Preconditioned Spectral Clustering for Stochastic Block Partition Streaming Graph Challenge
David Zhuzhunashvili, Andrew Knyazev

TL;DR
This paper presents an efficient spectral clustering method using preconditioned eigenvalue solvers for static and streaming graphs, significantly reducing computation time while maintaining high accuracy in identifying graph partitions.
Contribution
The paper introduces a preconditioned spectral clustering approach with LOBPCG that accelerates eigenvalue computations for static and streaming graphs, outperforming baseline methods in speed and accuracy.
Findings
Achieves 10x error reduction in 10-20 iterations without preconditioning.
Clusters 98-160 groups in seconds for large graphs, outperforming baseline times.
Streaming approach reduces iterations and maintains cluster quality over multiple stages.
Abstract
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is demonstrated to efficiently solve eigenvalue problems for graph Laplacians that appear in spectral clustering. For static graph partitioning, 10-20 iterations of LOBPCG without preconditioning result in ~10x error reduction, enough to achieve 100% correctness for all Challenge datasets with known truth partitions, e.g., for graphs with 5K/.1M (50K/1M) Vertices/Edges in 2 (7) seconds, compared to over 5,000 (30,000) seconds needed by the baseline Python code. Our Python code 100% correctly determines 98 (160) clusters from the Challenge static graphs with 0.5M (2M) vertices in 270 (1,700) seconds using 10GB (50GB) of memory. Our single-precision MATLAB code calculates the same clusters at half time and memory. For streaming graph partitioning, LOBPCG is initiated with approximate eigenvectors of the graph Laplacian…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
MethodsSpectral Clustering
