Enhancing Clustering Performance With Tensorized High-Order Bipartite Graphs: A Structured Graph Learning Approach

Clustering based on structured graph learning involves acquiring a proximity matrix with an explicit clustering structure from the original one. However, the original proximity matrix often lacks some must-links compared to the groundtruth, constraining the upper bound of clustering performance. High-order proximity information can mitigate this limitation, yet traditional high-order proximity matrix-based methods are time-intensive. To tackle this, we propose the Tensorized High-order Bipartite Graphs-based structured proximity matrix learning method (THBG). Firstly, we introduce a high-order bipartite graph proximity matrix with a swift computation method, incorporating high-order information and significantly reducing computational overhead. Secondly, we apply tensor nuclear norm minimization to the tensor composed of high-order bipartite graphs, learning a low-rank tensor representation that effectively harnesses the consistency of high-order information. Concurrently, a structured bipartite graph proximity matrix with an explicit clustering structure is adaptively learned based on the low-rank tensor representation and Laplace rank constraint. Experimental results demonstrate the superiority and great potential of this method. 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/THBG-D10D</uri>.