Alzheimer’s disease classification using mutual information generated graph convolutional network for functional MRI

Abstract

Background:

High-order cognitive functions depend on collaborative actions and information exchange between multiple brain regions. These inter-regional interactions can be characterized by mutual information (MI). Alzheimer's Disease (AD) is known to affect many high-order cognitive functions, suggesting an alteration to inter-regional MI, which remains unstudied.

Objective:

To examine whether inter-regional MI can effectively distinguish different stages of AD from normal control (NC) through a connectome-based graph convolutional network (GCN).

Methods:

MI was calculated between the mean time series of each pair of brain regions, forming the connectome which was input to a multi-level connectome based GCN (MLC-GCN) to predict the different stages of AD and NC. The spatio-temporal feature extraction (STFE) in MLC-GCN was used to capture multi-level functional connectivity patterns generating connectomes. The GCN predictor learns and optimizes graph representations at each level, concatenating the representations for final classification. We validated our model on 552 subjects from ADNI and OASIS3. The MI-based model was compared to models with several different connectomes defined by Kullback-Leibler divergence, cross-entropy, cross-sample entropy, and correlation coefficient. Model performance was evaluated using 5-fold cross-validation.

Results:

The MI-based connectome achieved the highest prediction performance for both ADNI2 and OASIS3 where it’s accuracy/AUC/F1 were 87.72%/0.96/0.88 and 84.11%/0.96/0.91 respectively. Model visualization revealed that prominent MI features located in temporal, prefrontal, and parietal cortices.

Conclusion:

MI-based connectomes can reliably differentiate NC, mild cognitive impairment and AD. Compared to other four measures, MI demonstrated the best performance. The model should be further tested with other independent datasets.

Introduction

Alzheimer's disease (AD) is a currently incurable neurodegenerative disorder characterized by pathological depositions of insoluble amyloid plaque and neurofibrillary tangles, along with clinical symptoms such as cognitive impairments and loss of daily functions.¹ Early interventions offer the best hope for delaying or modifying AD.^2-4 To achieve this goal, accurate and reliable tools for detecting AD at its early stages are crucial.^4-6

AD disrupts high-order cognitive functions, many of which rely on interactions between different functional brain regions. It is, therefore, not surprising that AD affects inter-regional interactions, a phenomenon that has been widely assessed through functional connectivity (FC) analysis. Over the past decades, FC changes in AD have been repeatedly observed using resting state fMRI (rsfMRI).^7-9 In the vast majority of FC studies, FC is calculated through the Pearson correlation coefficient (CC), which measures the linear dependence between the mean time series of two brain regions. However, CC is limited to capturing only linear relationships and may not fully characterize nonlinear dependencies often present in the blood oxygen level dependent (BOLD) signals.^10,11 To overcome this limitation, alternative similarity metrics have been proposed in FC analysis, including the Kullback-Leibler (KL) divergence,¹² cross-entropy (CE),¹³ and mutual information (MI).^11,14

Among these nonlinear metrics, MI represents the most widely used one in fMRI. For Gaussian distributed data, MI and CC can be directly linked through a nonlinear function $I=-\frac{1}{2}log(1-{\rho }^2)$,¹¹ where $I$ is MI and $\rho$ is CC. This relationship does not exist when data distribution is not Gaussian. Obviously, CC is insufficient to capture the nonlinear and non-Gaussian relationship between two variables while MI can do. In a preliminary study, Tsai et al. used MI as an alternative to CC for fMRI task activation detection.¹⁴ Task activation was derived from MI between the task design paradigm and each voxel's fMRI time series. Salvador et al. used MI as a FC metric in the frequency domain of the fMRI time series.¹⁵ Wang et al. proposed a kernel density estimation-based MI algorithm and used it to calculate MI.¹⁶ They found a progressive FC decline in the default mode network (DMN) in AD patients compared to normal controls (NCs). KL divergence and CE have also been introduced as alternative FC metrics in a few rsfMRI studies.^12,13 While encouraging, these studies are limited by the small sample size and the lack of direct comparison between CC and MI or other nonlinear relationship metrics. Furthermore, no studies have explored the nonlinear FC based AD classification particularly in the framework of graph convolutional networks (GCN).

Deep learning represents the state-of-the-art disease predictor for many different disorders.¹⁷ The most widely used network is the convolutional neural network, which consists of several layers of artificial neurons organized in a grid like manner. GCNs is a class of deep learning networks designed to process graph-structured data by extending the concept of convolution from traditional Euclidean domains (e.g. images or data saved in a grid-like format) to non-Euclidean spaces (e.g., brain connectomes, social networks). Unlike conventional neural networks, which operate on grid-like data, GCNs aggregate and transform information from neighboring nodes in the non-Euclidean space, enabling the model to learn hierarchical representations of graph structures. Specifically, GCNs apply spectral or spatial convolutions to capture relationships between nodes and their local neighborhoods, facilitating effective learning of both local and global connectivity patterns. This property makes GCNs particularly useful for analyzing complex systems such as brain networks, where each node represents a brain region, and edges encode functional or structural connections. By leveraging multi-layer message passing, GCNs can uncover latent patterns in connectomic data, making them powerful tools for tasks like disease classification, brain state prediction, and network-based biomarker discovery.

