6,035 research outputs found
R3MC: A Riemannian three-factor algorithm for low-rank matrix completion
We exploit the versatile framework of Riemannian optimization on quotient
manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank
matrix completion. The underlying search space of fixed-rank matrices is
endowed with a novel Riemannian metric that is tailored to the least-squares
cost. Numerical comparisons suggest that R3MC robustly outperforms
state-of-the-art algorithms across different problem instances, especially
those that combine scarcely sampled and ill-conditioned data.Comment: Accepted for publication in the proceedings of the 53rd IEEE
Conference on Decision and Control, 201
Distributed Dictionary Learning
The paper studies distributed Dictionary Learning (DL) problems where the
learning task is distributed over a multi-agent network with time-varying
(nonsymmetric) connectivity. This formulation is relevant, for instance, in
big-data scenarios where massive amounts of data are collected/stored in
different spatial locations and it is unfeasible to aggregate and/or process
all the data in a fusion center, due to resource limitations, communication
overhead or privacy considerations. We develop a general distributed
algorithmic framework for the (nonconvex) DL problem and establish its
asymptotic convergence. The new method hinges on Successive Convex
Approximation (SCA) techniques coupled with i) a gradient tracking mechanism
instrumental to locally estimate the missing global information; and ii) a
consensus step, as a mechanism to distribute the computations among the agents.
To the best of our knowledge, this is the first distributed algorithm with
provable convergence for the DL problem and, more in general, bi-convex
optimization problems over (time-varying) directed graphs
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