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CVPR
2009
IEEE

Sparse Subspace Clustering

14 years 10 months ago
Sparse Subspace Clustering
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 !1 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.
Ehsan Elhamifar, René Vidal
Added 09 May 2009
Updated 10 Dec 2009
Type Conference
Year 2009
Where CVPR
Authors Ehsan Elhamifar, René Vidal
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