Tensor Algebra and its Applications to Data Science and Statistics

TL;DR

This survey reviews the diverse applications of tensor algebra in data science and statistics, clarifying different usages of tensors and emphasizing tensor decompositions as a key tool.

Contribution

It unifies various tensor concepts across disciplines and highlights the importance of tensor decompositions in data analysis.

Findings

Clarified the commonality of tensor concepts across fields

Provided an overview of tensor applications in data science and statistics

Highlighted tensor decompositions as a central technique

Abstract

This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in the literature, and to explain how these usages are manifestations of a common concept. Not all relevant topics are discussed in detail, but the attempt is made to briefly describe and give references for some of the most important topics not included in the main survey. Particular attention is given to tensor decompositions.