GCN-based approaches have been introduced into AD prediction using rsfMRI-derived FC networks.^18-20 For the rsfMRI-derived connectome, nodes of the graph are different brain regions, and edges of the graph are the inter-regional connectivity (CC or MI). However, most prior studies have utilized connectivity information derived from the lowest scale of rsfMRI data, limiting the representation of multi-scale functional interactions. Additionally, existing GCN models typically employ shallow architectures with only two or three feature layers, restricting their ability to extract deeper connectivity patterns. To address these limitations, we have recently proposed a multi-level connectome based GCN (MLC-GCN) model for classifying aging and AD.²¹ This model integrates multi-scale connectomes from rsfMRI data and processes them using multiple GCNs, whose outputs are concatenated within a multi-layer perceptron (MLP). This hierarchical design enhances the model's capability to capture diverse and complex FC patterns, leading to improved classification accuracy.²¹

The purpose of this study was to evaluate MI-derived FC for early AD detection using the MLC-GCN. The novel contribution and the knowledge gap to fill are the use of MI for characterizing the non-linear functional connectivity and the use of MLC-GCN for extracting the multi-scale nonlinear connectome features to be used for AD classification. We hypothesize that in combination with MLC-GCN, MI-derived connectomes will enhance AD classification performance.

To test this hypothesis, we rebuilt the MLC-GCN architecture using MI and other nonlinear distance metrics to evaluate their performance in AD detection. Following the same architecture proposed in ref., ²¹ MLC-GCN contains a stack of spatio-temporal feature extraction (STFE) modules, the corresponding GCN predictors, and an MLP. STFE was used to extract rsfMRI features at different depths and generate corresponding connectomes. The GCN predictor then integrates these multi-level connectomes to build and optimize GCNs at each level, which were concatenated by the MLP to form the final AD classifier.

Methods

We validated our model on two public datasets: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies-3 (OASIS3).^22,23 We compared performance of several nonlinear similarity metrics: MI, KL divergence, CE, cross-Sample Entropy (CSE), and CC in the MLC-GCN-based AD classification.

Data and preprocessing

ADNI2 and OASIS3 were used to validate our method in this paper which distinguishes the NC subjects from AD patients and perform the multi-classification on both datasets. The demographic statistics are listed in Table. 1.

Table 1:

The demographic statistics of the datasets used in this work

Dataset	Group	Scans Number	Patients number	Gender (M/F)	Age (mean±std.)
ADNI2	NC	187	52	30/22	75.01±6.23
	EMCI	182	55	28/27	72.56±6.00
	LMCI	156	40	13/27	72.28±7.60
	AD	118	34	16/18	74.69±7.47
OASIS-3	NC	570	225	85/140	68.24±8.94
	MCI	225	96	58/38	76.90±7.49
	AD	105	50	27/23	76.83±8.03

NC: normal control, EMCI: early mild cognitive impairment, LMCI: late mild cognitive impairment, AD: Alzheimer’s Disease.

ADNI used in this paper were from the phase 2 (ADNI2) (http://adni.loni.usc.edu/).²² ADNI were launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. We selected 643 sessions, including 187 NCs, 118 ADs, 182 early MCIs (EMCIs) and 156 late MCIs (LMCIs) from 52, 55, 40 and 34 subjects respectively. Each subject had rsfMRI acquired with 3T Philip MRI scanners. Acquisition parameters were: TR/TE = 3000 ms/30 ms, imaging matrix = 64 × 64, voxel size = 3.3 mm × 3.3 mm × 3.3 mm, 48 slices, and 140 time points. In the multi-classification experiment, a four-classification task will be performed.

OASIS3 is a compilation of MRI and PET imaging and related clinical data collected across several ongoing studies in the Washington University Knight Alzheimer Disease Research Center over the course of 15 years.²³ rsfMRI data acquisition was performed using a 3T MRI scanner manufactured by Siemens with the following parameters: TR/TE of 2200ms/27ms, imaging matrix of 64×64, voxel size of 4.0 mm×4.0 mm×4.0 mm, 36 slices, 174 time points. We selected 900 samples of fMRI and labeled each data based on the clinical measurement rate (CDR),²⁴ including 570 with $CDR=0$, 225 with $CDR=0.5$ and 105 with $CDG>0.5$, which are respectively considered as NC, MCI and AD labels. All three categories were used for the multi-classification task.

All data were preprocessed using the Brainnetome Toolkit²⁵ following a standard pipeline: removing first 10 time points, slice timing correction, realignment to the first volume, spatial normalization to Montreal Neurological Institute (MNI) space, regression of nuisance signals and temporal bandpass filtering (0.01-0.08 Hz). No spatial smoothing was applied.

Mean rsfMRI time courses were extracted from the preprocessed data using the Brainnetome Atlas,²⁶ which consists of 210 cortical and 36 subcortical regions-of-interest (ROIs). Names of each ROI was listed in a table in supplement section. MI or other FC metrics between each pair of ROIs were calculated based on their mean rsfMRI time series, forming the lowest level FC matrices (connectome) $G_0$.

Nonlinear FC

Four nonlinear metrics, including KL divergence, CE, Cross-Sample Entropy (CSE) and MI, were assessed in this paper. MI calculation depends on probability distribution and the corresponding probability density function (PDF), which can be estimated using a few strategies, including histogram, Parzen window, $\mathsf{k}$ nearest neighbor²⁷ and kernel density estimation (KDE).¹⁶ We used histogram to estimate the probability distribution function. Denoting two rsfMRI time series by $x$ and $y$, and their probability distributions by $p$ and $q$, MI of $x$ and $y$ can be described as:

$$I(x,y)=H(x)+H(y)-H(x,y)$$ (1)

where $H(x)$ and $H(y)$ are the entropy of $x$ and $y$, $H(x,y)$ is the joint entropy of $x$ given $y$ given the joint probability distribution $p(x_i,y_i)$. Entropy and joint entropy are defined by the following formulas:

$$H(x)=E[\text{ln}p(x)]=-\sum _{i=1}^{t}p(x_i)\text{ln}p(x_i)$$ (2)

$$H(y)=E[\text{ln}p(y)]=-\sum _{i=1}^{t}p(y_i)\text{ln}p(y_i)$$ (3)

$$\tilde{H}(x,y)=-\sum _{i=1}^{t}p(x_i,y_i)\text{ln}p(x_i,y_i)$$ (4)

$I(x,y)$ indicates the similarity of the probability distributions of $x$ and $y$. High MI means that $x$ and $y$ shares strong statistical relationship: their random sampling results follow similar probability distributions; low MI means that the two variables have weak statistical dependence or relationships. This is fundamentally different from CC, which strictly depends on the sampling sequences and can only account for linear relationship. Definitions and formulas for KL divergence, CE and CSE are described in the supplement materials.

