用于并行谱聚类的分布式块Chebyshev-Davidson算法
A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering
AI总结：
本文提出一种分布式块Chebyshev-Davidson算法，通过解析谱估计解决大规模前特征值问题，并实现具有$\sqrt{p}$加速比的并行计算，显著提升了谱聚类在大数据环境下的效率与可扩展性。
摘要：
我们开发了一种分布式块Chebyshev-Davidson算法，用于求解谱聚类中谱分析的大规模前特征值问题。首先，Chebyshev-Davidson算法的效率依赖于特征值谱的先验知识，而估计该谱可能成本高昂。通过谱聚类中Laplacian或归一化Laplacian矩阵的解析谱估计，可以缓解这一问题，使所提算法在谱聚类中非常高效。其次，为使该算法能够分析大数据，我们开发了具有良好可扩展性的分布式并行版本。并行计算带来的加速比近似等价于$\sqrt{p}$，其中$p$表示进程数。数值结果将展示其在谱聚类中的效率，以及在并行计算环境中相比现有特征值求解器的可扩展性优势。
英文摘要：
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.}
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