Finding dependent and independent components from related data sets: A generalized canonical correlation analysis based method

Multiway canonical correlation analysis of brain data

Brain data recorded with electroencephalography (EEG), magnetoencephalography (MEG) and related techniques often have poor signal-to-noise ratios due to the presence of multiple competing sources and artifacts. A common remedy is to average responses over repeats of the same stimulus, but this is not applicable for temporally extended stimuli that are presented only once (speech, music, movies, natural sound). An alternative is to average responses over multiple subjects that were presented with identical stimuli, but differences in geometry of brain sources and sensors reduce the effectiveness of this solution. Multiway canonical correlation analysis (MCCA) brings a solution to this problem by allowing data from multiple subjects to be fused in such a way as to extract components common to all. This paper reviews the method, offers application examples that illustrate its effectiveness, and outlines the caveats and risks entailed by the method.

Including signal intensity increases the performance of blind source separation on brain imaging data

When analyzing brain imaging data, blind source separation (BSS) techniques critically depend on the level of dimensional reduction. If the reduction level is too slight, the BSS model would be overfitted and become unavailable. Thus, the reduction level must be set relatively heavy. This approach risks discarding useful information and crucially limits the performance of BSS techniques. In this study, a new BSS method that can work well even at a slight reduction level is presented. We proposed the concept of "signal intensity" which measures the significance of the source. Only picking the sources with significant intensity, the new method can avoid the overfitted solutions which are nonexistent artifacts. This approach enables the reduction level to be set slight and retains more useful dimensions in the preliminary reduction. Comparisons between the new and conventional algorithms were performed on both simulated and real data.

Spatio-chromatic adaptation via higher-order canonical correlation analysis of natural images

Independent component and canonical correlation analysis are two general-purpose statistical methods with wide applicability. In neuroscience, independent component analysis of chromatic natural images explains the spatio-chromatic structure of primary cortical receptive fields in terms of properties of the visual environment. Canonical correlation analysis explains similarly chromatic adaptation to different illuminations. But, as we show in this paper, neither of the two methods generalizes well to explain both spatio-chromatic processing and adaptation at the same time. We propose a statistical method which combines the desirable properties of independent component and canonical correlation analysis: It finds independent components in each data set which, across the two data sets, are related to each other via linear or higher-order correlations. The new method is as widely applicable as canonical correlation analysis, and also to more than two data sets. We call it higher-order canonical correlation analysis. When applied to chromatic natural images, we found that it provides a single (unified) statistical framework which accounts for both spatio-chromatic processing and adaptation. Filters with spatio-chromatic tuning properties as in the primary visual cortex emerged and corresponding-colors psychophysics was reproduced reasonably well. We used the new method to make a theory-driven testable prediction on how the neural response to colored patterns should change when the illumination changes. We predict shifts in the responses which are comparable to the shifts reported for chromatic contrast habituation.