Skip to yearly menu bar Skip to main content


On the Power of SVD in the Stochastic Block Model

Xinyu Mao · Jiapeng Zhang

Great Hall & Hall B1+B2 (level 1) #819
[ ]
[ Paper [ Poster [ OpenReview
Tue 12 Dec 8:45 a.m. PST — 10:45 a.m. PST


A popular heuristic method for improving clustering results is to apply dimensionality reduction before running clustering algorithms.It has been observed that spectral-based dimensionality reduction tools, such as PCA or SVD, improve the performance of clustering algorithms in many applications. This phenomenon indicates that spectral method not only serves as a dimensionality reduction tool, but also contributes to the clustering procedure in some sense. It is an interesting question to understand the behavior of spectral steps in clustering problems.As an initial step in this direction, this paper studies the power of vanilla-SVD algorithm in the stochastic block model (SBM). We show that, in the symmetric setting, vanilla-SVD algorithm recovers all clusters correctly. This result answers an open question posed by Van Vu (Combinatorics Probability and Computing, 2018) in the symmetric setting.

Chat is not available.