Adaptive structured subspace clustering algorithm

Abstract

Sparse subspace clustering (SSC) algorithm, founds a new pattern for the subspace clustering, and has led to the satisfactory results in many applications. SSC is implemented in two phases: learning a sparse affinity matrix and performing spectral clustering on the affinity matrix. However, SSC can not commendably cluster together the correlated data within cluster, as well as explicitly capture the natural relationship between the affinity matrix and the segmentation of the data. Motivated by some of the CASS and S3C algorithms, a combinatorial algorithm is presented in this paper. Using trace Lasso instead of l 1 norm as regularization constraint, it can adaptively segment subspace and lead to more dense intra-cluster and more sparse inter-cluster. Using a joint optimization framework, it can organically connect two phases of SSC. The optimization model is solved by combining efficient alternating minimization and alternating direction method of multipliers. Experiments on Synthetic data, Handwritten Digits dataset, Extended Yale B and ORL facial databases demonstrate the effectiveness of ASSC approach.