Tensor Decomposition via Joint Matrix Schur Decomposition
Abstract
We describe an approach to tensor decomposition that involves extracting a set of observable matrices from the tensor and applying an approximate joint Schur decomposition on those matrices, and we establish the corresponding first-order perturbation bounds. We develop a novel iterative Gauss-Newton algorithm for joint matrix Schur decomposition, which minimizes a nonconvex objective over the manifold of orthogonal matrices, and which is guaranteed to converge to a global optimum under certain conditions. We empirically demonstrate that our algorithm is faster and at least as accurate and robust than state-of-the-art algorithms for this problem.
Cite
Text
Colombo and Vlassis. "Tensor Decomposition via Joint Matrix Schur Decomposition." International Conference on Machine Learning, 2016.Markdown
[Colombo and Vlassis. "Tensor Decomposition via Joint Matrix Schur Decomposition." International Conference on Machine Learning, 2016.](https://mlanthology.org/icml/2016/colombo2016icml-tensor/)BibTeX
@inproceedings{colombo2016icml-tensor,
title = {{Tensor Decomposition via Joint Matrix Schur Decomposition}},
author = {Colombo, Nicolo and Vlassis, Nikos},
booktitle = {International Conference on Machine Learning},
year = {2016},
pages = {2820-2828},
volume = {48},
url = {https://mlanthology.org/icml/2016/colombo2016icml-tensor/}
}