论文标题
平行光谱群集的分布式块Chebyshev-Davidson算法
A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering
论文作者
论文摘要
我们开发了一个分布式的Chebyshev-Davidson算法，以解决在光谱群集中的大规模领先特征值问题来进行光谱分析。首先，Chebyshev-Davidson算法的效率取决于特征值频谱的先验知识，这可能是昂贵的。可以通过光谱聚类中拉普拉斯或归一化laplacian矩阵的分析频谱估计来减少这个问题，从而使所提出的算法对光谱聚类非常有效。其次，为了使所提出的能够分析大数据的算法，已经开发了具有吸引人的可扩展性的分布式和并行版本。通过并行计算加速大约等于$ \ sqrt {p} $，其中$ p $表示过程数。 {将提供数值结果，以证明其在光谱群集和可伸缩性优势中的效率比在并行计算环境中用于光谱聚类的现有特征界面的效率。}
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.}
