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.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-yang18c, title = {Dimensionality Reduced $\ell^{0}$-Sparse Subspace Clustering}, author = {Yang, Yingzhen}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {2065--2074}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/yang18c/yang18c.pdf}, url = {https://proceedings.mlr.press/v84/yang18c.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Dimensionality Reduced $\ell^{0}$-Sparse Subspace Clustering %A Yingzhen Yang %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-yang18c %I PMLR %P 2065--2074 %U https://proceedings.mlr.press/v84/yang18c.html %V 84 %X 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.
APA
Yang, Y.. (2018). Dimensionality Reduced $\ell^{0}$-Sparse Subspace Clustering. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:2065-2074 Available from https://proceedings.mlr.press/v84/yang18c.html.

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