Temporal kernel CCA and its application in multimodal neuronal data analysis

Felix Biebmann, Frank C. Meinecke, Arthur Gretton, Alexander Rauch, Gregor Rainer, Nikos K. Logothetis, Klaus Robert Müller

Research output: Contribution to journalArticlepeer-review

77 Citations (Scopus)


Data recorded from multiple sources sometimes exhibit non-instantaneous couplings. For simple data sets, cross-correlograms may reveal the coupling dynamics. But when dealing with high-dimensional multivariate data there is no such measure as the crosscorrelogram. We propose a simple algorithm based on Kernel Canonical Correlation Analysis (kCCA) that computes a multivariate temporal filter which links one data modality to another one. The filters can be used to compute a multivariate extension of the crosscorrelogram, the canonical correlogram, between data sources that have different dimensionalities and temporal resolutions. The canonical correlogram reflects the coupling dynamics between the two sources. The temporal filter reveals which features in the data give rise to these couplings and when they do so. We present results from simulations and neuroscientific experiments showing that tkCCA yields easily interpretable temporal filters and correlograms. In the experiments, we simultaneously performed electrode recordings and functional magnetic resonance imaging (fMRI) in primary visual cortex of the non-human primate. While electrode recordings reflect brain activity directly, fMRI provides only an indirect view of neural activity via the Blood Oxygen Level Dependent (BOLD) response. Thus it is crucial for our understanding and the interpretation of fMRI signals in general to relate them to direct measures of neural activity acquired with electrodes. The results computed by tkCCA confirm recent models of the hemodynamic response to neural activity and allow for a more detailed analysis of neurovascular coupling dynamics.

Original languageEnglish
Pages (from-to)5-27
Number of pages23
JournalMachine Learning
Issue number1-2
Publication statusPublished - 2010 May

Bibliographical note

Funding Information:
Acknowledgements This work has been supported by the Max-Planck Society and the Bernstein Cooperation (German Federal Ministry of Education and Science), Förderkennzeichen 01 GQ 0711. We would like to thank Paul von Bünau for sharing his MatGrid toolbox, without which we could not have performed the extensive simulations presented. Moreover, we thank Francis R Bach for sharing his kernel ICA code, we used parts of it for the multi-way kCCA implementation in Sect. 3.2.2. Furthermore, we thank Marc Augath and Axel Öltermann for their invaluable expertise at the scanner.


  • CCA
  • Canonical correlation analysis
  • KCCA
  • Neurovascular coupling
  • TkCCA

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence


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