Multi-order graph clustering with adaptive node-level weight learning

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Current graph clustering methods emphasize individual node and edge connections, while ignoring higher-order organization at the level of motif. Recently, higher-order graph clustering approaches have been designed by motif-based hypergraphs. However, these approaches often suffer from hypergraph fragmentation issue seriously, which degrades the clustering performance greatly. Moreover, real-world graphs usually contain diverse motifs, with nodes participating in multiple motifs. A key challenge is how to achieve precise clustering results by integrating information from multiple motifs at the node level. In this paper, we propose a multi-order graph clustering model (MOGC) to integrate multiple higher-order structures and edge connections at node level. MOGC employs an adaptive weight learning mechanism to automatically adjust the contributions of different motifs for each node. This not only tackles hypergraph fragmentation issue but enhances clustering accuracy. MOGC is efficiently solved by an alternating minimization algorithm. Experiments on seven real-world datasets illustrate the effectiveness of MOGC.