Dataset Information

Guided graph spectral embedding: Application to the C. elegans connectome.

ABSTRACT: Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-for example, based on wavelets and Slepians-that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show that these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows us to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode's neural network in terms of functionality and importance of cells. Compared with Laplacian embedding, the guided approach, focused on a certain class of cells (sensory neurons, interneurons, or motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low- or high-order processing functions.

SUBMITTER: Petrovic M

PROVIDER: S-EPMC6663470 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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Publications

Guided graph spectral embedding: Application to the <i>C. elegans</i> connectome.

Petrovic Miljan M Bolton Thomas A W TAW Preti Maria Giulia MG Liégeois Raphaël R Van De Ville Dimitri D

Network neuroscience (Cambridge, Mass.) 20190701 3

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-for example, based on wavelets and Slepians-that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modi ...[more]

PMID: 31410381

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Project description:BACKGROUND: Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices) and interactions (edges) that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. RESULTS: Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis) and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors). CONCLUSION: SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is available upon request.

Dataset Information

Guided graph spectral embedding: Application to the C. elegans connectome.

Publications

Guided graph spectral embedding: Application to the <i>C. elegans</i> connectome.

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