MLC-GCN

Figure 1 illustrates the overall procedure for the rsfMRI FC connectome-based MLC-GCN in AD prediction. The left most module (within the leftmost dashed rectangle) represents the rsfMRI data preprocessing and mean time series extraction process, as described above. The classifier consists of two inter-connected components, enclosed within the two dashed rectangles in the middle and the rightmost sections of Figure 1. In the middle is the multi-level connectome generator, while the rightmost module represents the multi-level GCNs and MLP-based predictor. Below is a brief introduction to each element of the MLC-GCN. More details can be found in a preprint.²¹

Figure 1:

The overall workflow of the rsfMRI connectome-based MLC-GCN AD classification.

Multi-level connectome generator.

The multi-graph generator follows a hierarchical structure comprising a feature extractor and a graph generation module. At the lowest level, MI of the preprocessed rsfMRI time series from different brain regions is calculated to form an FC matrix. This FC matrix serves as both the adjacency matrix and the node feature matrix, forming the original connectome at the lowest scale. Next, an embedding operation is applied to the preprocessed rsfMRI time-series, followed by a spatio-temporal feature extraction (STFE) module that extracts different level of spatio-temporal features from the embedded rsfMRI time series. These features are used to construct corresponding connectomes by recalculating MI between each pair of brain regions, generating FC matrices for different hierarchical levels. Each subsequent level in the hierarchy receives the output from the previous STFE module, processes it through a new STFE module, and generates a higher-level connectome from the further refined spatio-temporal features.

The embedding operation is introduced at the second level before the STFE module. It consists of a 1D-CNN designed to extract compact feature representations from all $t$ timepoints. We denote the original connectome as $G_0$ and the generated graphs $G=\{G_1,G_2,\cdots ,G_K\}$, where $K$ indicates the maximum feature level.

For MLC-GCNs using different FC metrics, MI in the above procedure is replaced by the respective FC metric.

Multi-level GCN predictor.

Multi-level GCNs predictor encodes each generated connectome into an embedding vector through an independent GCN. Each GCN architecture consists of two graph convolution layers that extract spatial features from the generated connectome by automatically aggregating node information (node is a brain region defined by brain atlas). The outputs of all GCNs are concatenated into a single feature vector, which is then fed into an MLP for predicting AD status or other clinical outcomes in different disease contexts.

The coarsest scale connectome $G_0$ and the generated connectomes $G=\{G_1,G_2,\cdots ,G_K\}$ at $K$ levels are sent to a $K+1$ level GCNs-based predictor as the input. At each level $i(i=0,1,2,\cdots ,K)$, a dedicated GCN will be learned from the corresponding input connectome $G_i$ to generate the output graph embedding $E_i$.

The output of the last graph convolutional layer of the $k$–th GCN will be transformed into a 1D embedding vector $E_k$. All embeddings from the $K$ GCNs are then concatenated in order, forming the final multi-level graph embedded vector $E=\{E_0,E_1,\cdots ,E_k\}$. This fused vector is subsequently input to an MLP for clinical outcome prediction.

Experiment setting

Our model was implemented in PyTorch and trained on a single NVIDIA RTX 4090 GPU. Model parameters were initialized using a Gaussian distribution with a mean of zero and a standard deviation of one. We trained the model using the AdamW optimizer²⁸ with a learning rate of 0.001, a commonly used setting for GCN-based models in various applications including medical imaging²⁹. Empirically, reducing the learning rate below 0.001 led to slower convergence, while increasing it caused instability. AdamW dynamically adjusts the learning rate via an exponential decaying moving average of past gradients, which helps stabilize updates and improve convergence speed. The weight decay was set to 0.001, and the dropout rate was set to 0.2 to prevent overfitting. Weight decay penalizes large weight updates. A decay rate of 0.001 was chosen based on a prior study.²⁸ A dropout rate of 0.2 was chosen to balance overfitting prevention and information retention. This is line with best practices for neuroimaging-based deep learning models, where a dropout rate between 0.2 and 0.5 is shown to be effective.³⁰

The maximum number of epochs was set to 300 for all experiments. A kernel size of 5 and 64 layers were used for feature extraction. We performed manual tuning based on performance on a held-out validation set. Initially, a grid search was used to find the optimal value over a range of values for the learning rate (0.0001 to 0.01), dropout (0.1 to 0.5), and weight decay (0.0001 to 0.01). The final hyperparameter values were selected based on the best performance in terms of accuracy and AUC.

To enhance generalization and improve model robustness, the Mixup data augmentation technique was applied.³¹ This method generates augmented data representations by blending pairs of training samples. We used 5-fold stratified cross-validation to ensure robust model evaluation. Model performance was assessed using five key metrics: Accuracy (Acc), Area Under the Curve (AUC), Specificity (Spe), Sensitivity (Sen) and F1-score.

