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Finding dependencies between frequencies with the kernel cross-spectral density


Conference Paper


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

Department(s): Empirical Inference
Research Project(s): Medical and Neuroscientific Imaging
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1109/ICASSP.2011.5946735
Event Name: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2011)
Event Place: Praha, Czech Republic

Address: Piscataway, NJ, USA
Digital: 0
ISBN: 978-1-4577-0538-0
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web


  title = {Finding dependencies between frequencies with the kernel cross-spectral density},
  author = {Besserve, M. and Janzing, D. and Logothetis, NK. and Sch{\"o}lkopf, B.},
  pages = {2080-2083 },
  publisher = {IEEE},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Piscataway, NJ, USA},
  month = may,
  year = {2011},
  month_numeric = {5}