Spectral Clustering: Methodology and Statistical Analysis

报告题目：Spectral Clustering: Methodology and Statistical Analysis

报告人：章叶（宾夕法尼亚大学）

报告时间：2023年6月2日（周五）16:00

报告地点：海纳苑2幢312

摘要：Spectral clustering is one of the most popular algorithms to group high-dimensional data. It is easy to implement, computationally efficient, and has achieved tremendous success in many applications. The idea behind spectral clustering is dimensionality reduction. It first performs a spectral decomposition on the dataset and only keeps the leading few spectral components to reduce the dimension of the data. It then applies some standard methods such as the k-means on the low-dimensional space to do clustering. In this talk, we demystify the success of spectral clustering by providing a sharp statistical analysis of its performance under mixture models. For isotropic Gaussian mixture models, we show spectral clustering is optimal. For sub-Gaussian mixture models, we derive exponential error rates for spectral clustering. To establish these results, we develop a new spectral perturbation analysis for singular subspaces.

报告人简介：章叶，宾夕法尼亚大学统计与数据科学系助理教授。2013年本科毕业于浙江大学数学科学学院统计学专业，曾获浙江大学竺可桢奖学金。2018年在耶鲁大学获统计学博士学位。2018-2019访问芝加哥大学一年。2019年入职宾夕法尼亚大学统计与数据科学系，担任助理教授。章博士的研究领域涵盖网络分析、聚类与混合模型分析、谱分析、平均场变分推断（mean field variational inference）、排序和同步化（ranking and synchronization）等等。他已在统计学和机器学习领域的国际顶级期刊（例如，Annals of Statistics，JASA，Journal of Machine Learning Research，IEEE Transactions on Information Theory等）发表学术论文多篇。 他于2018年获耶鲁大学Francis J. Anscombe Award，2019年获ICSA New Researcher Award。（个人主页：https://statistics.wharton.upenn.edu/profile/ayz/）

联系人：庞天晓（txpang@zju.edu.cn）