Guided graph spectral embedding: Application to the C. elegans connectome
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 filt...
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doaj-87cb364a729c40d380d3d512106e0fa12020-11-24T22:11:35ZengThe MIT PressNetwork Neuroscience2472-17512019-07-013380782610.1162/netn_a_00084netn_a_00084Guided graph spectral embedding: Application to the C. elegans connectomeMiljan Petrovic0Thomas A. W. Bolton1Maria Giulia Preti2Raphaël Liégeois3Dimitri Van De Ville4Institute of Bioengineering, École Polytechnique Fédérale de Lausanne, Campus Biotech, Geneva, SwitzerlandInstitute of Bioengineering, École Polytechnique Fédérale de Lausanne, Campus Biotech, Geneva, SwitzerlandInstitute of Bioengineering, École Polytechnique Fédérale de Lausanne, Campus Biotech, Geneva, SwitzerlandInstitute of Bioengineering, École Polytechnique Fédérale de Lausanne, Campus Biotech, Geneva, SwitzerlandInstitute of Bioengineering, École Polytechnique Fédérale de Lausanne, Campus Biotech, Geneva, SwitzerlandGraph 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.https://www.mitpressjournals.org/doi/pdf/10.1162/netn_a_00084Spectral graph domainGraph embeddingLow-dimensional spaceFocused connectomics |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Miljan Petrovic Thomas A. W. Bolton Maria Giulia Preti Raphaël Liégeois Dimitri Van De Ville |
spellingShingle |
Miljan Petrovic Thomas A. W. Bolton Maria Giulia Preti Raphaël Liégeois Dimitri Van De Ville Guided graph spectral embedding: Application to the C. elegans connectome Network Neuroscience Spectral graph domain Graph embedding Low-dimensional space Focused connectomics |
author_facet |
Miljan Petrovic Thomas A. W. Bolton Maria Giulia Preti Raphaël Liégeois Dimitri Van De Ville |
author_sort |
Miljan Petrovic |
title |
Guided graph spectral embedding: Application to the C. elegans connectome |
title_short |
Guided graph spectral embedding: Application to the C. elegans connectome |
title_full |
Guided graph spectral embedding: Application to the C. elegans connectome |
title_fullStr |
Guided graph spectral embedding: Application to the C. elegans connectome |
title_full_unstemmed |
Guided graph spectral embedding: Application to the C. elegans connectome |
title_sort |
guided graph spectral embedding: application to the c. elegans connectome |
publisher |
The MIT Press |
series |
Network Neuroscience |
issn |
2472-1751 |
publishDate |
2019-07-01 |
description |
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. |
topic |
Spectral graph domain Graph embedding Low-dimensional space Focused connectomics |
url |
https://www.mitpressjournals.org/doi/pdf/10.1162/netn_a_00084 |
work_keys_str_mv |
AT miljanpetrovic guidedgraphspectralembeddingapplicationtothecelegansconnectome AT thomasawbolton guidedgraphspectralembeddingapplicationtothecelegansconnectome AT mariagiuliapreti guidedgraphspectralembeddingapplicationtothecelegansconnectome AT raphaelliegeois guidedgraphspectralembeddingapplicationtothecelegansconnectome AT dimitrivandeville guidedgraphspectralembeddingapplicationtothecelegansconnectome |
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1725805062539706368 |