An Application of Neighbourhoods in Digraphs to the Classification of Binary Dynamics

Network Neuroscience 2022
Pedro Conceição, Dejan Govc, Jānis Lazovskis, Ran Levi, Henri Riihimaki, Jason P. Smith

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.

DOI
10.1162/netn_a_00228
Hyperlink
https://direct.mit.edu/netn/article/6/2/528/109067/

Conceição, P., Govc, D., Lazovskis, J., Levi, R., Riihimaki, H., Smith, J. An Application of Neighbourhoods in Digraphs to the Classification of Binary Dynamics. Network Neuroscience, 2022, Vol. 6, No. 2, pp. 528-551. e-ISSN 2472-1751. Available from: doi:10.1162/netn_a_00228

Publication language
English (en)