Perspectives on CUR Decompositions

TL;DR

This paper explores the CUR decomposition, a matrix factorization technique, by comparing different perspectives and introducing a new characterization that unifies these views in the exact case.

Contribution

It provides a new characterization of CUR decompositions that consolidates various existing viewpoints into a unified understanding.

Findings

Different viewpoints of CUR decomposition are compared and contrasted.

A new characterization shows the equivalence of viewpoints in the exact case.

The paper enhances understanding of the theoretical foundations of CUR decompositions.

Abstract

This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization of CUR decompositions which synergizes these viewpoints and shows that they are indeed the same in the exact decomposition case.