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/}
}