报告题目：Randomized Spectral Clustering in Large-Scale Stochastic Block Models

报告时间： 2021年5月24日，星期一，15:30-16:30，

报告地点：数学楼二层2-3室

报告人：郭骁，西北大学

报告摘要：

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the full eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, where we typically assume the network data are generated from a stochastic block model that is not necessarily of full rank. To do this, we first use the recently developed sketching algorithms to obtain two randomized spectral clustering algorithms, namely, the random projection-based and the random sampling-based spectral clustering. Then we study the theoretical bounds of the resulting algorithms in terms of the approximation error for the population adjacency matrix, the misclassification error, and the estimation error for the link probability matrix. It turns out that, under mild conditions, the randomized spectral clustering algorithms lead to the same theoretical bounds as those of the original spectral clustering algorithm. We also extend the results to degree-corrected stochastic block models. Numerical experiments support our theoretical findings and show the efficiency of randomized methods. A new R package called Rclust is developed and made available to the public.

报告人简介：

   郭骁，西北大学数学学院统计系讲师，2019年12月博士毕业于西北大学统计学专业。哥伦比亚大学、威斯康辛大学麦迪逊分校统计系访问学者。研究方向为高维统计、统计机器学习、数据隐私保护等。