Unbiased Sparse Subspace Clustering by Selective Pursuit

Sparse subspace clustering (SSC) is an elegant approach for unsupervised segmentation if the data points of each cluster are located in linear subspaces. This model applies, for instance, in motion segmentation if some restrictions on the camera model hold. SSC requires that problems based on the l1-norm are solved to infer which points belong to the same subspace. If these unknown subspaces are well-separated this algorithm is guaranteed to succeed. The question how the distribution of points on the same subspace effects their clustering has received less attention. One case has been reported in which points of the same model are erroneously classified to belong to different subspaces. In this work, it will be theoretically shown when and why such spurious clusters occur. This claim is further substantiated by experimental evidence. Two algorithms based on the Dantzig selector and subspace selector are proposed to overcome this problem, and good results are reported.