[Paper Review] Kernel classification of connectomes based on earth mover's distance between graph spectra

Yulia Dodonova, Mikhail Belyaev+3 more|arXiv (Cornell University)|Nov 27, 2016

Advanced Graph Neural Networks10 references3 citations

TL;DR

This paper proposes a kernel-based machine learning approach for classifying structural connectomes using earth mover's distance (EMD) between normalized Laplacian spectral distributions. By computing EMD on eigenvalue distributions of brain networks, the method constructs a robust kernel for SVM classification, achieving an AUC of 0.71 in distinguishing autism spectrum disorder from typical development, outperforming baseline graph embedding methods.

ABSTRACT

In this paper, we tackle a problem of predicting phenotypes from structural connectomes. We propose that normalized Laplacian spectra can capture structural properties of brain networks, and hence graph spectral distributions are useful for a task of connectome-based classification. We introduce a kernel that is based on earth mover's distance (EMD) between spectral distributions of brain networks. We access performance of an SVM classifier with the proposed kernel for a task of classification of autism spectrum disorder versus typical development based on a publicly available dataset. Classification quality (area under the ROC-curve) obtained with the EMD-based kernel on spectral distributions is 0.71, which is higher than that based on simpler graph embedding methods.

Motivation & Objective

• To improve classification of brain connectomes by capturing structural network properties through spectral analysis.
• To develop a kernel method that effectively compares spectral distributions of brain networks without requiring density estimation.
• To evaluate the performance of the proposed EMD-based kernel on a real connectome dataset for autism spectrum disorder (ASD) classification.
• To demonstrate that spectral distributions of normalized Laplacian matrices encode meaningful structural differences between normal and pathological brain networks.

Proposed method

• The normalized Laplacian matrix is computed from weighted, undirected connectome graphs using adjacency and degree matrices.
• The eigenvalue distributions of the normalized Laplacian are extracted as spectral representations of brain networks.
• Earth mover's distance (EMD) is used to compute pairwise distances between empirical spectral distributions, capturing shape and location differences.
• A kernel matrix is constructed using the EMD distances, enabling the use of kernelized SVM for classification.
• The method is applied to a public connectome dataset with connectomes weighted by both streamline count and physical distance to reduce tractography bias.
• Classification performance is evaluated via 100-fold cross-validation with area under the ROC curve (AUC) as the primary metric.

Experimental results

Research questions

• RQ1 Can spectral distributions of the normalized Laplacian matrix effectively represent structural properties of brain networks for classification tasks?
• RQ2 Does EMD between spectral distributions outperform simpler graph embedding methods in connectome classification?
• RQ3 How does incorporating both connection strength and physical length in connectome weighting affect classification performance?
• RQ4 Is the EMD-based kernel more robust than probabilistic kernel methods in capturing differences in spectral distributions?

Key findings

• The EMD-based kernel achieved an average AUC of 0.706 with a standard deviation of 0.022 across 100 runs, indicating robust performance.
• The method outperformed baseline approaches using linear kernels on raw eigenvalues or edge vectors, confirming the advantage of spectral-based EMD.
• The Gram matrix revealed that ASD subjects were more similar to each other, while TD subjects showed higher pairwise variability in spectral distributions.
• The classifier demonstrated higher recall (0.737) for ASD detection but lower precision (0.670) for TD subjects, indicating a tendency to misclassify TD as ASD.
• The EMD kernel does not require density reconstruction of empirical eigenvalue distributions, making it more robust than probabilistic distance metrics.