Multiway Spherical Clustering Via Degree-Corrected Tensor Block Models

作者：Jiaxin Hu, Miaoyan Wang · 发表于：IEEE Transactions on Information Theory · 年份：2023 · DOI：10.1109/tit.2023.3239521 · 被引用次数：3 · 研究领域：Tensor decomposition and applications、Advanced Neuroimaging Techniques and Applications、Sparse and Compressive Sensing Techniques

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.