Canonical Tensor Scaling

TL;DR

This paper extends the concept of positive matrix scaling to selected-rank subtensors of arbitrary tensors, aiming to enhance sparse-tensor completion for complex multidimensional recommender systems.

Contribution

It introduces a generalized framework for tensor scaling that can handle higher-dimensional data beyond matrices, facilitating advanced recommender system applications.

Findings

Framework for tensor scaling of selected-rank subtensors

Potential improvements in sparse-tensor completion tasks

Application to multidimensional recommender systems

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.).