The embedding length could affect the STFE feature extraction and the subsequent GCN and disease prediction. Meanwhile, the number of bins used to build the histogram for estimating probability distribution can affect MI, CE, and KL calculation as the algorithms we used in this paper were based on the histogram-derived probability distribution.³² A small number of bins is too small, the histogram may oversimplify the underlying distribution, leading to a biased estimate. Whereas, if the number of bins is set to be too big, many bins may contain few or no data points, leading to sparse estimates of the joint and marginal distributions. The optimal bin number depends on the length of the time series: a general guideline is that the number of bins should be approximately the square root of the total number of samples (Freedman-Diaconis rule) or determined through cross-validation. To evaluate the effects of the embedding length and the number of bins, we repeated the entire model building and testing procedure by varying the embedding length from 16 to 32, 64, or 128 and the number of bins from 20 to 50, or 100. For each embedding length and each number of bins, the above model building and testing procedures were repeated and the performance indices were collected.

Statistical analysis on method performance

A series of paired t-test was performed to compare different MLC-GCNs assessed in this work. T-test was performed for each performance index and for ADNI and OASIS3 datasets. False discovery rate (FDR) was calculated to control the number of false positives induced by multiple comparisons.³³ An FDR was considered statistically significant.

Results

This section presents results for model parameter effects, the disease status prediction using five different FC connectome based MLC-GCN models, MI, KL divergence, CC, CE and CSE, and the experiments for assessing the effects of histogram calculations, data embedding length, and model visualization and understanding.

Sensitivity of MI MLC-GCN to embedding length and number of histogram bins

Figure 2 shows the model prediction accuracy at four different embedding length: 16, 32, 64, and 128. Prediction accuracy on both datasets increases with the embedding length from 16 to 64, but decreases after the embedding length is greater than 64. Based on this evaluation, our results reported below were all based on an embedding length of 64.

Figure 2:

Effects of embedding length $l$ on MLC-GCN prediction accuracy based on 5-fold cross validation.

Table 2 shows the histogram bin number evaluation results. For both CE and MI, model performance increases with the number of histogram bins. While this result suggests that ⩾100 bins would provide further improved model performance, 100 was empirically chosen because it is close to the minimum of the rsfMRI data length of the two datasets included in this study. Further increasing histogram bins will increase the risk of having too many sparse bins (with 0 or very few data samples). Based on these evaluation results, we chose 100 to be the final number of bins and only showed results based on this number. KL showed the best performance when 50 bins were used. These evaluations showed that MLC-GCN-MI achieved the best performance, followed by MLC-GCN-CE and MLC-GCN-KL in second and the third place, respectively though MLC-GCN-KL outperformed MLC-GCN-CE for the OASIS3 data.

Table 2:

Prediction performance of different MLC-GCNs with different non-linear FC estimated based on histograms with different number of bins. The numbers after each model name means the number of histogram bins.

Dataset	Method	Acc	AUC	Spe	Sen	F1-score
ADNI2	MLC-GCN-CE20	75.43±3.68	91.092±2.08	91.688±1.25	74.976±3.50	74.958±3.52
	MLC-GCN-CE50	76.05±4.36	91.156±2.26	91.878±1.40	75.688±3.97	75.762±4.67
	MLC-GCN-CE100	80.24±4.78	92.23±2.41	93.28±1.65	80.38±5.15	80.57±4.73
	MLC-GCN-KL20	71.858±4.85	88.624±1.68	90.424±1.66	71.476±4.99	71.816±5.05
	MLC-GCN-KL50	77.284±3.69	91.328±1.69	92.272±1.21	76.888±3.77	77.32±3.87
	MLC-GCN-KL100	75.90±2.08	90.32±1.15	91.85±0.68	75.83±2.04	75.76±2.34
	MLC-GCN-MIKDE	78.188±1.55	91.38±0.70	92.572±0.46	77.344±1.74	77.96±1.85
	MLC-GCN-MI20	76.822±3.57	90.972±2.28	92.156±1.22	77.42±3.98	77.24±3.87
	MLC-GCN-MI50	82.7±4.67	93.668±1.00	94.182±1.58	83.176±4.06	82.906±4.35
	MLC-GCN-MI100	84.612±2.72	94.566±1.59	94.832±0.87	84.73±2.63	84.574±2.48
OASIS-3	MLC-GCN-CE20	79.112±2.17	84.59±3.30	86.52±2.34	67.02±2.42	68.226±1.93
	MLC-GCN-CE50	79.446±1.89	83.874±3.78	86.264±2.38	66.54±2.18	68.098±1.91
	MLC-GCN-CE100	81.334±2.85	86.876±3.04	87.494±3.18	72.694±4.54	73.448±4.01
	MLC-GCN-KL20	83.556±0.93	89.504±1.52	88.436±0.72	75.226±1.03	77.656±1.37
	MLC-GCN-KL50	83.89±1.04	89.582±1.43	88.968±1.08	75.93±1.57	77.862±1.67
	MLC-GCN-KL100	82.776±1.24	89.176±1.62	88.424±1.43	74.212±4.95	75.88±3.71
	MLC-GCN-MIKDE	88.556±3.41	93.012±1.44	92.08±1.85	80.178±5.09	83.026±5.66
	MLC-GCN-MI20	89.466±2.69	93.356±2.51	92.788±2.04	82.46±6.59	84.242±5.14
	MLC-GCN-MI50	89.222±2.93	93.376±2.47	93.11±1.86	83.904±5.2	84.954±4.43
	MLC-GCN-MI100	91.566±2.56	94.572±2.84	94.582±1.79	87.904±4.56	88.272±4.04

Kernel density estimation (KDE) is another popular method for probability distribution estimation.³⁴ KDE can be relatively more robust and more adaptive to the data than histogram. In Table 2, we also tested KDE-based MI and subsequently the MLC-GCN-MI model performance. In general, MLC-GCN-MI_KDE showed comparable performance to MLC-GCN-MI₂₀ and MLC-GCN-MI₅₀ but not as good as MLC-GCN-MI₁₀₀. For this reason, MI connectome based MLC-GCN AD prediction results shown below were based MLC-GCN-MI₁₀₀ only.

