Classification of multivariate signals using the Hilbert transform and Riemannian geometry
Gemborn Nilsson, Martin LU
and Bernhardsson, Bo
LU
(2027)
In Signal Processing
250.
- Abstract
We describe two Hilbert transform-based methods for augmenting covariance matrices from multivariate signals. The two methods are shown to be isometric under the Riemannian affine-invariant metric on the manifold of symmetric/Hermitian positive definite matrices. The augmented representations distinguish cases that standard covariances clearly cannot and, when paired with a Riemannian minimum distance to mean classifier, improve classification of both synthetic data and real electroencephalography (EEG) data without introducing any extra hyperparameters. This novel combination of methods also significantly improves tangent space classifier accuracy on the same dataset, outperforming state-of-the-art classifiers with similarly sized... (More)
We describe two Hilbert transform-based methods for augmenting covariance matrices from multivariate signals. The two methods are shown to be isometric under the Riemannian affine-invariant metric on the manifold of symmetric/Hermitian positive definite matrices. The augmented representations distinguish cases that standard covariances clearly cannot and, when paired with a Riemannian minimum distance to mean classifier, improve classification of both synthetic data and real electroencephalography (EEG) data without introducing any extra hyperparameters. This novel combination of methods also significantly improves tangent space classifier accuracy on the same dataset, outperforming state-of-the-art classifiers with similarly sized parameter grids. We also examine how the augmented covariances interact with the minimum distance to mean classifier and show how multivariate cross-covariance functions behave under the Hilbert transform.
(Less)
- author
- Gemborn Nilsson, Martin
LU
and Bernhardsson, Bo
LU
- organization
- publishing date
- 2027-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- EEG classification, Hermitian positive definite matrices, Hilbert transform, Machine learning, Riemannian geometry
- in
- Signal Processing
- volume
- 250
- article number
- 110786
- publisher
- Elsevier
- external identifiers
-
- scopus:105044699732
- ISSN
- 0165-1684
- DOI
- 10.1016/j.sigpro.2026.110786
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2026 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license. http://creativecommons.org/licenses/by/4.0/
- id
- 1dbb6b7e-9e0a-4dc1-8c74-233ef2bc8b8b
- date added to LUP
- 2026-08-25 13:04:27
- date last changed
- 2026-09-28 10:11:04
@article{1dbb6b7e-9e0a-4dc1-8c74-233ef2bc8b8b,
abstract = {{<p>We describe two Hilbert transform-based methods for augmenting covariance matrices from multivariate signals. The two methods are shown to be isometric under the Riemannian affine-invariant metric on the manifold of symmetric/Hermitian positive definite matrices. The augmented representations distinguish cases that standard covariances clearly cannot and, when paired with a Riemannian minimum distance to mean classifier, improve classification of both synthetic data and real electroencephalography (EEG) data without introducing any extra hyperparameters. This novel combination of methods also significantly improves tangent space classifier accuracy on the same dataset, outperforming state-of-the-art classifiers with similarly sized parameter grids. We also examine how the augmented covariances interact with the minimum distance to mean classifier and show how multivariate cross-covariance functions behave under the Hilbert transform.</p>}},
author = {{Gemborn Nilsson, Martin and Bernhardsson, Bo}},
issn = {{0165-1684}},
keywords = {{EEG classification; Hermitian positive definite matrices; Hilbert transform; Machine learning; Riemannian geometry}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Signal Processing}},
title = {{Classification of multivariate signals using the Hilbert transform and Riemannian geometry}},
url = {{http://dx.doi.org/10.1016/j.sigpro.2026.110786}},
doi = {{10.1016/j.sigpro.2026.110786}},
volume = {{250}},
year = {{2027}},
}