Hierarchical Multi-resolution Mesh Networks for Brain Decoding

We propose a new framework, called Hierarchical Multi-resolution Mesh Networks (HMMNs), which establishes a set of brain networks at multiple time resolutions of fMRI signal to represent the underlying cognitive process. The suggested framework, first, decomposes the fMRI signal into various frequency subbands using wavelet transforms. Then, a brain network, called mesh network, is formed at each subband by ensembling a set of local meshes. The locality around each anatomic region is defined with respect to a neighborhood system based on functional connectivity. The arc weights of a mesh are estimated by ridge regression formed among the average region time series. In the final step, the adjacency matrices of mesh networks obtained at different subbands are ensembled for brain decoding under a hierarchical learning architecture, called, fuzzy stacked generalization (FSG). Our results on Human Connectome Project task-fMRI dataset reflect that the suggested HMMN model can successfully discriminate tasks by extracting complementary information obtained from mesh arc weights of multiple subbands. We study the topological properties of the mesh networks at different resolutions using the network measures, namely, node degree, node strength, betweenness centrality and global efficiency; and investigate the connectivity of anatomic regions, during a cognitive task. We observe significant variations among the network topologies obtained for different subbands. We, also, analyze the diversity properties of classifier ensemble, trained by the mesh networks in multiple subbands and observe that the classifiers in the ensemble collaborate with each other to fuse the complementary information freed at each subband. We conclude that the fMRI data, recorded during a cognitive task, embed diverse information across the anatomic regions at each resolution.Comment: 18 page

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Interplay between functional connectivity and scale-free dynamics in intrinsic fMRI networks

International audienceStudies employing functional connectivity-type analyses have established that sponta-neous fluctuations in functional magnetic resonance imaging (fMRI) signals are orga-nized within large-scale brain networks. Meanwhile, fMRI signals have been shown to exhibit 1/f-type power spectra – a hallmark of scale-free dynamics. We studied the interplay between functional connectivity and scale-free dynamics in fMRI signals, utilizing the fractal connectivity framework – a multivariate extension of the univari-ate fractional Gaussian noise model, which relies on a wavelet formulation for robust parameter estimation. We applied this framework to fMRI data acquired from healthy young adults at rest and performing a visual detection task. First, we found that scale-invariance existed beyond univariate dynamics, being present also in bivariate cross-temporal dynamics. Second, we observed that frequencies within the scale-free range do not contribute evenly to inter-regional connectivity, with a systematically stronger contribution of the lowest frequencies, both at rest and during task. Third, in addition to a decrease of the Hurst exponent and inter-regional correlations, task performance modified cross-temporal dynamics, inducing a larger contribution of the highest fre-quencies within the scale-free range to global correlation. Lastly, we found that across individuals, a weaker task modulation of the frequency contribution to inter-regional Rev.#1, Q

Learning parametric dictionaries for graph signals

In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Dynamic brain networks explored by structure-revealing methods

The human brain is a complex system able to continuously adapt. How and where brain activity is modulated by behavior can be studied with functional magnetic resonance imaging (fMRI), a non-invasive neuroimaging technique with excellent spatial resolution and whole-brain coverage. FMRI scans of healthy adults completing a variety of behavioral tasks have greatly contributed to our understanding of the functional role of individual brain regions. However, by statistically analyzing each region independently, these studies ignore that brain regions act in concert rather than in unison. Thus, many studies since have instead examined how brain regions interact. Surprisingly, structured interactions between distinct brain regions not only occur during behavioral tasks but also while a subject rests quietly in the MRI scanner. Multiple groups of regions interact very strongly with each other and not only do these groups bear a striking resemblance to the sets of regions co-activated in tasks, but many of these interactions are also progressively disrupted in neurological diseases. This suggests that spontaneous fluctuations in activity can provide novel insights into fundamental organizing principles of the human brain in health and disease. Many techniques to date have segregated regions into spatially distinct networks, which ignores that any brain region can take part in multiple networks across time. A more natural view is to estimate dynamic brain networks that allow flexible functional interactions (or connectivity) over time. The estimation and analysis of such dynamic functional interactions is the subject of this dissertation. We take the perspective that dynamic brain networks evolve in a low-dimensional space and can be described by a small number of characteristic spatiotemporal patterns. Our proposed approaches are based on well-established statistical methods, such as principal component analysis (PCA), sparse matrix decompositions, temporal clustering, as well as a multiscale analysis by novel graph wavelet designs. We adapt and extend these methods to the analysis of dynamic brain networks. We show that PCA and its higher-order equivalent can identify co-varying functional interactions, which reveal disturbed dynamic properties in multiple sclerosis and which are related to the timing of stimuli for task studies, respectively. Further we show that sparse matrix decompositions provide a valid alternative approach to PCA and improve interpretability of the identified patterns. Finally, assuming an even simpler low-dimensional space and the exclusive temporal expression of individual patterns, we show that specific transient interactions of the medial prefrontal cortex are disturbed in aging and relate to impaired memory

Graph Spectral Characterization of Brain Cortical Morphology

The human brain cortical layer has a convoluted morphology that is unique to each individual. Characterization of the cortical morphology is necessary in longitudinal studies of structural brain change, as well as in discriminating individuals in health and disease. A method for encoding the cortical morphology in the form of a graph is presented. The design of graphs that encode the global cerebral hemisphere cortices as well as localized cortical regions is proposed. Spectral metrics derived from these graphs are then studied and proposed as descriptors of cortical morphology. As proof-of-concept of their applicability in characterizing cortical morphology, the metrics are studied in the context of hemispheric asymmetry as well as gender dependent discrimination of cortical morphology.Comment: arXiv admin note: substantial text overlap with arXiv:1810.1033