A literature survey of matrix methods for data science

TL;DR

This survey reviews how matrix methods and numerical linear algebra techniques are essential for advancing data science, emphasizing recent developments like randomized algorithms and high-dimensional data handling.

Contribution

It provides a comprehensive overview of matrix methods in data science, highlighting recent innovations and their impact on computational efficiency and effectiveness.

Findings

Matrix factorizations are fundamental in data analysis.

Randomized algorithms significantly improve computational speed.

Numerical linear algebra techniques are integral to deep learning.

Abstract

Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial role in enabling and improving data science computations with many new developments being fueled by the availability of data and computing resources. We highlight the role of various different factorizations and the power of changing the representation of the data as well as discussing topics such as randomized algorithms, functions of matrices, and high-dimensional problems. We briefly touch upon the role of techniques from numerical linear algebra used within deep learning.