`Prediction with CC and four nonlinear FC metrics

Table 3 showed the multi-classification results with 4 classes (NC, EMCI, LMCI and AD) identified on ADNI2 and 3 classes (NC, MCI and AD) on OASIS3. The evaluation values were presented in the form of (%, mean ± standard deviation) in all experiments. Note that several other AD prediction methods, including traditional machine learning methods, DNNs, and standard graph neural networks (GNNs) were compared in our previous work. We incorporated the corresponding results along with the results of the nonlinear FC metrics based MLC-GCN to have a more comprehensive comparison across various prediction methods. We should also note that the previous results shown in Table 3 for Random Forest, SVM, DNN, BrainnetCNN, FCNet, GAT, GCN, FBNetGNN-GRU and FBNetGNN-CNN were based on CC connectome derived from the coarsest level of the rsfMRI data. All MLC-GCN classifiers were based on 6 levels of STFE and GCNs.

Table 3:

Multi-classification performance of different methods on ADNI2 and OASIS-3

Dataset	Method	Acc	AUC	Spe	Sen	F1-score
ADNI2	Random Forest [35 ]	54.42±3.69	80.29±2.90	84.20±1.33	51.28±3.66	51.13±3.89
	SVM [36 ]	63.39±1.65	86.51±1.06	87.65±0.57	63.75±1.53	63.36±1.67
	DNN [37 ]	72.27±2.43	88.31±2.83	90.76±0.78	72.26±1.95	72.99±2.10
	BrainnetCNN [38 ]	72.51±5.03	88.18±4.18	90.65±1.68	72.61±4.77	72.87±4.98
	FCNet [39 ]	69.20±3.82	86.27±1.50	89.56±1.26	69.31±3.85	69.24±4.09
	GAT [40 ]	67.04±4.09	83.56±3.16	88.58±1.59	66.41±4.65	66.53±4.62
	GCN [41]	73.56±2.63	88.68±1.69	91.07±0.91	73.71±2.62	73.67±2.51
	FBNetGNN-GRU [42 ]	73.09±2.64	88.76±2.44	88.86±4.47	73.02±3.55	73.09±2.99
	FBNetGNN-CNN [42 ]	71.85±4.31	88.00±2.72	90.26±1.09	71.89±4.44	72.12±4.38
	MLC-GCN-CC	80.4±2.37	91.6±2.16	93.32±0.81	80.09±2.41	80.44±2.4
	MLC-GCN-CE	77.41±2.33	91.65±2.02	92.3±0.82	77.89±2.53	78±2.33
	MLC-GCN-CSE	39.19±1.36	59.85±3.63	79.16±0.49	36.39±1.74	32.78±2.42
	MLC-GCN-KL	79.78±1.31	92.45±1.67	93.61±0.98	79.91±2.11	79.58±1.69
	MLC-GCN-MI	87.72±1.9	95.9±1.08	95.86±0.6	87.7±1.5	87.68±1.89
OASIS-3	Random Forest [35 ]	68.22±0.91	80.13±3.58	72.72±0.46	41.84±1.54	41.14±2.85
	SVM [36 ]	76.44±2.80	85.91±2.79	81.99±1.32	55.82±4.09	57.89±6.24
	DNN [37 ]	84.22±2.24	89.20±1.78	88.59±1.46	76.19±2.91	77.93±4.27
	BrainnetCNN [38 ]	85.56±2.12	91.16±1.81	88.69±2.01	75.21±3.32	79.19±2.25
	FCNet [39 ]	78.44±4.02	85.87±3.98	86.30±3.09	70.22±6.61	70.12±5.92
	GAT [40 ]	79.33±1.44	85.62±2.38	85.42±1.27	67.94±1.82	70.91±1.77
	GCN [41 ]	83.33±0.88	89.68±1.14	87.98±0.95	73.49±3.52	75.27±2.92
	FBNetGNN-GRU [42 ]	85.89±2.44	90.37±1.73	90.14±1.81	77.68±5.16	79.92±4.04
	FBNetGNN-CNN [42]	85.67±2.87	90.58±2.31	89.70±1.37	77.96±4.82	79.19±5.44
	MLC-GCN-CC	89±1.44	93.88±1.44	92.06±0.91	82.11±2.37	84.08±2.09
	MLC-GCN-CE	84.78±1.82	89.72±1.79	89.53±1.7	75.97±4.37	78.38±3.53
	MLC-GCN-CSE	65.67±0.46	60.85±4.69	71.77±2.66	41.89±4.24	41.02±5.71
	MLC-GCN-KL	83.78±1.26	89.72±1.25	89.26±1.15	76.88±2.56	78±2.09
	MLC-GCN-MI	94.11±1.28	95.79±1.64	96.27±1.31	89.92±2.56	91.18±1.92

Linear and nonlinear FC connectome based MLC-GCN outperformed the other methods as shown in Table 3. On the ADNI2 dataset, all MLC-GCNs models with four linear or nonlinear metrics, except CSE, achieved the best performance and outperformed all other models. On OASIS-3, MLC-GCN-CC and MLC-GCN-MI showed the best performance. MI consistently outperformed CC for both datasets and for all performance indices. Compared with CC, MI achieved significantly better performance across all metrics, including a 7.32 increase in ACC, 4.3 increase in AUC, 2.54 increase in Spe, 7.61 increase in Sen and 7.24 increase in F1-score on ADNI2. The corresponding performance increase for OASIS3 data were 5.11 in ACC, 1.91 in AUC, 4.21 in Spe, 7.81 in Sen, and 7.1 in F1-score. MLC-GCN-CE demonstrated comparative performance to MLC-GCN-CC, slightly outperforming it on ADNI2.

