Spectral Graph Convolutions for Population based Disease Prediction

01 Aug 2017

Paper: arxiv
Code: github (tensorflow)

Key idea:

Graph Convolutional Networks (GCN) for brain analysis in populations, combining imaging and non-imaging data.

Network Outline:

Task: to assign to each acquisition, corresponding to a subject and time point, a label l ∈ L describing the corresponding subject’s disease state (e.g. control or diseased).
Vertex: We represent the population as a graph where each subject is associated with an imaging feature vector and corresponds to a graph vertex.
Edge: The graph edge weights are derived from phenotypic data, and encode the pairwise similarity between subjects and the local neighbourhood system.
population graph’s adjacency matrix W is defined as follows:

$$W(v,w)=Sim(S_v,S_w)\sum_{h=1}^H \rho(M_h(v),M_h(w))$$

where $Sim(S_v,S_w)$ is similarity between subjects based on image measures. $\rho$ is a measure of distance between phenotypic measures (non-imaging measures). Here is a set of H non-imaging measures $M=\{M_h\}$ (e.g. subject’s gender and age.

$$\rho(M_h(v),M_h(w)) = \begin{cases} 1, & \text{if $|M_h(v)-M_h(w)|<\theta$} \\ 0, & \text{otherwise} \end{cases}$$

GCN: check this blog and this paper Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
Training: This structure is 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.
Network detail:

• ReLU activation after graph convolutional layer ($max(0,x)$)
• Softmax activation in final layer $\sigma (\mathbf {z} )_{j}={\frac {e^{z_{j}}}{\sum _{k=1}^{K}e^{z_{k}}}}$
• Loss: cross-entropy
• Unlabelled nodes are then assigned the labels maximising the softmax output.
• Dropout
• l2 regularisation

Dataset Detail:

Autism Brain Imaging Data Exchange (ABIDE)

• Task: classify subjects healthy or suffering from Autism Spectrum Disorders (ASD).
• Objective: exploit the acquisition information which can strongly affect the comparability of subjects.
• Dataset: ABIDE
• Dataset Detail:
  1. 871 subjects, 403 ASD and 468 healthy controls.
  2. 20 different sites
  3. Preprocessing pipeline from C-PAC & ROI from Harvard Oxford (HO) atlas, same as Ruckert2016
  4. The individual connectivity matrices are estimated by computing the Fisher transformed Pearson’s correlation coefficient between the representative rs-fMRI timeseries of each ROI in the HO atlas.
• Input feature (vertex): vectorised functional connectivity matrix. And a ridge classifier is employed to select the most discriminative features from the training set.
• Adjacency matrix (edge and weight):
  • $Sim(S_v,S_w)$ is the correlation distance between the subjects’ rs-fMRI connectivity networks after feature selection.
  • $H=2$ non-imaging measures: subject’s gender and acquisition site

Alzheimer’s Disease Neuroimaging Initiative (ADNI)

• Task: predict whether an MCI patient will convert to AD.
• Objective: demonstrate the importance of exploiting longitudinal information, which can be easily integrated into our graph structure, to increase performance.
• Dataset: ADNI
• Dataset Detail:
  1. 540 subjects (1675 samples) with early/late MCI and contained longitudinal T1 MR images, 289 subjects (843 samples) diagnosed as AD
  2. Acquisitions after conversion to AD were not included.
• Input feature (vertex): volumes of all 138 segmented brain structures
• Adjacency matrix (edge and weight):
  • $Sim(S_v,S_w)$:
    $Sim(S_v,S_w) = \begin{cases} \lambda, & \text{if two samples correspond to the same subject ($\lambda >1$)} \\ 1, & \text{otherwise} \end{cases}$
  • $H=2$ non-imaging measures: subject’s gender and age information

Results

• 10-fold stratified cross validation strategy used.
• K = 3 order Chebyshev polynomials.
• In ADNI, longitudinal acquisitions of the same subject are in the same fold.

Autism Brain Imaging Data Exchange (ABIDE)

• Result: We show how integrating acquisition information allows to outperform the current state of the art on the whole dataset with a global accuracy of 69.5%.

Alzheimer’s Disease Neuroimaging Initiative (ADNI)

• Result: an average accuracy of 77% on par with state of the art results, corresponding to a 10% increase over a standard linear classifier.