Sparse subspace clustering

E. Elhamifar, R. Vidal
2009 2009 IEEE Conference on Computer Vision and Pattern Recognition  
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
more » ... e 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.
doi:10.1109/cvprw.2009.5206547 fatcat:3yogs2jzirhl3npbdj4i2f7rmq