A Riemannian gossip approach to subspace learning on Grassmann manifold View Full Text


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Article Info

DATE

2019-01-24

AUTHORS

Bamdev Mishra, Hiroyuki Kasai, Pratik Jawanpuria, Atul Saroop

ABSTRACT

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. More... »

PAGES

1-21

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10994-018-05775-x

DOI

http://dx.doi.org/10.1007/s10994-018-05775-x

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https://app.dimensions.ai/details/publication/pub.1111641878


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52 schema:description 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.
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