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Disease Prediction using Graph Convolutional Networks: Application to Autism Spectrum Disorder and Alzheimer's Disease
Sarah Parisot, Sofia Ira Ktena, Enzo Ferrante, Matthew Lee, Ricardo Guerrero, Ben Glocker, Daniel Rueckert
TL;DR
Large-scale medical datasets require computational models that represent populations while combining imaging and non-imaging information. This paper evaluates a GCN framework using sparse population graphs and reports state-of-the-art accuracy on ABIDE and ADNI.
Problem
Growing imaging and non-imaging datasets require models that represent large populations while exploiting multiple information sources.
Method
The framework represents imaging acquisitions as nodes in a weighted sparse graph, integrates phenotypic information through edges, and trains a GCN for semi-supervised node classification.
Results
70.4% accuracy on ABIDE and 80% on ADNI achieved state-of-the-art performance on both datasets.
Takeaways & Limitations
Accurate graph construction and contextual phenotypic information are important for improving disease classification performance.
Takeaways & Limitations
Generalisation to unseen sites may reduce performance, and modelling multiple ADNI scans per subject independently may bias results toward subjects with more visits.
Abstract
from arXiv · showhide
Graphs are widely used as a natural framework that captures interactions between individual elements represented as nodes in a graph. In medical applications, specifically, nodes can represent individuals within a potentially large population (patients or healthy controls) accompanied by a set of features, while the graph edges incorporate associations between subjects in an intuitive manner. This representation allows to incorporate the wealth of imaging and non-imaging information as well as individual subject features simultaneously in disease classification tasks. Previous graph-based approaches for supervised or unsupervised learning in the context of disease prediction solely focus on pairwise similarities between subjects, disregarding individual characteristics and features, or rather rely on subject-specific imaging feature vectors and fail to model interactions between them. In this paper, we present a thorough evaluation of a generic framework that leverages both imaging and non-imaging information and can be used for brain analysis in large populations. This framework exploits Graph Convolutional Networks (GCNs) and involves representing populations as a sparse graph, where its nodes are associated with imaging-based feature vectors, while phenotypic information is integrated as edge weights. The extensive evaluation explores the effect of each individual component of this framework on disease prediction performance and further compares it to different baselines. The framework performance is tested on two large datasets with diverse underlying data, ABIDE and ADNI, for the prediction of Autism Spectrum Disorder and conversion to Alzheimer's disease, respectively. Our analysis shows that our novel framework can improve over state-of-the-art results on both databases, with 70.4% classification accuracy for ABIDE and 80.0% for ADNI.
1. Introduction
The paper motivates population graphs and graph convolutional networks as a way to combine imaging features with phenotypic and other non-imaging information for disease prediction. It extends and evaluates this framework on ABIDE and ADNI against multiple baselines.
- Large collaborative initiatives generate extensive imaging, genetic, phenotypic, and behavioural data, creating a need for models that represent large populations and integrate multiple data sources.
- Graphs represent subjects or acquisitions as nodes and their associations or similarities as edges, while weighted edges preserve more information than binary connections.
- Spectral graph convolutional networks generalise convolutional neural networks to irregular graph domains using graph signal-processing concepts.
- The framework models populations as sparse graphs combining subject-specific imaging features with phenotypic pairwise interactions, then applies a semi-supervised GCN for node classification.
- The extended evaluation investigates model components, graph structures, feature selection, and new baselines on ABIDE and ADNI.
- 70.4% accuracy was achieved on ABIDE and 80% on ADNI, representing improved state-of-the-art performance on both databases.
2. Methods
The method represents a population of imaging acquisitions as a weighted sparse graph and uses a GCN to classify graph nodes using imaging features and population connectivity.
- Each imaging acquisition is represented as a graph vertex associated with subject-specific imaging, phenotypic, and demographic information.
- The diagnosis task assigns healthy or diseased labels to graph nodes in a binary node-classification formulation.
- The GCN is trained semi-supervisedly using all node features and the population graph, while only a subset of nodes has labels during optimisation.
2.1. Databases and Preprocessing
The evaluation uses ABIDE for ASD classification and ADNI for predicting conversion from MCI to Alzheimer’s disease, with heterogeneous and longitudinal imaging data.
- The study demonstrates the model on the ABIDE and ADNI databases, each providing subject-specific information for population-graph construction.
- ABIDE contains multisite functional MRI and phenotypic data for subjects with ASD and healthy controls.
- ADNI provides longitudinal T1 MRI data from early and late MCI subjects for predicting conversion to Alzheimer’s disease.
- The ABIDE data are heterogeneous because acquisition sites use different imaging protocols, reducing comparability across subjects.
2.2. Population graph construction
The population graph represents imaging acquisitions as nodes and uses phenotypic information and imaging similarity to weight edges, combining complementary data for disease classification.
- Population graph: Each graph node represents an imaging acquisition described by an imaging-derived feature vector, while edges model relationships between nodes or subjects.The framework supports multiple acquisitions per subject, including longitudinal scans.
- Population graph: Graph construction requires choosing node features and defining edges and weights that accurately model similarity between subjects, scans, and their features.The authors warn that inaccurate graph structures can worsen performance relative to a simple linear classifier.
- Edge weights: Edge weights combine imaging similarity with distances across selected phenotypic measures such as sex, age, acquisition site, and genetic information.Categorical measures use a Kronecker delta, whereas quantitative measures use a threshold-based unit-step function.
- ABIDE graph: For ABIDE, the imaging similarity uses correlation distance, with σ controlling the kernel width, while acquisition site, sex, and age provide candidate phenotypic measures.The selected measures reflect ABIDE’s heterogeneity across imaging sites and protocols.
