Multiway Spherical Clustering via Degree-Corrected Tensor Block Models
This work addresses clustering challenges in applications such as recommendation systems and neuroimaging, offering a flexible model with theoretical guarantees, though it is incremental in extending existing block models to tensors.
The paper tackles multiway clustering with unknown degree heterogeneity by developing a degree-corrected tensor block model, achieving exact clustering under mild conditions and demonstrating efficacy on real datasets like human brain connectome and Peru Legislation network.
We consider the problem of multiway clustering in the presence of unknown degree heterogeneity. Such data problems arise commonly in applications such as recommendation system, neuroimaging, community detection, and hypergraph partitions in social networks. The allowance of degree heterogeneity provides great flexibility in clustering models, but the extra complexity poses significant challenges in both statistics and computation. Here, we develop a degree-corrected tensor block model with estimation accuracy guarantees. We present the phase transition of clustering performance based on the notion of angle separability, and we characterize three signal-to-noise regimes corresponding to different statistical-computational behaviors. In particular, we demonstrate that an intrinsic statistical-to-computational gap emerges only for tensors of order three or greater. Further, we develop an efficient polynomial-time algorithm that provably achieves exact clustering under mild signal conditions. The efficacy of our procedure is demonstrated through two data applications, one on human brain connectome project, and another on Peru Legislation network dataset.