PCA by determinant optimisation has no spurious local optima

Author: 

Hauser, R
Eftekhari, A
Matzinger, H

Publication Date: 

19 July 2018

Journal: 

24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 2018, 19 - 23 August, 2018, London

Last Updated: 

2021-08-24T18:32:48.11+01:00

DOI: 

10.1145/3219819.3220069

page: 

1504-1511

abstract: 

Principal Component Analysis (PCA) finds the best linear representation for data and is an indispensable tool in many learning tasks. Classically, principal components of a dataset are interpreted as the directions that preserve most of its “energy”, an interpretation that is theoretically underpinned by the celebrated Eckart-Young-Mirsky Theorem. There are yet other ways of interpreting PCA that are rarely exploited in practice, largely because it is not known how to reliably solve the corresponding non-convex optimisation programs. In this paper, we consider one such interpretation of principal components as the directions that preserve most of the “volume” of the dataset. Our main contribution is a theorem that shows that the corresponding non-convex program has no spurious local optima, and is therefore amenable to many convex solvers. We also confirm our findings numerically.

Symplectic id: 

853002

Submitted to ORA: 

Submitted

Publication Type: 

Conference Paper

ISBN-13: 

9781450355520