Low-Rank and Structured Sparse Subspace Clustering

High dimensional data often lie approximately in low dimensional subspaces corresponding to multiple classes or categories. Segmenting the high dimensional data into their corresponding low dimensional subspaces is referred as subspace clustering. State of the art methods solve this problem in two steps. First, an affinity matrix is built from data based on self expressiveness model, in which each data point is expressed as a linear combination of other data points. Second, the segmentation is obtained by spectral clustering. However, solving two dependent steps separately is still suboptimal. In this paper, we propose a joint affinity learning and spectral clustering approach for low rank representation based subspace clustering, termed Low-Rank and Structured Sparse Subspace Clustering (LRS3C), where a subspace structured norm that depends on subspace clustering result is introduced into the objective of low-rank representation problem. We solve it efficiently via a combination of Linearized Alternation Direction Method (LADM) with spectral clustering. Experiments on Hopkins 155 motion segmentation database and Extended Yale B data set demonstrated the effectiveness of our method.