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PCA by Determinant Optimization has no Spurious Local Optima
- Publication Year :
- 2018
-
Abstract
- Principal component analysis (PCA) is an indispensable tool in many learning tasks that finds the best linear representation for data. 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. We apply a number of solvers for empirical confirmation.
- Subjects :
- Mathematics - Optimization and Control
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1803.04049
- Document Type :
- Working Paper