# Tensor Factorization via Matrix Factorization

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Volodymyr Kuleshov,
Arun Chaganty,
Percy Liang
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Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:507-516, 2015.

#### Abstract

Tensor factorization arises in many machine learning applications, such as knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new algorithm for CP tensor factorization that uses random projections to reduce the problem to simultaneous matrix diagonalization. Our method is conceptually simple and also applies to non-orthogonal and asymmetric tensors of arbitrary order. We prove that a small number random projections essentially preserves the spectral information in the tensor, allowing us to remove the dependence on the eigengap that plagued earlier tensor-to-matrix reductions. Experimentally, our method outperforms existing tensor factorization methods on both simulated data and two real datasets.

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