An application of neighbourhoods in digraphs to the classification of binary dynamics.
An application of neighbourhoods in digraphs to the classification of binary dynamics.
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DOI：
10.1162/netn_a_00228
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发表时间：
2022-06
影响因子：
4.7
通讯作者：
Smith, Jason P.
中科院分区：
文献类型：
--
作者：
Conceicao, Pedro;Govc, Dejan;Lazovskis, Janis;Levi, Ran;Riihimaki, Henri;Smith, Jason P.
关键词：
图上的二进制状态意味着将二进制值分配给它的顶点。与时间相关的二进制状态序列称为二进制动力学。我们描述了一种利用封闭邻域的特殊选择来对有向图的二元动态进行分类的方法。我们的动机和应用来自神经科学，有向图是神经元及其联系的抽象，而大量数据的简化是任何计算的关键。我们提出了一种拓扑/图论方法，用于从图的二进制动态中提取信息，该方法基于相对较少的顶点及其邻域的选择。我们考虑了闭邻域上的现有实值函数，并引入了新的实值函数，通过比较它们对不同二元动力学的精确分类的能力。我们描述了一种使用两个参数并建立机器学习流水线的分类算法。我们在一个大鼠皮质组织的数字重建和具有相似密度的非生物随机图上展示了该方法在模拟活动上的有效性。我们探索有向图中封闭邻域的数学概念，与有向图上的二元动力学分类有关，特别强调神经元网络上的动力学。使用基于选择邻域并通过组合和拓扑参数对其进行矢量化的方法，我们使用在Blue Brain Project上实现的新皮质柱重建的数据集和在Nest模拟器上实现的具有随机底层图形的人工神经网络进行了实验。在这两种情况下，结果都通过支持向量机算法运行，蓝脑项目数据的分类准确率高达88%，Nest数据的分类准确率高达81%。这项工作可以推广到其他类型的网络及其上的动力学。
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. 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.
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影响因子：
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