Explicit Local Coupling Global Structure Clustering

Abstract

Graph-based clustering has become an active topic due to the efficiency in characterizing the relationships between the samples via graph. To improve the quality of graph, recent works propose to utilize global and local information. However, existing methods may lead to a degenerated graph when facing noisy and uneven distributed data. Since (1) they preserve the local information by referring the similarity between each sample-pair, whose confidence is easily disturbed by the poor quality samples; and, (2) although the global information is relatively robust to the noisy, existing methods have island effect that lies between local and global structures learning, such that the information of both can not be utilized mutually. To alleviate these issues, this paper presents explicit local coupling global structure clustering (ELGSC) to explicitly learn the local structure and global structure information via a coupling scheme. To be specific, we learn <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> (≪ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ) pseudo samples as the anchors to reflect local hot spots distribution, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> is the number of samples. By referring the relationship between each anchor-sample pair, ELGSC is capable of obtaining an effective local bipartite graph to capture the local structure. Meanwhile, the self-expressiveness learning is adopted to pursue a lower-rank global affinity graph. Finally, a higher-order coupling learning framework is proposed to couple the learning of global affinity graph and local bipartite graph. Thus, local and global structure information could be propagated each other on both graphs. The experimental results on real datasets demonstrate the efficacy of the proposed method over state-of-the-arts.