An Improved Latent Low Rank Representation for Automatic Subspace Clustering

There is growing interest in low rank representation (LRR) for subspace clustering. Existing latent LRR methods can exploit the global structure of data when the observations are insufficient and/or grossly corrupted, but it cannot capture the intrinsic structure due to the neglect of the local information of data. In this paper, we proposed an improved latent LRR model with a distance regularization and a non-negative regularization jointly, which can effectively discover the global and local structure of data for graph learning and improve the expression of the model.Then, an efficiently iterative algorithm is developed to optimize the improved latent LRR model. In addition, traditional subspace clustering characterizes a fixed numbers of cluster, which cannot efficiently make model selection. An efficiently automatic subspace clustering is developed via the bias and variance trade-off, where the numbers of cluster can be automatically added and discarded on the fly.