ROLE OF NORMALIZATION IN SPECTRAL CLUSTERING FOR STOCHASTIC BLOCKMODELS
成果类型：
Article
署名作者：
Sarkar, Purnamrita; Bickel, Peter J.
署名单位：
University of Texas System; University of Texas Austin; University of California System; University of California Berkeley
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/14-AOS1285
发表日期：
2015
页码：
962-990
关键词：
摘要：
Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both the normalized and unnormalized variants in recent random matrix theory literature. However, normalization for spectral clustering is commonly believed to be beneficial [Stat. Comput. 17 (2007) 395-416]. Indeed, our experiments show that normalization improves prediction accuracy. In this paper, for the popular stochastic blockmodel, we theoretically show that normalization shrinks the spread of points in a class by a constant fraction under a broad parameter regime. As a byproduct of our work, we also obtain sharp deviation bounds of empirical principal eigenvalues of graphs generated from a stochastic blockmodel.