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Spectral Graph Convolutions for Population-based Disease Prediction
Sarah Parisot, Sofia Ira Ktena, Enzo Ferrante, Matthew Lee, Ricardo Guerrerro Moreno, Ben Glocker, Daniel Rueckert
TL;DR
Disease prediction from large populations must jointly represent individual imaging features and associations between subjects. The paper uses graph convolutional networks on population graphs whose nodes carry imaging features and whose edges encode phenotypic relationships. Across ABIDE and ADNI, the approach achieved improved classification performance, including 69.5% accuracy on ABIDE and 77% accuracy for ADNI MCI-conversion prediction.
Problem
Existing approaches either model pairwise similarities without individual subject features or use imaging vectors without modelling interactions between subjects.
Method
The method represents populations as sparse graphs with imaging feature vectors on vertices and phenotypic similarities on edges, then trains a GCN on partially labelled graphs.
Results
The method significantly improved performance over competing methods, achieving 69.5% accuracy for ABIDE and 77% accuracy for ADNI MCI-conversion prediction.
Takeaways & Limitations
Integrating contextual pairwise information with patient-specific imaging information improved classification in the tested ABIDE and ADNI population analyses.
Takeaways & Limitations
Constructing an effective population graph is essential and far from obvious, while the current feature vectors are relatively simple.
Abstract
from arXiv · showhide
Exploiting the wealth of imaging and non-imaging information for disease prediction tasks requires models capable of representing, at the same time, individual features as well as data associations between subjects from potentially large populations. Graphs provide a natural framework for such tasks, yet previous graph-based approaches focus on pairwise similarities without modelling the subjects' individual characteristics and features. On the other hand, relying solely on subject-specific imaging feature vectors fails to model the interaction and similarity between subjects, which can reduce performance. In this paper, we introduce the novel concept of Graph Convolutional Networks (GCN) for brain analysis in populations, combining imaging and non-imaging data. We represent populations as a sparse graph where its vertices are associated with image-based feature vectors and the edges encode phenotypic information. This structure was used to train a GCN model on partially labelled graphs, aiming to infer the classes of unlabelled nodes from the node features and pairwise associations between subjects. We demonstrate the potential of the method on the challenging ADNI and ABIDE databases, as a proof of concept of the benefit from integrating contextual information in classification tasks. This has a clear impact on the quality of the predictions, leading to 69.5% accuracy for ABIDE (outperforming the current state of the art of 66.8%) and 77% for ADNI for prediction of MCI conversion, significantly outperforming standard linear classifiers where only individual features are considered.
1 Introduction
Large-scale disease prediction needs models that combine subject-specific imaging features with relationships among subjects. The paper introduces population-graph GCNs to integrate these information sources for classification.
- Large medical datasets require models that represent populations while exploiting imaging and non-imaging information.
- Graph-based approaches encode pairwise similarities but omit subjects’ individual characteristics, whereas imaging-only classifiers omit interactions between subjects.
- GCNs combine imaging feature vectors at graph vertices with phenotypic information encoded by graph edges.
- The model trains on partially labelled population graphs to infer unlabelled-node classes from node features and pairwise subject associations.
- 77% accuracy was achieved for ADNI prediction of MCI conversion to Alzheimer’s disease.
2 Methods
The method represents each acquisition as an imaging-feature graph node and encodes phenotypic similarities in sparse graph edges. A semi-supervised spectral GCN propagates labels through this population graph while using localized polynomial filters.
- Population representation: Each acquisition becomes a graph vertex with an imaging-derived feature vector, while edges encode phenotypic similarity in a sparse population graph.The GCN is trained on a subset of labelled vertices to infer labels for unlabelled acquisitions.
- Datasets and features: ABIDE separates ASD patients from healthy controls using functional-connectivity feature vectors and acquisition-site information.The selected cohort contains 871 subjects acquired at 20 sites.
- Datasets and features: ADNI predicts MCI conversion using longitudinal T1 MRI samples and a graph built from gender and age information.The dataset subset includes 1,675 samples from 540 MCI subjects, with longitudinal information spanning 6–96 months.
- Population graph construction: The adjacency matrix combines subject similarity with phenotypic distances, using Kronecker delta functions for categorical measures and thresholded unit-step distances for quantitative measures.For ABIDE, gender and acquisition site define phenotypic similarity; for ADNI, gender and age are used.
- Spectral GCN: The GCN applies convolutional layers with ReLU activations, using Chebyshev-polynomial approximations to implement graph filters on irregular population graphs.The broader motivation is that ordinary image convolutions are defined for regular grids and do not directly generalize to graphs.
- Spectral GCN: Spectral graph convolutions use the graph Laplacian’s eigenbasis, with low-frequency eigenvectors varying smoothly across strongly connected vertices.Polynomial filters provide spatial localization and reduce convolutional computational complexity.
3 Results
The model was evaluated with stratified 10-fold cross-validation against ridge classification and a random-support GCN. It improved accuracy and AUC over competing methods on both databases, reaching 69.5% on ABIDE and 77% on ADNI.
- Evaluation: 10-fold stratified cross-validation evaluated the GCN, ridge classification, and a same-density random-graph GCN.Longitudinal acquisitions from each ADNI subject were kept within the same fold.
- Ablation: The random graph support produced results equivalent to or worse than the linear classifier.This comparison investigates the contribution of the population graph structure.
- Comparative results: Significant increases in accuracy and AUC were observed for the proposed method on both databases relative to competing methods.The reported significance threshold was p < 0.05.
- ABIDE: 69.5% average accuracy on ABIDE outperformed the reported state-of-the-art result of 66.8%.The task was ASD-versus-control classification.
- ADNI: 77% average accuracy on ADNI matched reported state-of-the-art performance and represented a 10% increase over a standard linear classifier.The task was predicting conversion from MCI to Alzheimer’s disease.
4 Discussion
The proposed population-graph GCN combines patient-specific imaging information with contextual pairwise information for semi-supervised brain-disease classification. Results support the value of contextual information, while discussion identifies graph construction and feature representation as important areas for extension.
- Results: About 4.1% improvement for ABIDE and 10% for ADNI over a standard linear classifier using only individual features.The comparison is reported for semi-supervised classification on the two databases.
- Mechanism: Conditioning the GCN on the adjacency matrix distributes supervised loss gradient information across the network, enabling representations for unlabelled nodes.This mechanism is described within the proposed semi-supervised learning setting.
- Method: The population graph combines image-based patient-specific information with non-imaging pairwise interactions for classification.The graph structure was tested on ABIDE for ASD classification and ADNI for predicting MCI conversion from longitudinal information.
- Limitations and extensions: Effective construction of the population graph is essential and far from obvious.The authors identify graph construction as a central area for future extension.
- Limitations and extensions: The graph currently combines several information types into scalar edges, while richer attributed edges could preserve complementary measures and weight them differently.The authors also propose integrating time information and evaluating richer feature vectors, potentially using MRI and rs-fMRI-derived representations.