Table 4 and Table 5 present the performance metrics (obtained from the test cases during cross-validations) for each sub-group from ADNI2 and OASIS-3 separately. In the four groups of ADNI2 (NC, EMCI, LMCI and AD) and three groups of OASIS3 (NC, MCI and AD), MLC-GCN-MI, using MI as the FC metric, achieved the best performance across all five evaluation metrics, signficantly outperforming the other FC metric based MLC-GCNs. In the AD group on ADNI2, CE showed better performance than CC and KL. Figure 3 illustrates the distribution of accuracy for the EMCI, LMCI, and AD groups of ADNI2 as well as NC, MCI and AD groups of OASIS-3 for all five metrics. Both datasets showed MLC-GCN with MI as an FC metric achieved the best diagnosis performance, with the highest average prediction accuracy and small standard deviation.

Table 4:

Group comparison of different FC metrics on ADNI2

Group	Method	Acc	AUC	Spe	Sen	F1-score
NC	MLC-GCN-CC	87.71±3.45	90.39±3.55	89.46±4.45	86.42±3.13	85.52±3.71
	MLC-GCN-CE	85.21±3.32	90.27±2.63	87.06±5.85	83.93±2.72	82.17±2.76
	MLC-GCN-CSE	68.6±4.16	59.32±1.68	80.48±10.82	59.97±2.57	59.79±0.86
	MLC-GCN-KL	89.899±0.58	93.68±1.68	91.88±2.41	88.47±1.92	87.89±0.86
	MLC-GCN-MI	94.25±1.5	96.41±1.02	95.61±2.2	93.26±1.12	93.09±1.65
EMCI	MLC-GCN-CC	89.27±1.61	91.9±3.73	91.75±1.99	87.36±1.39	86.94±1.79
	MLC-GCN-CE	86.78±0.75	89.13±3.62	92.19±3.02	82.61±3.26	83.23±1.71
	MLC-GCN-CSE	56.9±9.82	63.62±5.58	51.63±2.35	61.11±2.28	53.94±5.17
	MLC-GCN-KL	87.87±1.97	88.75±3.15	92.62±0.91	84.19±3.35	84.73±2.81
	MLC-GCN-MI	92.85±1.26	95.8±1.51	95.23±1.24	91.02±2.7	91.12±1.75
LMCI	MLC-GCN-CC	90.36±1.87	90.2±3.92	95.49±1.37	84.95±4.23	86.24±3.05
	MLC-GCN-CE	88.18±1.78	90.75±3.55	93.02±2.57	83.01±3.77	83.54±2.76
	MLC-GCN-CSE	75.28±3.87	57.05±5.95	92.82±3.28	56.65±2.99	56.65±4.05
	MLC-GCN-KL	89.89±2.56	92.36±3.53	94.46±2.66	85.05±2.56	85.95±3.29
	MLC-GCN-MI	92.54±2.35	93.69±4.38	95.28±3.28	89.65±3.44	89.81±3.02
AD	MLC-GCN-CC	93.47±1.3	93.61±2.78	96.57±1.45	88.09±2.74	88.85±2.28
	MLC-GCN-CE	94.71±1.7	95.9±2.09	96.95±1.26	90.85±3.38	91.1±2.82
	MLC-GCN-CSE	77.62±6.62	59.95±2.81	91.69±13.06	53.6±4.39	50.51±5.48
	MLC-GCN-KL	91.9±2.86	95.19±1.63	93.91±3.39	88.55±5.6	86.99±4.66
	MLC-GCN-MI	95.8±1.51	97.47±1.78	97.34±2.24	93.38±2.44	93.06±2.29

Table 5:

Group comparison of different FC metrics on OASIS-3

Group	Method	Acc	AUC	Spe	Sen	F1-score
NC	MLC-GCN-CC	91.44±1.6	94.95±1.31	81.21±2.03	89.29±1.62	90.48±1.75
	MLC-GCN-CE	88.22±1.9	93.18±1.69	77.58±6	85.98±2.56	86.9±2.27
	MLC-GCN-CSE	67.44±1.69	62.3±4.7	23.33±14.07	58.16±4.24	55.43±6.99
	MLC-GCN-KL	87.55±1.87	90.81±2.11	78.18±3.8	85.58±2.23	86.3±2.13
	MLC-GCN-MI	96.22±1.44	97.8±1.59	93.03±5.31	95.55±2.18	95.88±1.61
MCI	MLC-GCN-CC	91.78±1.44	93.88±1.09	97.48±1.53	86.07±1.97	88.32±2.02
	MLC-GCN-CE	87.44±1.6	88.74±2.16	93.03±1.53	81.85±3.56	86.68±2.77
	MLC-GCN-CSE	75.67±0.46	59.89±7.61	93.48±4.78	57.85±5.05	57.13±6.70
	MLC-GCN-KL	86.11±0.97	87.92±1.86	92.74±1.32	80.02±1.59	80.67±1.36
	MLC-GCN-MI	95.22±1.28	96.09±2.51	97.04±1.38	93.41±2.36	93.59±1.77
AD	MLC-GCN-CC	94.78±0.93	95.3±2.1	97.49±1.26	85.88±3.64	86.92±2.43
	MLC-GCN-CE	93.89±1.36	92.12±3.31	97.99±0.81	80.42±6.03	66.3±37.32
	MLC-GCN-CSE	88.22±0.91	62.16±6.43	98.49±1.92	54.48±3.42	54.66±5.55
	MLC-GCN-KL	93.89±1.47	93.01±1.62	96.86±0.99	84.14±4.29	84.83±3.64
	MLC-GCN-MI	96.79±0.91	95.87±2.21	98.74±0.89	90.32±2.57	91.89±2.25

Figure 3:

The distributions of the accuracy in EMCI, LMCI and AD group of the ADNI2 as well as NC, MCI and AD group of OASIS-3 datasets for all five metrics, respectively.

