Tensor Factorization via Matrix Factorization

Volodymyr Kuleshov, Arun Chaganty, Percy Liang
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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-kuleshov15, title = {{Tensor Factorization via Matrix Factorization}}, author = {Kuleshov, Volodymyr and Chaganty, Arun and Liang, Percy}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {507--516}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/kuleshov15.pdf}, url = {https://proceedings.mlr.press/v38/kuleshov15.html}, 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.} }
Endnote
%0 Conference Paper %T Tensor Factorization via Matrix Factorization %A Volodymyr Kuleshov %A Arun Chaganty %A Percy Liang %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-kuleshov15 %I PMLR %P 507--516 %U https://proceedings.mlr.press/v38/kuleshov15.html %V 38 %X 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.
RIS
TY - CPAPER TI - Tensor Factorization via Matrix Factorization AU - Volodymyr Kuleshov AU - Arun Chaganty AU - Percy Liang BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-kuleshov15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 507 EP - 516 L1 - http://proceedings.mlr.press/v38/kuleshov15.pdf UR - https://proceedings.mlr.press/v38/kuleshov15.html AB - 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. ER -
APA
Kuleshov, V., Chaganty, A. & Liang, P.. (2015). Tensor Factorization via Matrix Factorization. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:507-516 Available from https://proceedings.mlr.press/v38/kuleshov15.html.

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