- ADNI graph: For ADNI, sex, age, and APOE ε4 are integrated because brain volumes can be affected by age and sex, while longitudinal acquisitions from one subject receive enhanced similarity.The longitudinal weighting distinguishes this graph construction from classifiers treating each entry independently.
- Data limitation: Handedness could not be integrated because this phenotypic information was missing for many subjects.The authors identify phenotypic-measure availability as a scope boundary for graph construction.
2.3. Feature Selection Strategies
The study evaluates feature-selection strategies for high-dimensional ABIDE connectivity vectors, including recursive elimination, PCA, MLP, and autoencoder representations.
- RFE: Recursive Feature Elimination trains a ridge classifier, ranks features by coefficient magnitude, and prunes the least discriminative features until a target count remains.The study also investigates how the selected feature count C influences performance.
- PCA: PCA uses singular value decomposition to project the data into a lower-dimensional space, but its linear projection is poorly matched to the feature-to-sample dimensionality.The feature vector contains 6105 dimensions compared with 871 samples.
- MLP: The supervised MLP learns a C-dimensional hidden-layer representation for classification, but its limited training data may lead to overfitting.The model uses one hidden layer of size C.
- Autoencoder: The unsupervised autoencoder learns a lower-dimensional code through an encoder-decoder architecture trained to reconstruct the original input.It uses one hidden layer of size C and mean square error for training.
2.4. Graph Labelling using Graph Convolutional Neural Networks
The model applies spectral graph convolutions within a fully convolutional GCN that performs semi-supervised node classification on the whole population graph.
- Spectral graph convolutions: Spectral graph convolutions address the difficulty of applying image convolutions to irregular graphs by using graph signal processing and spectral theory.Unlike image convolutions, graph data lack a regular gridlike structure.
- Graph Laplacian: The graph Laplacian is normalized as L = I_N − D^-1/2WD^-1/2, where D is the diagonal degree matrix.The Laplacian acts as a graph difference operator over neighboring vertices.
- Spectral graph convolutions: A spectral convolution transforms a graph signal into the Fourier domain, multiplies it by a filter, and maps the result back using the Laplacian eigendecomposition.The filter parameters are defined in the Fourier domain.
- Polynomial filters: Polynomial filters provide strictly K-localized convolutions and reduce computational complexity through recursively computed Chebyshev approximations.The polynomial filter is expressed as gθ(Λ) = Σ_k θ_kΛ^k.
- Model choice: The authors use the more expressive Defferrard-style convolution rather than a simpler alternative because their datasets are relatively small and complex.The selected approach is less efficient but more powerful and expressive in the authors’ assessment.
- GCN model: The GCN uses ReLU-activated hidden layers, a softmax output, and cross-entropy optimization on the entire population graph.Loss is evaluated on labelled training nodes, while unlabelled test nodes influence convolutions during training.
3. Results
Results across ABIDE and ADNI show that performance depends on feature-selection choices, polynomial order, graph structure, and phenotypic measures. The GCN is most effective with suitable graph construction and intermediate polynomial degrees, while higher degrees can worsen performance.
- ABIDE Feature Selection Strategy: RFE performs best at C = 2000 features, whereas the autoencoder performs best at 500 and 1000 features.The paper therefore uses RFE with C = 2000 in the remaining experiments.
- Influence of polynomial order K: 70.4% accuracy and 0.75 AUC are achieved on ABIDE with the phenotypic graph at K = 4.This is only marginally better than K = 3, which reaches 69.5% accuracy with the same AUC.
- Influence of polynomial order K: 78.8% accuracy and 0.86 AUC are achieved on ADNI at K = 4, after performance rises from K = 1 and declines at K = 5.The authors associate intermediate K values with a receptive field large enough to capture neighbourhood structure.
- Influence of polynomial order K: Higher polynomial degrees can increase overfitting, and the relationship between optimal K and graph diameter remains unexplored.The authors identify this relationship as an open question for different graph structures.
- Graph construction strategy: The phenotypic graph generally outperforms baseline graph structures, while random and k-nearest-neighbour graphs perform worst for K ≥ 2.For ABIDE, the phenotypic graph is best at K = 3 and K = 4 and has the highest average AUC of 0.75 at K = 3; ADNI shows clearer superiority for K ≥ 2.
4. Discussion
The framework combines imaging features with phenotypic graph interactions and achieves strong performance across ABIDE and ADNI, while graph construction and data characteristics constrain its applicability.
- Performance: 70.4% ABIDE and 80% ADNI accuracy improved over node-feature-only classifiers by 5% and 9%, respectively.The framework also evaluates feature selection, polynomial degree, graph construction, and alternative baselines.
- Framework: The framework represents populations as sparse graphs combining subject-specific imaging data with pairwise phenotypic and other non-imaging information for semi-supervised node classification.The graph is trained using labelled nodes and evaluated on the remaining nodes.
- Task formulation: Binary diagnosis is used for ASD and AD because the database annotations support binary classification, although the diseases lie on a spectrum.The framework could be adapted to multiclass or continuous prediction by changing the output size and loss function.
- Limitations: ABIDE site and protocol differences limit image-feature comparability, with approximately 70% accuracy suggested as an intrinsic whole-dataset ceiling.Higher accuracy has been obtained using single-site analyses or cognitive test results.
- Limitations: Spectral GCNs require fixed graph structures, so substantially modified graphs or newly added subjects require retraining from scratch.Spatial GCNs may be preferable when graph structures vary considerably.
- Graph construction: Phenotypic graph construction yielded the best performance, showing that graph design and phenotypic measure selection substantially affect classification accuracy.Integrating wrong or redundant phenotypic information can reduce effectiveness.