Statistical test

Table 6 shows the FDR corrected p-values of the pairwise comparison of each performance index between different MLC-GCNs. Performance indices were also shown in the violin plot in Figure 3. MI demonstrated significant differences compared to CE, KL and CSE on both datasets and to CC on OASIS-3 with the exception of AUC, where no significant difference was observed between MI and CC. On ADNI2, the p-value of Acc, Spe, Sen and F1 were close to 0.05, indicating a marginal significance.

Table 6:

P-value of t-test on ADNI2 and OASIS-3 for five FC metrics

Dataset	Compared Metrics	Acc	AUC	Spe	Sen	F1-score
ADNI2	MI-CC	0.0499	0.1356	0.0505	0.058	0.0579
	MI-CE	0.0004	0.0026	0.0006	0.0001	0.0002
	MI-KL	6.92e-06	0.0002	1.49e-05	1.91e-06	3.68e-06
	MI-CSE	7.76e-11	1.29e-05	9.49e-08	3.07e-08	3.58e-05
	CE-CC	0.0482	0.1634	0.0528	0.0613	0.058
	CE-KL	0.0765	0.9673	0.0794	0.0383	0.0715
	CE-CSE	1.42e-06	3.34e-06	1.98e-07	1.71e-08	1.46e-06
	KL-CC	0.1968	0.1737	0.2163	0.2764	0.2031
OASIS-3	MI-CC	0.0023	0.2239	0.0005	0.0032	0.0188
	MI-CE	1.35e-05	0.0013	1.92e-05	8.86e-06	4.39e-05
	MI-KL	0.0001	0.0095	1.42e-05	0.0003	0.0019
	MI-CSE	1.43e-07	1.62e-05	1.35e-05	1.51e-07	3.72e-05
	CE-CC	0.0002	0.0026	0.0008	0.0023	0.002
	CE-KL	0.1372	0.0616	0.9205	0.0683	0.055
	CE-CSE	2.42e-06	2.65e-05	1.84e-05	3.64e-06	0.0001
	KL-CC	0.0031	0.0247	0.0003	0.049	0.0616

Model understanding

To better understand the performance of the multiple scale STFE and the corresponding GCN model, we visualized both the multi-level connectome matrices and the generated connectomes from the multi-level matrices. Figure 4 (a) illustrates the mean CC and MI connectomes of both ADNI2 and OASIS3 datasets at scale 0 (the scale of the input data). Figure 4 (b) are the mean connectomes of both datasets at all other scales. The generated graphs in Figure 4 (b) showed a similar sparsity pattern in MI connectomes and their generated graphs as those derived from CC. To calculate the sparsity of different connectomes, we used the Gini index of the FC matrices, which indicates higher sparsity with greater value. The CC connectome sparsity was 0.0789 for ADNI2, and 0.0419 for OASIS3. By contrast, the MI connectome sparsity was 0.0902 and 0.2160 for ADNI2 and OASIS3, respectively. By keeping the top 1% edges of the connectomes, where connection strengths exceeded 0.354 for ADNI2 and 0.336 for OASIS3 using CC and 0.372 for ADNI and 0.339 for OASIS3 using MI, Figure 4 (c) shows the 3D rendering results of the most salient nodes and connections. The node size reflects the number of connections remaining after thresholding. Similar connectome patterns were observed in both ADNI2 and OASIS3, with nodes covering the frontal gyrus, inferior frontal gyrus, temporal gyrus, fusiform gyrus, parahippocampal gyrus and other place--regions known to undergo structural and functional changes associated with AD.^4,7,43-48

Figure 4:

Visualizations of the FC matrix bying choosing top 1% dedges to form the brain network matrix and the generated graph for both CC and MI. (a) Manual-designed FC matrices based on the given metrics from the preprocessed BOLD time seriers signals. (b) Generated brain graph by averaging different feature levels and rs-fMRI data. (c) 3D generated connectome only including the top 1% edges from (b).

To further understand STFE and GCN learned connectomes, Figure 5 highlights the top 20 most connected nodes in the mean connectomes generated by MLC-GCN for both datasets. The upper half represents connectomes computed using CC as the FC metric, while the lower half represents those using MI. Across two datasets (ADNI2 and OASIS-3) and two FC metrics (CC and MI), the most connected regions were located in very similar regions.

Figure 5:

Top 20 important brain regions associated with AD in the generated connectomes captured by MLC-GCN with by CC and MI separately on (a) ADNI2 and (b) OASIS-3 according.

Discussion

This study assessed the feasibility of using nonlinear FC and GCNs to predict AD. A key component of the predictor is the multi-layer STFE and GCN used to extract spatio-temporal features and generate the graph-based deep neural networks. STFE is a natural choice for brain connectivity feature extractions because brain activity is spatially and temporally integrated and segregated. Multi-layer processing is widely used in multiple layer perception and deep learning, which is motivated by the hierarchical feature learning and extraction in brain cortex. Graph network is used because functional connectome is a representation of brain graph and brain information processing is performed in the graph rather than the Euclidean grid space.

