We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly distributed among a set of computational nodes. We propose a new quantized variant of Riemannian gradient descent to solve this problem, and prove that the algorithm converges with high probability under a set of necessary spherical-convexity properties. We give bounds on the number of bits transmitted by the algorithm under common initialization schemes, and investigate the dependency on the problem dimension in each case.
翻译:当数据在一组计算节点之间随机分布时,我们研究关于球体主元件分析和主要源子计算的基本问题的有效分布式算法。我们提出了一种新的里曼梯度梯度下降的量化变方程式,以解决这个问题,并证明算法在一套必要的球体调和特性下具有很高的概率。我们给出了根据共同初始化计划由算法传输的位数的界限,并调查每个案例对问题层面的依赖性。