Graph regularized compact low rank representation for subspace clustering

Low rank representation (LRR) is one of the state-of-the-art methods for subspace clustering and it has been used widely in machine learning, data mining, and pattern recognition. The main objective of LRR is to seek the lowest rank representations for data points based on a given dictionary. However, the current LRR-based approaches have the following drawbacks: 1) the original data, which are used as a dictionary in LRR, usually contain noise and they may not be representative; and 2) the affinity matrix and subspace clustering are obtained in two independent steps; thus, an overall optimum cannot be guaranteed. Therefore, we propose an improved LRR-based approach, called Graph regularized Compact LRR (GCLRR), where dictionary learning and low-rank, low-dimensional representation are achieved simultaneously, and the low-dimensional representation used for subspace clustering captures both the global subspace structure (by the low-rankness) and the local manifold structure (by manifold regularization) of the original data. Finally, the mixed norm l2, 1 is used to measure the dissimilarity between the original data and its low rank approximation to make the model robust. An efficient optimization procedure based on Alternating Direction Method of Multipliers is used for GCLRR optimization. We verified the effectiveness and robustness of the proposed method based on extensive experiments using both synthetic and real data sets, which demonstrated its higher clustering capacity compared with state-of-the-art LRR-based clustering algorithms.