Graph-Based Clustering: High-Order Bipartite Graph for Proximity Learning

Structured proximity matrix learning, one of the mainstream directions in clustering research, refers to learning a proximity matrix with an explicit clustering structure from the original first-order proximity matrix. Due to the complexity of the data structure, the original first-order proximity matrix always lacks some must-links compared to the groundtruth proximity matrix. It is worth noting that high-order proximity matrices can provide missed must-link information. However, the computation of high-order proximity matrices and clustering based on them are expensive. To solve the above problem, inspired by the anchor bipartite graph, we present a novel high-order bipartite graph proximity matrix and a fast method to compute it. This proposed high-order bipartite graph proximity matrix contains high-order proximity information and can significantly reduce the computational complexity of the whole clustering process. Furthermore, we introduce an efficient and simple high-order bipartite graph fusion framework that can adaptively assign weights to each order of the high-order bipartite graph matrices. Finally, under the Laplace rank constraint, a consensus structured bipartite graph proximity matrix is obtained. At the same time, an efficient solution algorithm is proposed for this model. The model's efficacy is underscored through rigorous experiments, highlighting its superior clustering performance and time efficiency. Code available: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://anonymous.4open.science/r/HBGC-F6C4</uri>.