Efficient Algorithms for Constructing an Interpolative Decomposition

TL;DR

This paper introduces two optimized algorithms for constructing interpolative decompositions, a type of low-rank approximation that preserves matrix properties and reduces memory usage, with demonstrated superior performance.

Contribution

The paper presents novel, optimized algorithms for interpolative decomposition that outperform existing methods in efficiency and accuracy.

Findings

Algorithms outperform current state-of-the-art methods

Preserves matrix properties like sparsity and non-negativity

Reduces memory usage in low-rank approximations

Abstract

Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix properties such as sparsity and non-negativity. It also helps save space in memory. In this work, we introduce two optimized algorithms to construct an interpolative decomposition along with numerical evidence that they outperform the current state of the art.