title: Genuine cross-correlations: which surrogate based measure reproduces analytical results best?
abstract: The analysis of short segments of noise-contaminated, multivariate real world data constitutes a challenge. In this paper we compare several techniques of analysis, which are supposed to correctly extract the amount of genuine cross-correlations from a multivariate data set. In order to test for the quality of their performance we derive time series from a linear test model, which allows the analytical derivation of genuine correlations. We compare the numerical estimates of the four measures with the analytical results for different correlation pattern. In the bivariate case all but one measure performs similarly well. However, in the multivariate case measures based on the eigenvalues of the equal-time cross-correlation matrix do not extract exclusively information about the amount of genuine correlations, but they rather reflect the spatial organization of the correlation pattern. This may lead to failures when interpreting the numerical results as illustrated by an application to three electroencephalographic recordings of three patients suffering from pharmacoresistent epilepsy.
authors.affiliation: Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, 62209 Cuernavaca, Morelos, Mexico.
authors.forename: Arlex Oscar
authors.initials: AO
authors.lastname: Marín García
authors.forename: Markus Franziskus
authors.initials: MF
authors.lastname: Müller
authors.forename: Kaspar
authors.initials: K
authors.lastname: Schindler
authors.forename: Christian
authors.initials: C
authors.lastname: Rummel
mesh_terms: D004569:Electroencephalography / Q000379:methods; D016014:Linear Models; D008959:Models, Neurological; D012815:Signal Processing, Computer-Assisted; D013223:Statistics as Topic / Q000379:methods; D013997:Time Factors
keywords: EEG; Epilepsy; Genuine correlations; Multivariate analysis; Random correlations