Subspace segmentation with a large number of subspaces using infinity norm minimization

Spectral-clustering based methods have recently attracted considerable attention in the field of subspace segmentation. The approximately block-diagonal graphs achieved by this kind of methods usually contain some noise, i.e., nonzero elements in the off-diagonal region, due to outlier contamination or complex intrinsic structure of the dataset. In the experiment of most previous work, the number of the subspaces is often no more than 10. In this situation, this kind of noise almost has no influence on the segmentation results. However, the segmentation performance could be negatively affected by the noise when the number of subspaces is large, which is quite common in the real-world applications. In this paper, we address the problem of LSN subspace segmentation, i.e., large subspace number subspace segmentation. We first show that the approximately block-diagonal graph with the smaller difference in its diagonal blocks will be more robust to the off-diagonal noise mentioned above. Then, by using the infinity norm to control the bound of the difference in the diagonal blocks, we propose infinity norm minimization for LSN subspace segmentation. Experimental results demonstrate the effectiveness of our method. (C) 2018 Elsevier Ltd. All rights reserved.