# Study of Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations in Data Science

## TL;DR

This paper introduces CoR-UTV, a novel randomized matrix decomposition method that efficiently computes low-rank approximations of large matrices with fewer data passes, suitable for modern computational platforms.

## Contribution

The paper proposes the CoR-UTV algorithm, a new randomized low-rank matrix decomposition technique with variants, improving efficiency and robustness in data science applications.

## Key findings

- CoR-UTV requires only a few passes over the data.
- It runs in $O(mnk)$ operations, suitable for large matrices.
- Simulations show CoR-UTV outperforms existing methods.

## Abstract

In this work, a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV) decomposition along with a CoR-UTV variant aided by the power method technique is proposed. CoR-UTV computes an approximation to a low-rank input matrix by making use of random sampling schemes. Given a large and dense matrix of size $m\times n$ with numerical rank $k$, where $k \ll \text{min} \{m,n\}$, CoR-UTV requires a few passes over the data, and runs in $O(mnk)$ floating-point operations. Furthermore, CoR-UTV can exploit modern computational platforms and can be optimized for maximum efficiency. CoR-UTV is also applied for solving robust principal component analysis problems. Simulations show that CoR-UTV outperform existing approaches.