10,259 research outputs found
A dual framework for low-rank tensor completion
One of the popular approaches for low-rank tensor completion is to use the
latent trace norm regularization. However, most existing works in this
direction learn a sparse combination of tensors. In this work, we fill this gap
by proposing a variant of the latent trace norm that helps in learning a
non-sparse combination of tensors. We develop a dual framework for solving the
low-rank tensor completion problem. We first show a novel characterization of
the dual solution space with an interesting factorization of the optimal
solution. Overall, the optimal solution is shown to lie on a Cartesian product
of Riemannian manifolds. Furthermore, we exploit the versatile Riemannian
optimization framework for proposing computationally efficient trust region
algorithm. The experiments illustrate the efficacy of the proposed algorithm on
several real-world datasets across applications.Comment: Aceepted to appear in Advances of Nueral Information Processing
Systems (NIPS), 2018. A shorter version appeared in the NIPS workshop on
Synergies in Geometric Data Analysis 201
DFacTo: Distributed Factorization of Tensors
We present a technique for significantly speeding up Alternating Least
Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor
factorization. By exploiting properties of the Khatri-Rao product, we show how
to efficiently address a computationally challenging sub-step of both
algorithms. Our algorithm, DFacTo, only requires two sparse matrix-vector
products and is easy to parallelize. DFacTo is not only scalable but also on
average 4 to 10 times faster than competing algorithms on a variety of
datasets. For instance, DFacTo only takes 480 seconds on 4 machines to perform
one iteration of the ALS algorithm and 1,143 seconds to perform one iteration
of the GD algorithm on a 6.5 million x 2.5 million x 1.5 million dimensional
tensor with 1.2 billion non-zero entries.Comment: Under review for NIPS 201
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