# Fast approximation of orthogonal matrices and application to PCA

arXiv: https://arxiv.org/abs/1907.08697 · HTML: https://mlsanity.com/paper/1907.08697/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [An iterative coordinate descent algorithm to compute sparse low-rank approximations](https://mlsanity.com/paper/2107.14608/) (2021)

## Abstract (arXiv)

We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended orthogonal Givens transformations, including Givens rotations as a special case. We propose an efficient greedy algorithm to solve such a problem and show that it strikes a balance between approximation accuracy and speed of computation. The approach is relevant to spectral methods and we illustrate its application to PCA.