Tensor Decomposition via Simultaneous Power Iteration

Po-An Wang, Chi-Jen Lu
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3665-3673, 2017.

Abstract

Tensor decomposition is an important problem with many applications across several disciplines, and a popular approach for this problem is the tensor power method. However, previous works with theoretical guarantee based on this approach can only find the top eigenvectors one after one, unlike the case for matrices. In this paper, we show how to find the eigenvectors simultaneously with the help of a new initialization procedure. This allows us to achieve a better running time in the batch setting, as well as a lower sample complexity in the streaming setting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-wang17i, title = {Tensor Decomposition via Simultaneous Power Iteration}, author = {Po-An Wang and Chi-Jen Lu}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {3665--3673}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/wang17i/wang17i.pdf}, url = {https://proceedings.mlr.press/v70/wang17i.html}, abstract = {Tensor decomposition is an important problem with many applications across several disciplines, and a popular approach for this problem is the tensor power method. However, previous works with theoretical guarantee based on this approach can only find the top eigenvectors one after one, unlike the case for matrices. In this paper, we show how to find the eigenvectors simultaneously with the help of a new initialization procedure. This allows us to achieve a better running time in the batch setting, as well as a lower sample complexity in the streaming setting.} }
Endnote
%0 Conference Paper %T Tensor Decomposition via Simultaneous Power Iteration %A Po-An Wang %A Chi-Jen Lu %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-wang17i %I PMLR %P 3665--3673 %U https://proceedings.mlr.press/v70/wang17i.html %V 70 %X Tensor decomposition is an important problem with many applications across several disciplines, and a popular approach for this problem is the tensor power method. However, previous works with theoretical guarantee based on this approach can only find the top eigenvectors one after one, unlike the case for matrices. In this paper, we show how to find the eigenvectors simultaneously with the help of a new initialization procedure. This allows us to achieve a better running time in the batch setting, as well as a lower sample complexity in the streaming setting.
APA
Wang, P. & Lu, C.. (2017). Tensor Decomposition via Simultaneous Power Iteration. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:3665-3673 Available from https://proceedings.mlr.press/v70/wang17i.html.

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