Low-rank tensor completion: a Riemannian manifold preconditioning approach

Abstract

We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry that exists in Tucker decomposition. The specific metric allows to use the versatile framework of Riemannian optimization on quotient manifolds to develop preconditioned nonlinear conjugate gradient and stochastic gradient descent algorithms for batch and online setups, respectively. Concrete matrix representations of various optimization-related ingredients are listed. Numerical comparisons suggest that our proposed algorithms robustly outperform state-of-the-art algorithms across different synthetic and real-world datasets.

The 33rd International Conference on Machine Learning (ICML 2016). arXiv admin note: substantial text overlap with arXiv:1506.02159

References in corpus (1)

• Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors

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