Title :
Finding dependencies between frequencies with the kernel cross-spectral density
Author :
Besserve, M. ; Janzing, D. ; Logothetis, N.K. ; Schölkopf, B.
Author_Institution :
Max Planck Inst. for Biol. Cybern., Tubingen, Germany
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.
Keywords :
Hilbert spaces; fast Fourier transforms; signal processing; time series; Hilbert-Schmidt norm; complex valued time series; cross-spectral density; fast Fourier transform; kernel Hilbert space; kernel cross-spectral density; Band pass filters; Fast Fourier transforms; Frequency estimation; Hilbert space; Kernel; Random variables; Time series analysis; Reproducing kernel; cross-frequency interactions; cross-spectrum; higher order statistics;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on
Conference_Location :
Prague
Print_ISBN :
978-1-4577-0538-0
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2011.5946735