Regularized Spectral Clustering Under the Degree-Corrected Stochastic Blockmodel

• Activity Number: 61
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Tai Qin*+
• Companies: University of Wisconsin-Madison
• Keywords: Spectral Clustering ; Network ; Community Detection

Abstract

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri (2012) and Amini (2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for improved statistical performance. The current paper extends the previous statistical estimation results to the more canonical spectral clustering algorithm in a way that removes any assumption on the minimum degree and provides guidance on the choice of tuning parameter. Moreover, our results show how the "star shape" in the eigenvectors-a common feature of empirical networks-can be explained by the Degree-Corrected Stochastic Blockmodel and the Extended Planted Partition model, two statistical model that allow for highly heterogeneous degrees. Throughout, the paper characterizes and justifies several of the variations of the spectral clustering algorithm in terms of these models.