Sparse subspace clustering

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Sparse subspace clustering (2009)

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by Ehsan Elhamifar , René Vidal

Venue:	In CVPR
Citations:	239 - 14 self

BibTeX

@INPROCEEDINGS{Elhamifar09sparsesubspace,
    author = {Ehsan Elhamifar and René Vidal},
    title = {Sparse subspace clustering},
    booktitle = {In CVPR},
    year = {2009}
}

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Abstract

We propose a method based on sparse representation (SR) to cluster data drawn from multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all other data points. In general, finding such a SR is NP hard. Our key contribution is to show that, under mild assumptions, the SR can be obtained ’exactly ’ by using ℓ1 optimization. The segmentation of the data is obtained by applying spectral clustering to a similarity matrix built from this SR. Our method can handle noise, outliers as well as missing data. We apply our subspace clustering algorithm to the problem of segmenting multiple motions in video. Experiments on 167 video sequences show that our approach significantly outperforms state-of-the-art methods. 1.

Keyphrases

sparse subspace data point spectral clustering video sequence high-dimensional space mild assumption multiple motion sparse representation state-of-the-art method similarity matrix affine subspace multiple low-dimensional linear key contribution

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