Mixed-order spectral clustering for complex networks

Spectral clustering (SC) is a popular approach for gaining insights from complex networks. Conventional SC focuses on second-order structures (e.g. edges) without direct consideration of higher-order triangles). This has motivated extensions that directly consider structures. However, both approaches are limited to considering single order. To address this issue, paper proposes novel Mixed-Order Clustering (MOSC) framework model and third-order simultaneously. mixed-order structures, we propose two new methods based Graph Laplacian (GL) Random Walks (RW). MOSC-GL combines edge triangle adjacency matrices, with theoretical performance guarantee. MOSC-RW first-order random walks probabilistic interpretation. Moreover, design cut criteria enable existing preserve develop evaluation metrics structure-level evaluation. Experiments community detection superpixel segmentation show (1) the superior MOSC over methods, (2) enhanced conventional due criteria, (3) output clusters offered by metrics.