報告題目：Hierarchical Community Detection with Fiedler Vectors
報 告 人：Xiaodong Li 教授 美國加州大學戴維斯分校
報告時間：2019年7月10日上午11:00-11:40
報告地點：數學樓一樓第一報告廳
報告摘要:
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.
報告人簡介：
Xiaodong Li博士是美國加州大學戴維斯分校統計系助理教授。在此之前，他曾在美國賓夕法尼亞大學沃頓商學院統計系工作了兩年。 他于2013年獲得美國斯坦福大學數學博士學位，并于2008年獲得北京大學學士學位。他對網絡分析，無監督學習理論和數學信号處理有着廣泛的研究興趣。他的論文發表在各種統計學，數學和工程學期刊上，如AoS，ACHA，FOCM，JACM，IEEE TIT等等。
