报告题目：Hierarchical Community Detection with Fiedler Vectors
报 告 人：Xiaodong Li 教授 美国加州大学戴维斯分校
报告时间：2019年7月10日上午11:00-11:40
报告地点：数学楼一楼第一报告厅
报告摘要:
Hierarchical clustering of entities based on observations of their connections has already been widely studied and implemented in the practice of network analysis. However, the statistical properties of diverse hierarchical community detection are still majorly unclear. We here propose to extend the binary tree stochastic block model in the literature to accommodate much more general compositions of edge probabilities. It can be shown that the eigen-structures of the graph Laplacian of the population binary tree stochastic block model reveals the latent structure of the network at all levels. This fact inspires us to retrieve the hidden hierarchical structure of communities by using a recursive bi-partitioning algorithm with Fiedler vector, dividing a network into two communities repeatedly until a stopping rule indicates there are no further communities. The method is further theoretically justified in sparse networks with the help of the newly developed theory about entry-wise bound for eigenvector perturbations. The is based on an ongoing project with my student Xingmei Lou.
报告人简介：
Xiaodong Li博士是美国加州大学戴维斯分校统计系助理教授。在此之前，他曾在美国宾夕法尼亚大学沃顿商学院统计系工作了两年。 他于2013年获得美国斯坦福大学数学博士学位，并于2008年获得北京大学学士学位。他对网络分析，无监督学习理论和数学信号处理有着广泛的研究兴趣。他的论文发表在各种统计学，数学和工程学期刊上，如AoS，ACHA，FOCM，JACM，IEEE TIT等等。
