A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering

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 e...

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Bibliographic Details
Published in:Journal of scientific computing 2024-03, Vol.98 (3), p.69, Article 69
Main Authors: Pang, Qiyuan, Yang, Haizhao
Format: Article
Language:English
Subjects:
Algorithms
Chebyshev approximation
Clustering
Communication
Computational Mathematics and Numerical Analysis
Costs
Data science
Eigenvalues
Eigenvectors
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Sparsity
Spectrum analysis
Theoretical
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Summary: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 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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02455-y