A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering

TL;DR

This paper introduces a distributed Block Chebyshev-Davidson algorithm tailored for large-scale spectral clustering, leveraging spectrum estimation and parallel computing to enhance efficiency and scalability.

Contribution

It presents a novel distributed and parallel version of the Chebyshev-Davidson algorithm that efficiently solves large eigenvalue problems in spectral clustering.

Findings

Achieves near $ oot{p}{ }$ speedup with parallel processing

Demonstrates improved efficiency over existing eigensolvers

Shows scalability for big data spectral clustering

Abstract

We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on the prior knowledge of the eigenvalue spectrum, which could be expensive to estimate. This issue can be lessened by the analytic spectrum estimation of the Laplacian or normalized Laplacian matrices in spectral clustering, making the proposed algorithm very efficient for spectral clustering. Second, to make the proposed algorithm capable of analyzing big data, a distributed and parallel version has been developed with attractive scalability. The speedup by parallel computing is approximately equivalent to $\sqrt{p}$, where $p$ denotes the number of processes. {Numerical results will be provided to demonstrate its efficiency in spectral clustering and scalability advantage over existing eigensolvers used for spectral clustering in parallel computing environments.}