The effect of node features on GCN-based brain network classification: an empirical study

Problem formulation

We represent each subject as a graph G = (V, E), where V = v₁, v₂, ⋯, v_n denotes the node set, n is the number of nodes/ROIs, and E = e₁, e₂, ⋯, e_|ɛ| stands for the edge set that is determined by the relationship between different nodes. Accordingly, the node feature matrix and graph adjacency matrix are denoted by X ∈ R^n×d and A ∈ 0, 1^n×n, respectively, where x_i ∈ R^d is the feature of node v_i, d is the number of feature dimensions and A_ij = 1if(v_i, v_j) ∈ E, 0 otherwise. We split subjects/graphs into training and test sets. Given an adjacency matrix A and a feature matrix X in the training sets, we learn a GCN-based classification model and predict the labels of subjects in the test set.

Network architecture

Our analysis is based on a spectral GCN with two convolution layers  (Kipf & Welling, 2016), which has been empirically verified as an effective architecture for brain disorder identification in several recent works (Ying et al., 2018; Abu-El-Haija et al., 2020; Chu et al., 2022). Its mathematical model can be formulated as follows: (1)${\displaystyle f\left(X,A\right)=ReLU\left(\hat{A}\cdot ReLU\left(\hat{A}X{W}^0\right)\cdot W^1\right),}$ where $\hat{A}=D^{-\frac{1}{2}}A{D}^{-\frac{1}{2}},A=A+I^n$, Iⁿ is an identity matrix, and D is a diagonal matrix whose diagonal element D_ii = ∑_jA_ij represents the degree of the i-th node, W⁰ and W¹are two layers of model parameters that need to be learned from data, and ReLU is a nonlinear activation function.

Suppose that F = f_i(X, A) ∈ R^n×d′ is the learned representations of nodes, where f_i isthe embedding of node v_i, d′ is the dimension of the feature after embedding. We can further obtain a graph-level representation H^G = r(F) ∈ R^d′ for G by aggregating the node-level embedding. The readout function r(⋅) is a concatenation of the maximum pooling and average pooling operation  (Lee, Lee & Kang, 2019). It can be formulated as follows: (2)${\displaystyle H^G=\frac{1}{n}\sum _{i=1}^n{f}_i\parallel {max}_{i=1}{f}_i,}$ where ∥ denotes concatenation.

Data acquisition

In this article, two publicly available datasets are used to evaluate the effect of node feature on GCN-based method. One is from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset and the other is from the Autism Brain Imaging Data Exchange (ABIDE) dataset. The details of subjects involved in the two datasets are shown in Table 1, including distribution of ASD/MCI, gender (M/F), age and imaging parameters echo time (TE) and repetition time (TR). Specifically, the ADNI dataset consists of 137 subjects, including 69 HCs and 68 MCIs. The fMRI data were scanned by a 3.0-T Philips MRI scanner and the scanning parameters included TR = 3,000 ms, TE = 30 ms, flip angle = 80°, number of slices = 48, slice thickness = 3.3 mm, total volume = 140. For ABIDE dataset, 184 subjects are involved, including 79 ASDs and 105 HCs. All rs-fMRI data are obtained by 3.0-T Siemens Allegra scanner with the following imaging parameters: TR/TE = 2,000/15 ms, slices number = 33, voxel thickness = 4.0 mm, flip angle = 90°, and the scanning time is 6 min, resulting in 180 time points.

Data preprocessing

All the rs-fMRI data are preprocessed through DPARSF (Yan et al., 2016) and statistical parametric mapping (SPM12) based on the following standard pipeline: we discard the first five volumes of each functional time series and slice timing to allow signal stabilization. Then, the remaining nuisance signals, including ventricle and white matter signals, are regressed, and the Friston 24-parameter model is used to regress out the high-order effect of head motion. After that, the signals are spatially normalized to MNI space, and the fMRI data are spatially smoothed with the full-width-half-maximum of four mm. Finally, depending on the AAL atlas, the preprocessed rs-fMRI time series signals are partitioned into 116 ROIs and then averaged respectively to get a representative signal for each ROI.

Experimental details

As mentioned earlier, network architecture GCN with two convolution layers, due to its popularity and effectiveness, is used in our study. Furthermore, with the aim of conducting control experiments, we set the embedding dimension to 32, the number of epochs to 100, the learning rate to 0.001 and the weight decay to 1e⁻³. Four kinds of node features are involved to verify the classification performance as follows.

1. Original Signals (OS): OS capture the spontaneous fluctuations of brain activity associated with different ROIs, which is a manifestation of functional connectivity of the brain.

2. One-hot Encoding (OH): We associate each node with a one-hot indicator that uniquely identifies the spatial position of each ROI.

3. Node Statistics (NS): We design eight node statistics and concatenate them into a feature vector (Zhang et al., 2022). In particular, these statistics include three definitions of local clustering coefficients (Li, Shang & Yang, 2017), four centralities (Hamilton, 2020) (i.e., degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality), as well as local efficiency.

4. Correlation vector (CV): CV reflect the relationship between the current ROIs and other ROIs. The most popular measure is Pearson’s correlation (PC) as follows:

where s_i ∈ R^m(i = 1, 2, ⋯, n) is the extracted rs-fMRI time series from the ith ROI, m is the number of time points, n is the number of ROIs, ${\overline{s}}_i\in R^m$ is the mean of s_i, and c_ij is the correlation coefficient between the i-th and j-th ROIs.

Experimental setting

In this study, we randomly select 80% of the subjects for training and the remaining 20% for testing. For all datasets, we report the mean of 100-run results to evaluate the performance of the involved methods. The performance metrics include

Accuracy = (TP + TN)/(TP + FP + TN + FN),

Sensitivity = TP/(TP + FN),

Specificity = TN/(TN + FP),

Precision = TP/(TP + FP),

F1 − score = 2 × TP/(2 × TP + FP + FN).

where TP, TN, FP, and FN indicate the true positive, true negative, false positive and false negative, respectively. Additionally, the area under curve (AUC) is adopted for measuring the classification performance.