Sparse Subspace Clustering with Entropy-Norm

Liang Bai, Jiye Liang
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:561-568, 2020.

Abstract

In this paper, we provide an explicit theoretical connection between Sparse subspace clustering (SSC) and spectral clustering (SC) from the perspective of learning a data similarity matrix. We show that spectral clustering with Gaussian kernel can be viewed as sparse subspace clustering with entropy-norm (SSC+E). Compared to SSC, SSC+E can obtain an analytical, symmetrical, nonnegative and nonlinearly-representational similarity matrix. Besides, SSC+E makes use of Gaussian kernel to compute the sparse similarity matrix of objects, which can avoid the complex computation of the sparse optimization program of SSC. Finally, we provide the experimental analysis to compare the efficiency and effectiveness of sparse subspace clustering and spectral clustering on ten benchmark data sets. The theoretical and experimental analysis can well help users for the selection of high-dimensional data clustering algorithms.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-bai20b, title = {Sparse Subspace Clustering with Entropy-Norm}, author = {Bai, Liang and Liang, Jiye}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {561--568}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/bai20b/bai20b.pdf}, url = {http://proceedings.mlr.press/v119/bai20b.html}, abstract = {In this paper, we provide an explicit theoretical connection between Sparse subspace clustering (SSC) and spectral clustering (SC) from the perspective of learning a data similarity matrix. We show that spectral clustering with Gaussian kernel can be viewed as sparse subspace clustering with entropy-norm (SSC+E). Compared to SSC, SSC+E can obtain an analytical, symmetrical, nonnegative and nonlinearly-representational similarity matrix. Besides, SSC+E makes use of Gaussian kernel to compute the sparse similarity matrix of objects, which can avoid the complex computation of the sparse optimization program of SSC. Finally, we provide the experimental analysis to compare the efficiency and effectiveness of sparse subspace clustering and spectral clustering on ten benchmark data sets. The theoretical and experimental analysis can well help users for the selection of high-dimensional data clustering algorithms.} }
Endnote
%0 Conference Paper %T Sparse Subspace Clustering with Entropy-Norm %A Liang Bai %A Jiye Liang %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-bai20b %I PMLR %P 561--568 %U http://proceedings.mlr.press/v119/bai20b.html %V 119 %X In this paper, we provide an explicit theoretical connection between Sparse subspace clustering (SSC) and spectral clustering (SC) from the perspective of learning a data similarity matrix. We show that spectral clustering with Gaussian kernel can be viewed as sparse subspace clustering with entropy-norm (SSC+E). Compared to SSC, SSC+E can obtain an analytical, symmetrical, nonnegative and nonlinearly-representational similarity matrix. Besides, SSC+E makes use of Gaussian kernel to compute the sparse similarity matrix of objects, which can avoid the complex computation of the sparse optimization program of SSC. Finally, we provide the experimental analysis to compare the efficiency and effectiveness of sparse subspace clustering and spectral clustering on ten benchmark data sets. The theoretical and experimental analysis can well help users for the selection of high-dimensional data clustering algorithms.
APA
Bai, L. & Liang, J.. (2020). Sparse Subspace Clustering with Entropy-Norm. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:561-568 Available from http://proceedings.mlr.press/v119/bai20b.html.

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