Abstract
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 cross-correlogram. 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 cross-correlogram, 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.
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References
Akaho, S. (2001). A kernel method for canonical correlation analysis. In Proceedings of the international meeting of the psychometric society (IMPS). Berlin: Springer.
Anderson, T. W. (1958). An introduction to multivariate statistical analysis. New York: Wiley.
Bach, F. R., & Jordan, M. I. (2002). Kernel independent component analysis. Journal of Machine Learning Research.
Bach, F. R., & Jordan, M. I. (2006). A probabilistic interpretation of canonical correlation analysis. Technical Report.
Belitski, A., Gretton, A., Magri, C., Murayama, Y., Montemurro, M. A., Logothetis, N. K., & Panzeri, S. (2008). Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information. Journal of Neuroscience.
Blaschko, M. B., Lampert, C. H., & Gretton, A. (2008). Semi-supervised Laplacian regularization of kernel canonical correlation analysis. In W. Daelemans, B. Goethals, & K. Morik (Eds.), 19th European conference on machine learning. Antwerpen: Springer.
Buxton, R. B., Uludag, K., Dubowitz, D. J., & Liu, T. T. (2004). Modeling the hemodynamic response to brain activation. Neuroimage.
Friman, O., Borga, M., Lundberg, P., & Knutsson, H. (2002). Exploratory fMRI analysis by autocorrelation maximization. Neuroimage.
Friston, K. J., Mechelli, A., Turner, R., & Price, C. J. (2000). Nonlinear responses in fMRI: the Balloon model, Volterra kernels, and other hemodynamics. Neuroimage.
Fukumizu, K., Bach, F. R., & Gretton, A. (2007). Statistical consistency of kernel CCA. Journal of Machine Learning Research.
Goense, J. B. M., & Logothetis, N. K. (2008). Neurophysiology of the BOLD fMRI signal in awake monkeys. Current Biology.
Hardoon, D. R., Szedmak, S., & Shawe-Taylor, J. (2004). Canonical correlation analysis: an overview with application to learning methods. Neural Computation.
Hardoon, D. R., Mourao-Miranda, J., Brammer, M., & Shawe-Taylor, J. (2007). Unsupervised analysis of fMRI data using kernel canonical correlation. Neuroimage.
Harris, F. J. (1978). On then use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE.
Haynes, J. D., Sakai, K., Rees, G., Gilbert, S., Frith, C., & Passingham, R. E. (2007). Reading hidden intentions in the human brain. Current Biology.
Hotelling, H. (1936). Relations between two sets of variates. Biometrika.
Langleben, D. D., Loughead, J. W., Bilker, W. B., Ruparel, K., Childress, A. R., Busch, S. I., & Gur, R. C. (2005). Telling truth from lie in individual subjects with fast event-related fMRI. Human Brain Mapping.
Logothetis, N. K. (2008). What we can do and what we cannot do with fMRI. Nature.
Logothetis, N. K., & Wandell, B. A. (2004). Interpreting the bold signal. Annual Reviews of Physiology.
Logothetis, N. K., Guggenberger, H., Peled, S., & Pauls, J. (1999). Functional imaging of the monkey brain. Nature Neuroscience.
Logothetis, N. K., Pauls, J., Augath, M., Trinath, T., & Öltermann, A. (2001). Neurophysiological investigation of the basis of the fMRI signal. Nature.
Logothetis, N. K., Merkle, H., Augath, M., Trinath, T., & Ugurbil, K. (2002). Ultra high-resolution fMRI in monkeys with implanted RF coils. Neuron.
Macke, J. H., Zeck, G., & Bethge, M. (2008). Receptive fields without spike-triggering. In J. C. Platt, D. Koller, Y. Singer, & S. Roweis (Eds.), 21th neural information processing systems conference. Cambridge: MIT Press.
Müller, K. R., Mika, S., Rätsch, G., Tsuda, K., & Schölkopf, B. (2001). An introduction to kernel-based learning algorithms. IEEE Transactions on Neural Networks.
Norman, K. A., Polyn, S. M., Detre, G. J., & Haxby, J. V. (2006). Beyond mind-reading: multi-voxel pattern analysis of fMRI data. Trends in Cognitive Sciences.
Öltermann, A., Augath, M. A., & Logothetis, N. K. (2007). Simultaneous recording of neuronal signals and functional NMR imaging. Magnetic Resonance Imaging.
Ogawa, S., Lee, T. M., Nayak, A. S., & Glynn, P. (1990). Oxygenation-sensitive contrast in magnetic resonance image of rodent brain at high magnetic fields. Magnetic Resonance in Medicine.
Kettenring, J. R. (1971). Canonical analysis of several sets of variables. Biometrika.
Rauch, A., Rainer, G., Augath, M., Öltermann, A., & Logothetis, N. K. (2008a). Pharmacological MRI combined with electrophysiology in non-human primates: effects of lidocaine on primary visual cortex. Neuroimage.
Rauch, A., Rainer, G., & Logothetis, N. K. (2008b). The effect of a serotonin-induced dissociation between spiking and perisynaptic activity on bold functional MRI. Proceedings of the National Academy of Sciences.
Schölkopf, B., & Smola, A. J. (2001). Learning with kernels: support vector machines, regularization, optimization, and beyond. Adaptive computation and machine learning. Cambridge: MIT Press.
Shawe-Taylor, J., & Cristianini, N. (2004). Kernel methods for pattern analysis. Cambridge: Cambridge University Press.
SPM5. (2005). Statistical parametrical mapping toolbox. http://www.fil.ion.ucl.ac.uk/spm/.
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Editors: Nicolo Cesa-Bianchi, David R. Hardoon, and Gayle Leen.
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Bießmann, F., Meinecke, F.C., Gretton, A. et al. Temporal kernel CCA and its application in multimodal neuronal data analysis. Mach Learn 79, 5–27 (2010). https://doi.org/10.1007/s10994-009-5153-3
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DOI: https://doi.org/10.1007/s10994-009-5153-3