论文标题
一般特征值问题的一击分布式算法
One-shot Distributed Algorithm for Generalized Eigenvalue Problem
论文作者
论文摘要
如今，出于内存存储或数据隐私，以分布式方式存储越来越多的数据集。广义特征值问题（GEP）在大型高维统计模型家族中起着至关重要的作用。但是，现有的特征值分布方法不能用于GEP中，以使经验协方差矩阵的分歧。在这里，我们提出了一个通用的分布式GEP框架，其中包含用于GEP的单次通信。如果对称数据协方差重复了特征值，例如在规范组件分析中，我们将进一步修改该方法以更好地收敛。进行了近似误差的理论分析，并与数据协方差的差异，经验数据协方差的特征值以及本地服务器的数量进行了分析。数值实验还显示了所提出的算法的有效性。
Nowadays, more and more datasets are stored in a distributed way for the sake of memory storage or data privacy. The generalized eigenvalue problem (GEP) plays a vital role in a large family of high-dimensional statistical models. However, the existing distributed method for eigenvalue decomposition cannot be applied in GEP for the divergence of the empirical covariance matrix. Here we propose a general distributed GEP framework with one-shot communication for GEP. If the symmetric data covariance has repeated eigenvalues, e.g., in canonical component analysis, we further modify the method for better convergence. The theoretical analysis on approximation error is conducted and the relation to the divergence of the data covariance, the eigenvalues of the empirical data covariance, and the number of local servers is analyzed. Numerical experiments also show the effectiveness of the proposed algorithms.
