[Paper Review] Comparison of Brain Networks with Unknown Correspondences

Sofia Ira Ktena, Sarah Parisot+2 more|arXiv (Cornell University)|Nov 15, 2016

Functional Brain Connectivity Studies3 citations

TL;DR

This paper proposes a graph edit distance (GED)-based method for comparing brain networks without requiring predefined node correspondences, integrating spatial constraints and local network features to improve similarity assessment. Evaluated on 30 unrelated subjects and 40 twin pairs, the method successfully distinguishes higher similarity in monozygotic twin networks compared to unrelated pairs, with optimal performance at α=0.5 and nn=7 neighbors.

ABSTRACT

Graph theory has drawn a lot of attention in the field of Neuroscience during the last decade, mainly due to the abundance of tools that it provides to explore the interactions of elements in a complex network like the brain. The local and global organization of a brain network can shed light on mechanisms of complex cognitive functions, while disruptions within the network can be linked to neurodevelopmental disorders. In this effort, the construction of a representative brain network for each individual is critical for further analysis. Additionally, graph comparison is an essential step for inference and classification analyses on brain graphs. In this work we explore a method based on graph edit distance for evaluating graph similarity, when correspondences between network elements are unknown due to different underlying subdivisions of the brain. We test this method on 30 unrelated subjects as well as 40 twin pairs and show that this method can accurately reflect the higher similarity between two related networks compared to unrelated ones, while identifying node correspondences.

Motivation & Objective

• To address the challenge of comparing brain networks when node correspondences are unknown due to individualized parcellations.
• To develop a similarity measure that preserves both structural and semantic information in brain graphs.
• To enable accurate comparison of brain networks across individuals with varying anatomical and functional subdivisions.
• To evaluate the method’s ability to detect biological similarity, such as between monozygotic twins, using graph distance metrics.

Proposed method

• The method uses a customized graph edit distance (GED) that accounts for spatial proximity and local connectivity patterns (node 'signature') to compute similarity between brain graphs.
• Node substitution costs are computed using a weighted combination of spatial distance (α) and edge feature similarity (g(·)), defined in Eq. 4.
• The algorithm enforces spatial constraints on edit operations, reducing computational complexity while preserving biologically meaningful correspondences.
• A multi-scale neighborhood approach considers up to nn neighbors for each node during substitution, improving robustness to anatomical variation.
• The method is applied to structural and functional networks derived from dMRI and fMRI data, using individualized parcellations with 50 regions.
• An efficient GED computation pipeline is implemented, with parameters tuned via cross-validation to maximize separation between related and unrelated networks.

Experimental results

Research questions

• RQ1 Can graph edit distance effectively compare brain networks when node correspondences are unknown due to individualized parcellations?
• RQ2 How well does the proposed GED method distinguish between monozygotic twin networks and unrelated subject pairs?
• RQ3 What is the optimal balance between spatial proximity and local connectivity features in the GED cost function for brain network comparison?
• RQ4 Does the method preserve meaningful node correspondences while computing graph similarity?
• RQ5 Can the GED-based similarity measure detect biologically relevant relationships, such as genetic relatedness, in brain network topology?

Key findings

• The method achieved significant separation between within-subject and between-subject graph distances on structural networks, with p < 0.001 for α = 0.5 and nn = 7.
• Monozygotic twin pairs showed significantly lower GED values than unrelated pairs on structural networks (p < 0.001), confirming the method's ability to detect genetic similarity.
• For functional networks, the best separation was achieved at α = 0.2, indicating that local connectivity features dominate similarity assessment in functional graphs.
• The method successfully identified node correspondences, with smaller node edit distances observed between monozygotic twins than between unrelated subjects, as visualized in Figure 5.
• Increasing the number of neighbors (nn) beyond 7 had minimal impact on GED, suggesting saturation of local feature informativeness.
• The optimal parameter set (α = 0.5, nn = 7) provided the best overall discrimination between related and unrelated networks across both structural and functional data.