Towards Scalable Spectral Clustering via Spectrum-Preserving Sparsification release_b66skkg2mjbcdhomsvt3qe2v5e

by Yongyu Wang, Zhuo Feng

Released as a article .

2017  

Abstract

The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that enables to build ultra-sparse NN (u-NN) graphs with guaranteed preservation of the original graph spectrums, such as the first few eigenvectors of the original graph Laplacian. Our approach can immediately lead to scalable spectral clustering of large data networks without sacrificing solution quality. The proposed method starts from constructing low-stretch spanning trees (LSSTs) from the original graphs, which is followed by iteratively recovering small portions of "spectrally critical" off-tree edges to the LSSTs by leveraging a spectral off-tree embedding scheme. To determine the suitable amount of off-tree edges to be recovered to the LSSTs, an eigenvalue stability checking scheme is proposed, which enables to robustly preserve the first few Laplacian eigenvectors within the sparsified graph. Additionally, an incremental graph densification scheme is proposed for identifying extra edges that have been missing in the original NN graphs but can still play important roles in spectral clustering tasks. Our experimental results for a variety of well-known data sets show that the proposed method can dramatically reduce the complexity of NN graphs, leading to significant speedups in spectral clustering.
In text/plain format

Archived Files and Locations

application/pdf  748.9 kB
file_ffn5ukqqerbsjfeq7k3emdoelm
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2017-10-12
Version   v1
Language   en ?
arXiv  1710.04584v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 95a7b524-c639-4ca2-b492-bf3dd4aaba87
API URL: JSON