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...

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Bibliographic Details
Published in2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 2080 - 2083
Main Authors Besserve, M., Janzing, D., Logothetis, N. K., Scholkopf, B.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2011
Subjects
Band pass filters
cross-frequency interactions
cross-spectrum
Fast Fourier transforms
Frequency estimation
higher order statistics
Hilbert space
Kernel
Random variables
Reproducing kernel
Time series analysis
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Summary: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.
ISBN:9781457705380
1457705389
ISSN:1520-6149
2379-190X
DOI:10.1109/ICASSP.2011.5946735