We compared MLC-GCN with MI to several models reported in the literature, including two traditional shallow machine learning methods: random forest³⁵ and SVM³⁶, DNNs (BrainnetCNN,³⁸ FCNet,³⁹ and a DNN with two auto-encoders³⁷), and GNNs (GCN,⁴¹ GAT,⁴⁰ and FBNetGNN⁴²). All deep machine learning methods outperformed traditional machine learning yielded the worst performance, meaning that shallow machine learning and handcrafted feature extractions are limited for learning the complex brain vs symptom relationship. Graph-based deep neural networks outperformed the non-graph ones, suggesting a better FC feature representation through the graph convolution and processing. MLC-GCN showed better performance than the single-scale connectome based graph networks (FBNetGNN-GRU and FBNetGNN-CNN), indicating the benefit of multi-scale spatio-temporal feature extraction and connectome generation. Among all tested models, MLC-GCN-MI showed the best performance. Except for CSE, all other nonlinear FC-based MLC-GCN outperformed CC. This clearly demonstrates the benefit of exploiting nonlinear rsfMRI relationship in AD prediction. CSE showed the worst performance, suggesting that it is not a valid approximation to cross entropy.

We visualized the model learned connectome features to gain insights into the model's learned representations. Connectomes derived from the spatio-temporally fused features exhibited significantly higher sparsity than those based solely on the low-level rsfMRI signals. The increased sparsity of the learned connectomes is consistent with the better performance achieved by the MLC-GCNs as sparse representations often focus on the most salient features while ignoring noise and redundant information (corresponding to lower sparsity). Sparser representations are also more robust to noise. Meanwhile, we also found that the most prominent connections from the generated connectomes are between temporal cortex, inferior frontal cortex, medial prefrontal cortex, and dorso-lateral prefrontal cortex, which have been shown to be affected by the pathophysiological process in AD. Lateral parietal cortex and precuneus are among the regions showing the earliest and most prominent pathological changes in AD and have been shown to have reduced scale zero FC in AD. However, our visualization results showed that they are not within the 20 most prominent regions showing AD status contributing FC patterns at higher scales. This no-show indicates that AD effects on the larger scale FCs were more prominent in regions other than the well-documented lateral parietal cortex and precuneus. The top prominent regions overlapped to a large extent between the linear FC (CC) and nonlinear FC (MI), indicating that MLC-GCNs reliably learned disease related FC patterns from clinically relevant brain regions. While the visualization results need more independent studies to confirm, they demonstrate a potential of using deep graph networks to understand the brain mechanisms in AD and to identify inter-regional linear or nonlinear multi-scale connectivity-based markers for AD diagnosis, potential intervention development, and disease progression monitoring.

While the results are promising, several challenges and limitations must be acknowledged. First, the proposed method entails considerable computation complexity and load due to the use of intricate graph representations and deep learning architectures. Running these models requires high-performance computing resources, which may not be readily available in typical clinical settings. Optimization strategies, such as model compression and pruning,⁴⁹ could mitigate this constraint and enhance clinical translatability. Furthermore, interpretability remains a common challenge of deep learning methods. Although this study explored model visualization, additional techniques—such as saliency mapping or node importance scoring—can be integrated, particularly in an individualized manner, to identify subject-specific brain regions or connections that contribute most to the predicted risk scores. Another concern is the model's sensitivity to variations in data characteristics. FC can be influenced by multiple factors, including physiological status, scanner differences, and acquisition protocols. While traditional data harmonization approaches may alleviate such effects, a strength of deep learning lies in its ability to learn latent data representations across heterogeneous datasets. In this study, we trained and evaluated the model using multi-site data from the ADNI cohort and achieved comparably robust performance on the OASIS3 dataset, which was acquired at a single site with distinct imaging parameters. This suggests that the model is capable of capturing disease-relevant features while remaining resilient to some confounding sources of variability. The resting-state fMRI data used in both ADNI2 and OASIS-3 have relatively low temporal resolution (e.g., $\mathsf{TR}\ge 2s$) and short time series (typically 140–180 volumes).

Low temporal sampling restricts the ability to detect fast fluctuations in neural activity and limits the precision of functional connectivity estimation. Short time series are more susceptible to motion artifacts and physiological noise, potentially distorting the MI estimates and the derived connectivity patterns. Current state-of-the-art rsfMRI acquisition (e.g., HCP with multiband acceleration, TR≈0.72s) is with high spatial and temporal resolution, which will increase the stability of the non-linear FC calculation especially for those based on the data probability density function.

Despite the computational complexity of the workflow, the trained MLC-GCN model and associated processing pipeline can be packaged into a user-friendly software toolbox for research and clinical use. This toolbox could be integrated with MRI scanner consoles to enable real-time disease probability estimation from each new patient’s rsfMRI and structural MRI data. Such functionality may assist clinicians in early diagnosis, guide follow-up assessments, and facilitate lifestyle or therapeutic interventions. Moreover, individualized predictive connectivity patterns can inform region-specific changes, supporting personalized treatment planning. By retraining the model to use baseline rsfMRI data for forecasting future clinical status, the approach may also be extended to disease progression monitoring in longitudinal contexts.

Although the current model was designed to predict disease status, it can be readily adapted for continuous outcome prediction, such as cognitive test scores (e.g., MMSE, MoCA). Additionally, multimodal fusion with structural connectivity or other neuroimaging modalities, as shown in prior studies,^19,50-52 can further enhance predictive performance. Integration with fluid biomarkers (e.g., CSF or plasma) is also feasible, wherein scalar biomarker values can be incorporated at later network layers, and pathological imaging data (e.g., amyloid PET) can be processed through parallel subnetworks and merged with the MLC-GCN framework at the feature fusion stage. These extensions warrant further investigation in future studies.

Data availability

The datasets analyzed in this study are publicly available at the ADNI (http://adni.loni.usc.edu) and OASIS-3 (https://www.oasis-brains.org/) project websites.