Canonical Tensor Scaling
Numerical Analysis
2020-09-03 v1 Numerical Analysis
Abstract
In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion required for generalizations of the recommender system problem beyond a matrix of user-product ratings to multidimensional arrays involving coordinates based both on user attributes (e.g., age, gender, geographical location, etc.) and product/item attributes (e.g., price, size, weight, etc.).
Cite
@article{arxiv.2009.01175,
title = {Canonical Tensor Scaling},
author = {Tung D. Nguyen and Jeffrey Uhlmann},
journal= {arXiv preprint arXiv:2009.01175},
year = {2020}
}