Dataset Information

The Laplacian spectrum of neural networks.

ABSTRACT: The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks. Many popular graph metrics, however, encode average properties of individual network elements. Complementing these "conventional" graph metrics, the eigenvalue spectrum of the normalized Laplacian describes a network's structure directly at a systems level, without referring to individual nodes or connections. In this paper, the Laplacian spectra of the macroscopic anatomical neuronal networks of the macaque and cat, and the microscopic network of the Caenorhabditis elegans were examined. Consistent with conventional graph metrics, analysis of the Laplacian spectra revealed an integrative community structure in neural brain networks. Extending previous findings of overlap of network attributes across species, similarity of the Laplacian spectra across the cat, macaque and C. elegans neural networks suggests a certain level of consistency in the overall architecture of the anatomical neural networks of these species. Our results further suggest a specific network class for neural networks, distinct from conceptual small-world and scale-free models as well as several empirical networks.

SUBMITTER: de Lange SC

PROVIDER: S-EPMC3888935 | biostudies-literature | 2014 Jan

REPOSITORIES: biostudies-literature

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The Laplacian spectrum of neural networks.

de Lange Siemon C SC de Reus Marcel A MA van den Heuvel Martijn P MP

Frontiers in computational neuroscience 20140113

The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks. Many popular graph metrics, however, encode average properties of individual network elements. Complementing these "conventional" graph metrics, the eigenvalue spectrum of the normalized Laplacian describes a network's structure directly at a systems level, without referring to individual nodes or co ...[more]

PMID: 24454286

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Project description:Resting-state functional magnetic resonance imaging (rs-fMRI) data are 4-dimensional volumes (3-space + 1-time) that have been posited to reflect the underlying mechanisms of information exchange between brain regions, thus making it an attractive modality to develop diagnostic biomarkers of brain dysfunction. The enormous success of deep learning in computer vision has sparked recent interest in applying deep learning in neuroimaging. But the dimensionality of rs-fMRI data is too high (~20 M), making it difficult to meaningfully process the data in its raw form for deep learning experiments. It is currently not clear how the data should be engineered to optimally extract the time information, and whether combining different representations of time could provide better results. In this paper, we explored various transformations that retain the full spatial resolution by summarizing the temporal dimension of the rs-fMRI data, therefore making it possible to train a full three-dimensional convolutional neural network (3D-CNN) even on a moderately sized [~2,000 from Autism Brain Imaging Data Exchange (ABIDE)-I and II] data set. These transformations summarize the activity in each voxel of the rs-fMRI or that of the voxel and its neighbors to a single number. For each brain volume, we calculated regional homogeneity, the amplitude of low-frequency fluctuations, the fractional amplitude of low-frequency fluctuations, degree centrality, eigenvector centrality, local functional connectivity density, entropy, voxel-mirrored homotopic connectivity, and auto-correlation lag. We trained the 3D-CNN on a publically available autism dataset to classify the rs-fMRI images as being from individuals with autism spectrum disorder (ASD) or from healthy controls (CON) at an individual level. We attained results competitive on this task for a combined ABIDE-I and II datasets of ~66%. When all summary measures were combined the result was still only as good as that of the best single measure which was regional homogeneity (ReHo). In addition, we also applied the support vector machine (SVM) algorithm on the same dataset and achieved comparable results, suggesting that 3D-CNNs could not learn additional information from these temporal transformations that were more useful to differentiate ASD from CON.

Dataset Information

The Laplacian spectrum of neural networks.

Publications

The Laplacian spectrum of neural networks.

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