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

  • 2016. Dictionary Learning on Grassmann Manifolds in ALGORITHMIC ADVANCES IN RIEMANNIAN GEOMETRY AND APPLICATIONS
  • 2015-06. Decentralized and Privacy-Preserving Low-Rank Matrix Completion in JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA
  • 2008-12. Flexible latent variable models for multi-task learning in MACHINE LEARNING
  • 2014-06. Fixed-rank matrix factorizations and Riemannian low-rank optimization in COMPUTATIONAL STATISTICS
  • 2013-06. Parallel stochastic gradient algorithms for large-scale matrix completion in MATHEMATICAL PROGRAMMING COMPUTATION
  • 2009-12. Exact Matrix Completion via Convex Optimization in FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
  • 2008. Large-Scale Parallel Collaborative Filtering for the Netflix Prize in ALGORITHMIC ASPECTS IN INFORMATION AND MANAGEMENT
  • 2008-12. Convex multi-task feature learning in MACHINE LEARNING
  • 2016-12. Gene expression prediction using low-rank matrix completion in BMC BIOINFORMATICS
  • 2012-12. Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm in MATHEMATICAL PROGRAMMING COMPUTATION
  • 1997-07. A Bayesian/Information Theoretic Model of Learning to Learn via Multiple Task Sampling in MACHINE LEARNING
  • 1997-07. Multitask Learning in MACHINE LEARNING
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