A continuous-time quantum walk kernel for unattributed graphs

Kernel methods provide a way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. In this paper, we propose a novel kernel on unattributed graphs where the structure is characterized through the evolution of a continuous-time quantum walk. More precisely, given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic. With this new graph to hand, we compute the density operators of the quantum systems representing the evolutions of two suitably defined quantum walks. Finally, we define the kernel between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Manifold learning and the quantum Jensen-Shannon divergence kernel

The quantum Jensen-Shannon divergence kernel [1] was recently introduced in the context of unattributed graphs where it was shown to outperform several commonly used alternatives. In this paper, we study the separability properties of this kernel and we propose a way to compute a low-dimensional kernel embedding where the separation of the different classes is enhanced. The idea stems from the observation that the multidimensional scaling embeddings on this kernel show a strong horseshoe shape distribution, a pattern which is known to arise when long range distances are not estimated accurately. Here we propose to use Isomap to embed the graphs using only local distance information onto a new vectorial space with a higher class separability. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Where do bright ideas occur in our brain? Meta-analytic evidence from neuroimaging studies of domain-specific creativity

Many studies have assessed the neural underpinnings of creativity, failing to find a clear anatomical localization. We aimed to provide evidence for a multi-componential neural system for creativity. We applied a general activation likelihood estimation (ALE) meta-analysis to 45 fMRI studies. Three individual ALE analyses were performed to assess creativity in different cognitive domains (Musical, Verbal, and Visuo-spatial). The general ALE revealed that creativity relies on clusters of activations in the bilateral occipital, parietal, frontal, and temporal lobes. The individual ALE revealed different maximal activation in different domains. Musical creativity yields activations in the bilateral medial frontal gyrus, in the left cingulate gyrus, middle frontal gyrus, and inferior parietal lobule and in the right postcentral and fusiform gyri. Verbal creativity yields activations mainly located in the left hemisphere, in the prefrontal cortex, middle and superior temporal gyri, inferior parietal lobule, postcentral and supramarginal gyri, middle occipital gyrus, and insula. The right inferior frontal gyrus and the lingual gyrus were also activated. Visuo-spatial creativity activates the right middle and inferior frontal gyri, the bilateral thalamus and the left precentral gyrus. This evidence suggests that creativity relies on multi-componential neural networks and that different creativity domains depend on different brain regions.

To move or not to move, that is the question! Body schema and non-action oriented body representations:an fMRI meta-analytic study

Many studies have attempted to identify the different cognitive components of body representation (BR). Due to methodological issues, the data reported in these studies are often confusing. Here we summarize the fMRI data from previous studies and explore the possibility of a neural segregation between BR supporting actions (body-schema, BS) or not (non-oriented-to-action-body-representation, NA). We performed a general activation likelihood estimation meta-analysis of 59 fMRI experiments and two individual meta-analyses to identify the neural substrates of different BR. Body processing involves a wide network of areas in occipital, parietal, frontal and temporal lobes. NA selectively activates the somatosensory primary cortex and the supramarginal gyrus. BS involves the primary motor area and the right extrastriate body area. Our data suggest that motor information and recognition of body parts are fundamental to build BS. Instead, sensory information and processing of the egocentric perspective are more important for NA. In conclusion, our results strongly support the idea that different and segregated neural substrates are involved in body representations orient or not to actions.