Local Connectivity Enhanced Sparse Representation

During the past two decades, the subspace clustering problem has attracted much attention. Since the data set in real-world problems usually contains a lot of categories, it seems that the large subspace number (LSN) subspace clustering has great significance. According to the analysis in the recent work, concerning the spectral clustering-based methods, strong graph connectivity is highly desired by the LSN subspace clustering problem. However, previous works usually consider this property by the global structure of the representation matrix. In this paper, we attempt to address the local structure by the local difference of the representation matrix and propose Local Connectivity Enhanced Sparse Representation (LCESR). Our method can not only exhibit strong graph connectivity but also produce subspace-preserving affinities for independent subspaces, another favorable property concerned by many related works. Hence, it achieves state-of-the-art results in LSN subspace clustering. Besides, because the weight matrix in LCESR can take advantage of the label information available in the data set, it can also perform well in the problem of the graph-based semi-supervised learning. Extensive experimental results demonstrate the effectiveness of our proposed method.