# Spectral Graph Convolutions for Population based Disease Prediction

01 Aug 2017Paper: 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:

where is similarity between subjects based on image measures. is a measure of distance between phenotypic measures (non-imaging measures). Here is a set of H non-imaging measures (e.g. subject’s gender and age.

**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 ()
- Softmax activation in final layer
- 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**:- 871 subjects, 403 ASD and 468 healthy controls.
- 20 different sites
- Preprocessing pipeline from C-PAC & ROI from Harvard Oxford (HO) atlas, same as Ruckert2016
- 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)**:- is the correlation distance between the subjects’ rs-fMRI connectivity networks after feature selection.
- 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**:- 540 subjects (1675 samples) with early/late MCI and contained longitudinal T1 MR images, 289 subjects (843 samples) diagnosed as AD
- Acquisitions after conversion to AD were not included.

**Input feature (vertex)**: volumes of all 138 segmented brain structures**Adjacency matrix (edge and weight)**:- :

- 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.