Discrete regression methods on the cone of positive-definite matrices

Nicolas Boumal, P. A. Absil

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

We consider the problem of fitting a discrete curve to time-labeled data points on the set ℙn of all n-by-n symmetric positive-definite matrices. The quality of a curve is measured by a weighted sum of a term that penalizes its lack of fit to the data and a regularization term that penalizes speed and acceleration. The corresponding objective function depends on the choice of a Riemannian metric on ℙn. We consider the Euclidean metric, the Log-Euclidean metric and the affine-invariant metric. For each, we derive a numerical algorithm to minimize the objective function. We compare these in terms of reliability and speed, and we assess the visual appearance of the solutions on examples for n = 2. Notably, we find that the Log-Euclidean and the affine-invariant metrics tend to yield similar - and sometimes identical - results, while the former allows for much faster and more reliable algorithms than the latter.

Original languageEnglish (US)
Title of host publication2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Pages4232-4235
Number of pages4
DOIs
StatePublished - 2011
Event36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic
Duration: May 22 2011May 27 2011

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
Country/TerritoryCzech Republic
CityPrague
Period5/22/115/27/11

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Positive-definite matrices
  • Riemannian metrics
  • finite differences
  • non-parametric regression

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