$-SSC), which belongs to the subspace clustering methods with sparsity prior, guarantees the correctness of subspace clustering under less restrictive assumptions compared to its $\ell^{1}$ counterpart such as Sparse Subspace Clustering (SSC, Elhamifar et al., 2013) with demonstrated effectiveness in practice. In this paper, we present Dimensionality Reduced $\ell^{0}$-Sparse Subspace Clustering (DR-$\ell^{0}$-SSC). DR-$\ell^{0}$-SSC first projects the data onto a lower dimensional space by linear transformation, then performs $\ell^{0}$-SSC on the dimensionality reduced data. The correctness of DR-$\ell^{0}$-SSC in terms of the subspace detection property is proved, therefore DR-$\ell^{0}$-SSC recovers the underlying subspace structure in the original data from the dimensionality reduced data. Experimental results demonstrate the effectiveness of DR-$\ell^{0}$-SSC.

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