Finding dependencies between frequencies with the kernel cross-spectral density
Cross-spectral density (CSD), is widely used to find linear dependency between two real or complex valued time series. We define a non-linear extension of this measure by mapping the time series into two Reproducing Kernel Hilbert Spaces. The dependency is quantified by the Hilbert Schmidt norm of a cross-spectral density operator between these two spaces. We prove that, by choosing a characteristic kernel for the mapping, this quantity detects any pairwise dependency between the time series. Then we provide a fast estimator for the Hilbert-Schmidt norm based on the Fast Fourier Trans form. We demonstrate the interest of this approach to quantify non-linear dependencies between frequency bands of simulated signals and intra-cortical neural recordings.
| Author(s): | Besserve, M. and Janzing, D. and Logothetis, NK. and Schölkopf, B. |
| Pages: | 2080-2083 |
| Year: | 2011 |
| Month: | May |
| Day: | 0 |
| Publisher: | IEEE |
| Bibtex Type: | Conference Paper (inproceedings) |
| Address: | Piscataway, NJ, USA |
| DOI: | 10.1109/ICASSP.2011.5946735 |
| Event Name: | IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2011) |
| Event Place: | Praha, Czech Republic |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| ISBN: | 978-1-4577-0538-0 |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
| Links: | |
BibTex
@inproceedings{7047,
title = {Finding dependencies between frequencies with the kernel cross-spectral density},
abstract = {Cross-spectral density (CSD), is widely used to find linear dependency between two real or complex valued time series. We define a non-linear extension of this measure by mapping the time series into two Reproducing Kernel Hilbert Spaces. The dependency is quantified by the Hilbert Schmidt norm of a cross-spectral density operator between these two spaces. We prove that, by choosing a characteristic kernel for the mapping, this quantity detects any pairwise dependency between the time series. Then we provide a fast estimator for the Hilbert-Schmidt norm based on the Fast Fourier Trans form. We demonstrate the interest of this approach to quantify non-linear dependencies between frequency bands of simulated signals and intra-cortical neural recordings.},
pages = {2080-2083 },
publisher = {IEEE},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
address = {Piscataway, NJ, USA},
month = may,
year = {2011},
slug = {7047},
author = {Besserve, M. and Janzing, D. and Logothetis, NK. and Sch{\"o}lkopf, B.},
month_numeric = {5}
}