Tensor Decompositions via Two-Mode Higher-Order SVD (HOSVD)

Miaoyan Wang, Yun Song
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:614-622, 2017.

Abstract

Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal’s uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlike the classical higher-order singular value decomposition which unfolds a tensor along a single mode, we consider unfoldings along two modes and use rank-1 constraints to characterize the underlying components. This tensor decomposition method provably handles a greater level of noise compared to previous methods and achieves a high estimation accuracy. Numerical results demonstrate that our algorithm is robust to various noise distributions and that it performs especially favorably as the order increases.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-wang17a, title = {{Tensor Decompositions via Two-Mode Higher-Order SVD (HOSVD)}}, author = {Wang, Miaoyan and Song, Yun}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {614--622}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/wang17a/wang17a.pdf}, url = {https://proceedings.mlr.press/v54/wang17a.html}, abstract = {Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal’s uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlike the classical higher-order singular value decomposition which unfolds a tensor along a single mode, we consider unfoldings along two modes and use rank-1 constraints to characterize the underlying components. This tensor decomposition method provably handles a greater level of noise compared to previous methods and achieves a high estimation accuracy. Numerical results demonstrate that our algorithm is robust to various noise distributions and that it performs especially favorably as the order increases.} }
Endnote
%0 Conference Paper %T Tensor Decompositions via Two-Mode Higher-Order SVD (HOSVD) %A Miaoyan Wang %A Yun Song %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-wang17a %I PMLR %P 614--622 %U https://proceedings.mlr.press/v54/wang17a.html %V 54 %X Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal’s uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlike the classical higher-order singular value decomposition which unfolds a tensor along a single mode, we consider unfoldings along two modes and use rank-1 constraints to characterize the underlying components. This tensor decomposition method provably handles a greater level of noise compared to previous methods and achieves a high estimation accuracy. Numerical results demonstrate that our algorithm is robust to various noise distributions and that it performs especially favorably as the order increases.
APA
Wang, M. & Song, Y.. (2017). Tensor Decompositions via Two-Mode Higher-Order SVD (HOSVD). Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:614-622 Available from https://proceedings.mlr.press/v54/wang17a.html.

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