A Riemannian gossip approach to subspace learning on Grassmann manifold

Bamdev Mishra*, Hiroyuki Kasai, Pratik Jawanpuria, Atul Saroop

*この研究の対応する著者

研究成果査読

6 被引用数 (Scopus)

抄録

In this paper, we focus on subspace learning problems on the Grassmann manifold. Interesting applications in this setting include low-rank matrix completion and low-dimensional multivariate regression, among others. Motivated by privacy concerns, we aim to solve such problems in a decentralized setting where multiple agents have access to (and solve) only a part of the whole optimization problem. The agents communicate with each other to arrive at a consensus, i.e., agree on a common quantity, via the gossip protocol. We propose a novel cost function for subspace learning on the Grassmann manifold, which is a weighted sum of several sub-problems (each solved by an agent) and the communication cost among the agents. The cost function has a finite-sum structure. In the proposed modeling approach, different agents learn individual local subspaces but they achieve asymptotic consensus on the global learned subspace. The approach is scalable and parallelizable. Numerical experiments show the efficacy of the proposed decentralized algorithms on various matrix completion and multivariate regression benchmarks.

本文言語English
ページ(範囲)1783-1803
ページ数21
ジャーナルMachine Learning
108
10
DOI
出版ステータスPublished - 2019 10 14
外部発表はい

ASJC Scopus subject areas

  • ソフトウェア
  • 人工知能

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