Tensorial bipartite graph clustering based on logarithmic coupled penalty

Abstract

The graph-based multi-view clustering method has gained considerable attention in recent years. However, due to its large time complexity, it is limited to handling small-scale clustering datasets. Moreover, most existing models only consider the similarity within views and do not leverage the correlation between views and use the tensor nuclear norm (TNN) as a convex approximation to the tensor rank function. The TNN treats each singular value equally, leading to suboptimal results. To address this issue, this paper proposes a tensorial multi-view clustering model based on bipartite graphs. This paper first introduces a new non-convex logarithmic coupled penalty (LCP) function that treats different singular values differently and preserves the useful structural information required. Additionally, a tensorial bipartite graph clustering model based on logarithmic coupled penalty (LCP-TBGC) is proposed along with a corresponding solution algorithm. The paper also presents a theoretical proof that the obtained resulting sequence converges to the Karush–Kuhn–Tucker (KKT) point. Finally, to validate the effectiveness and superiority of the proposed model, experiments were conducted on eight datasets.