A Riemannian gossip approach to subspace learning on Grassmann manifold

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1783-1803
Number of pages21
JournalMachine Learning
Issue number10
Publication statusPublished - 2019 Oct 14
Externally publishedYes


  • Manifold optimization
  • Matrix completion
  • Multivariate regression
  • Non-linear gossip
  • Stochastic gradients

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence


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