Keywords: Principal Component Analysis, Leading Eigenvector, Bit Complexity, Riemannian Optimization, Sphere
TL;DR: Bit complexity of leading eigenvector computation via quantized Riemannian gradient descent.
Abstract: 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.
Code Of Conduct: I certify that all co-authors of this work have read and commit to adhering to the NeurIPS Statement on Ethics, Fairness, Inclusivity, and Code of Conduct.
Supplementary Material: pdf