Time Series-Based Affinity Matrix Construction for Graph Analysis: VB Index and ReHo Calculation
Author
Christine Farrugia
Title
Time Series-Based Affinity Matrix Construction for Graph Analysis: VB Index and ReHo Calculation
Description
This notebook generates a time series for each vertex in a graph, constructs an affinity matrix using modified Pearson correlation between vertices, and calculates the VB index and ReHo value for the graph.
Category
Academic Articles & Supplements
Keywords
Spectral graph theory, regional homogeneity, VB index
URL
http://www.notebookarchive.org/2023-05-4m1mlah/
DOI
https://notebookarchive.org/2023-05-4m1mlah
Date Added
2023-05-10
Date Last Modified
2023-05-10
File Size
144.63 kilobytes
Supplements
Rights
CC BY 4.0
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Time Series-Based Affinity Matrix Construction for Graph Analysis: VB Index and ReHo Calculation
Christine Farrugia
What the notebook doesThis notebook constructs an affinity matrix for the graph below by generating a time series for each of its vertices, then (following the method described in [Bajada et al, NeuroImage 221:117140 (2020)]) using the modified Pearson correlation between the time series of any two vertices as the weight of the edge joining said vertices. The affinity matrix is tailored to the graph, in the sense that vertices not sharing an edge have orthogonal time series (and a corresponding [effectively] zero entry in the affinity matrix).Once the affinity matrix has been obtained, the Vogt-Bailey (VB) index [Bajada et al, NeuroImage 221:117140 (2020)] and Regional Homogeneity (ReHo) value [Zang et al, NeuroImage 22(1):394 (2004)] are calculated.The notebook can easily be modified to accommodate other graph designs. 
Publication
Publication
This notebook was prepared as part of the research work outlined in the article Local gradient analysis of human brain function using the Vogt-Bailey Index.
doi: https://doi.org/10.1101/2022.10.14.511925
Authors: C. Farrugia, P. Galdi, I. Arenzana Irazu, K. Scerri, C. J. Bajada
Abstract: In this work, we take a closer look at the Vogt-Bailey (VB) index, proposed in [Bajada et al, NeuroImage 221:117140 (2020)] as a tool for studying local functional homogeneity in the human cortex. We interpret the VB index in terms of the minimum ratio cut, a parameter that indicates whether a network can easily be disconnected into two parts having a comparable number of nodes. In our case, the nodes of the network consist of a brain vertex/voxel and its nearest neighbours, and a given edge is weighted according to the affinity of the nodes it connects (as reflected by the modified Pearson correlation between their fMRI time series). Consequently, the minimum ratio cut quantifies the degree of small-scale similarity in brain activity: the greater the similarity, the `heavier’ the edges and the more difficult it is to disconnect the network, hence the higher the value of the minimum ratio cut. We compare the performance of the VB index with that of the Regional Homogeneity (ReHo) algorithm, commonly used to assess whether voxels in close proximity have synchronised fMRI signals, and find that the VB index is uniquely placed to detect sharp changes in the (local) functional organization of the human cortex.
doi: https://doi.org/10.1101/2022.10.14.511925
Authors: C. Farrugia, P. Galdi, I. Arenzana Irazu, K. Scerri, C. J. Bajada
Abstract: In this work, we take a closer look at the Vogt-Bailey (VB) index, proposed in [Bajada et al, NeuroImage 221:117140 (2020)] as a tool for studying local functional homogeneity in the human cortex. We interpret the VB index in terms of the minimum ratio cut, a parameter that indicates whether a network can easily be disconnected into two parts having a comparable number of nodes. In our case, the nodes of the network consist of a brain vertex/voxel and its nearest neighbours, and a given edge is weighted according to the affinity of the nodes it connects (as reflected by the modified Pearson correlation between their fMRI time series). Consequently, the minimum ratio cut quantifies the degree of small-scale similarity in brain activity: the greater the similarity, the `heavier’ the edges and the more difficult it is to disconnect the network, hence the higher the value of the minimum ratio cut. We compare the performance of the VB index with that of the Regional Homogeneity (ReHo) algorithm, commonly used to assess whether voxels in close proximity have synchronised fMRI signals, and find that the VB index is uniquely placed to detect sharp changes in the (local) functional organization of the human cortex.
Useful functions
Useful functions
Construct the graph
Construct the graph
Calculate the VB index
Calculate the VB index
Calculate Kendall' s Coefficient of Concordance for the ReHo metric
Calculate Kendall' s Coefficient of Concordance for the ReHo metric
Cite this as: Christine Farrugia, "Time Series-Based Affinity Matrix Construction for Graph Analysis: VB Index and ReHo Calculation" from the Notebook Archive (2023), https://notebookarchive.org/2023-05-4m1mlah
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