@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}
}