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An application of neighbourhoods in digraphs to the classification of binary dynamics
Univ Aberdeen, Inst Math, Aberdeen, Scotland..
Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia..
Riga Tech Univ, Riga Business Sch, Riga, Latvia..
Univ Aberdeen, Inst Math, Aberdeen, Scotland..
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2022 (English)In: NETWORK NEUROSCIENCE, ISSN 2472-1751, Vol. 6, no 2, p. 528-551Article in journal (Refereed) Published
Abstract [en]

A binary state on a graph means an assignment of binary values to its vertices. A time-dependent sequence of binary states is referred to as binary dynamics. We describe a method for the classification of binary dynamics of digraphs, using particular choices of closed neighbourhoods. Our motivation and application comes from neuroscience, where a directed graph is an abstraction of neurons and their connections, and where the simplification of large amounts of data is key to any computation. We present a topological/graph theoretic method for extracting information out of binary dynamics on a graph, based on a selection of a relatively small number of vertices and their neighbourhoods. We consider existing and introduce new real-valued functions on closed neighbourhoods, comparing them by their ability to accurately classify different binary dynamics. We describe a classification algorithm that uses two parameters and sets up a machine learning pipeline. We demonstrate the effectiveness of the method on simulated activity on a digital reconstruction of cortical tissue of a rat, and on a nonbiological random graph with similar density. Author Summary We explore the mathematical concept of a closed neighbourhood in a digraph in relation to classifying binary dynamics on a digraph, with particular emphasis on dynamics on a neuronal network. Using methodology based on selecting neighbourhoods and vectorising them by combinatorial and topological parameters, we experimented with a dataset implemented on the Blue Brain Project reconstruction of a neocortical column, and on an artificial neural network with random underlying graph implemented on the NEST simulator. In both cases the outcome was run through a support vector machine algorithm reaching classification accuracy of up to 88% for the Blue Brain Project data and up to 81% for the NEST data. This work is open to generalisation to other types of networks and the dynamics on them.

Place, publisher, year, edition, pages
MIT PRESS , 2022. Vol. 6, no 2, p. 528-551
Keywords [en]
Binary dynamics, Directed graphs, Graph and topological parameters, Neural networks, Signal classification
National Category
Computer Sciences Philosophy Infrastructure Engineering
Identifiers
URN: urn:nbn:se:kth:diva-316804DOI: 10.1162/netn_a_00228ISI: 000835479900009PubMedID: 35733429Scopus ID: 2-s2.0-85131254066OAI: oai:DiVA.org:kth-316804DiVA, id: diva2:1691315
Note

QC 20220830

Available from: 2022-08-30 Created: 2022-08-30 Last updated: 2022-08-30Bibliographically approved

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Riihimaki, Henri

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