报告题目：Graph Laplacian, Spectral Clustering, and Community Detection

报告时间：2020年5月23日（周六）下午17:15—18:00

报告人：凌舒扬教授

报告地点：Zoom云会议（ID：937 6354 7091, 密码：nanxinda60）

报告摘要：Spectral clustering is arguably one of the most popular algorithms in data- and network clustering. The classical algorithm follows two-step procedure: compute the eigenvector associated to the second smallest eigenvalue of the Laplacian and then take the entrywise sign. Despite its high popularity, its theoretical understanding is far from its practice. In this talk, I will discuss two important progresses in the mathematical foundation of spectral clustering. (i) We will propose a convex relaxation of graph partition, namely ratio- and normalized cut, and establish a theoretical framework under which those two otherwise NP-hard problems are exactly solvable within polynomial time. (ii) We will discuss the performance of spectral clustering applied to community detection under stochastic block model. We show that the Fiedler eigenvector recovers the underlying hidden partition of the block model even if the signal-to-noise ratio is close to the information theoretical limits. (This work is jointly done with Shaofeng Deng and Thomas Strohmer from UC Davis.)

欢迎广大师生踊跃参加！

数学与统计学院

2020年5月22日

附：专家简介

凌舒扬，现任职于上海纽约大学，是数据科学方向的预聘制长聘制助理教授(tenure-track)。在加入上海纽约大学之前，凌舒扬于2017年至2019年在纽约大学柯朗数学研究所(CIMS)和数据科学研究所担任柯朗讲师；在此之前，在2017年6月从加州大学戴维斯分校应用数学专业获得博士学位。凌舒扬的研究主要在信号处理中的数学问题和理论机器学习、凸优化和非凸优化、计算调和分析、随机矩阵、谱图论等。其学术论文发表多个国际顶尖期刊，其中包括：Foundations of Computational Mathematics, SIAM Journal on Optimization/Imaging Sciences, Applied and Computational Harmonic Analysis, Mathematical Programming, IEEE Transaction on Information Theory等。