论文标题
多路球形聚类通过度校正张量块模型
Multiway Spherical Clustering via Degree-Corrected Tensor Block Models
论文作者
论文摘要
我们考虑了在不明程度异质性存在下多道路聚类的问题。这些数据问题通常在社交网络中的推荐系统，神经影像，社区检测和超图形分区等应用中产生。学位异质性的津贴在聚类模型中提供了极大的灵活性，但是额外的复杂性在统计和计算中都带来了重大挑战。在这里，我们开发了具有估计精度保证的学位校正张块模型。我们基于角度可分离性的概念介绍了聚类性能的相变，并且我们表征了与不同统计计算行为相对应的三个信噪比。特别是，我们证明了固有的统计到及时差距仅针对三个或更高阶的张量出现。此外，我们开发了一种有效的多项式时间算法，该算法可在轻度信号条件下实现精确的聚类。我们的程序的功效通过两个数据应用程序，一个在人脑连接项目中，另一个在秘鲁立法网络数据集上证明。
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.
