Hand somatosensory subcortical and cortical sources assessed by functional source separation:an EEG study

We propose a novel electroencephalographic application of a recently developed cerebral source extraction method (Functional Source Separation, FSS), which starts from extracranial signals and adds a functional constraint to the cost function of a basic independent component analysis model without requiring solutions to be independent. Five ad-hoc functional constraints were used to extract the activity reflecting the temporal sequence of sensory information processing along the somatosensory pathway in response to the separate left and right median nerve galvanic stimulation. Constraints required only the maximization of the responsiveness at specific latencies following sensory stimulation, without taking into account that any frequency or spatial information. After source extraction, the reliability of identified FS was assessed based on the position of single dipoles fitted on its retroprojected signals and on a discrepancy measure. The FS positions were consistent with previously reported data (two early subcortical sources localized in the brain stem and thalamus, the three later sources in cortical areas), leaving negligible residual activity at the corresponding latencies. The high-frequency component of the oscillatory activity (HFO) of the extracted component was analyzed. The integrity of the low amplitude HFOs was preserved for each FS. On the basis of our data, we suggest that FSS can be an effective tool to investigate the HFO behavior of the different neuronal pools, recruited at successive times after median nerve galvanic stimulation. As FSs are reconstructed along the entire experimental session, directional and dynamic HFO synchronization phenomena can be studied.

Unfolding kernel embeddings of graphs:enhancing class separation through manifold learning

In this paper, we investigate the use of manifold learning techniques to enhance the separation properties of standard graph kernels. The idea stems from the observation that when we perform multidimensional scaling on the distance matrices extracted from the kernels, the resulting data tends to be clustered along a curve that wraps around the embedding space, a behavior that suggests that long range distances are not estimated accurately, resulting in an increased curvature of the embedding space. Hence, we propose to use a number of manifold learning techniques to compute a low-dimensional embedding of the graphs in an attempt to unfold the embedding manifold, and increase the class separation. We perform an extensive experimental evaluation on a number of standard graph datasets using the shortest-path (Borgwardt and Kriegel, 2005), graphlet (Shervashidze et al., 2009), random walk (Kashima et al., 2003) and Weisfeiler-Lehman (Shervashidze et al., 2011) kernels. We observe the most significant improvement in the case of the graphlet kernel, which fits with the observation that neglecting the locational information of the substructures leads to a stronger curvature of the embedding manifold. On the other hand, the Weisfeiler-Lehman kernel partially mitigates the locality problem by using the node labels information, and thus does not clearly benefit from the manifold learning. Interestingly, our experiments also show that the unfolding of the space seems to reduce the performance gap between the examined kernels.