# Brain Networks and Intelligence: A Graph Neural Network Based Approach to
Resting State fMRI Data

Bishal Thapaliya 1, 2 Esra Akbas 1 Jiayu Chen 1, 2 Raam Sapkota 1, 2 Bhaskar
Ray 1, 2
Pranav Suresh 1, 2 Vince Calhoun 1, 2, 3 Jingyu Liu 1,2
1Georgia State University 2TReNDs Center 3Georgia Institute of Technology
Corresponding Author: Bishal Thapaliya<EMAIL_ADDRESS>
###### Abstract

Resting-state functional magnetic resonance imaging (rsfMRI) is a powerful
tool for investigating the relationship between brain function and cognitive
processes as it allows for the functional organization of the brain to be
captured without relying on a specific task or stimuli. In this paper, we
present a novel modeling architecture called BrainRGIN for predicting
intelligence (fluid, crystallized and total intelligence) using graph neural
networks on rsfMRI derived static functional network connectivity matrices.
Extending from the existing graph convolution networks, our approach
incorporates a clustering-based embedding and graph isomorphism network in the
graph convolutional layer to reflect the nature of the brain sub-network
organization and efficient network expression, in combination with TopK
pooling and attention-based readout functions. We evaluated our proposed
architecture on a large dataset, specifically the Adolescent Brain Cognitive
Development Dataset, and demonstrated its effectiveness in predicting
individual differences in intelligence. Our model achieved lower mean squared
errors, and higher correlation scores than existing relevant graph
architectures and other traditional machine learning models for all of the
intelligence prediction tasks. The middle frontal gyrus exhibited a
significant contribution to both fluid and crystallized intelligence,
suggesting their pivotal role in these cognitive processes. Total composite
scores identified a diverse set of brain regions to be relevant which
underscores the complex nature of total intelligence.

_Keywords_ Graph Neural Networks $\cdot$ Intelligence $\cdot$ Resting-State
fMRI Data $\cdot$ Static Functional Connectivity (sFNC)

##  1 Introduction

Intelligence is a complex construct that comprises various cognitive
processes. Researchers typically rely on a range of cognitive tests that
measure different aspects of cognition and form specific measures for
intelligence, such as fluid intelligence (the ability to reason and solve
problems in novel situations)(Kyllonen and Kell (2017)), crystallized
intelligence (the ability to use knowledge and experience to solve problems),
and total intelligence (a composite measure of overall cognitive ability).
There is always undamped human interest to reveal neural underpinnings of such
intelligence and to predict individual intelligence differences. Although
traditional MRI studies in the literature focused on structural brain measures
for various phenotypes (Suresh et al. (2023); Ray et al. (2023)), rapidly
growing studies have emerged to investigate the prediction of intelligence
based on brain functional features (Ferguson et al. (2017); He et al. (2020);
Dubois et al. (2018)). The review conducted by (Vieira et al. (2022)) further
concluded that functional MRI (fMRI) has become the most employed modality for
predicting intelligence, and resting-state fMRI (rs-fMRI) derived static
functional connectivity (FC) was the most studied predictor. rs-fMRI measures
spontaneous brain activity during rest through blood oxygen level-dependent
(BOLD) signals in response to neuronal activity. FC is defined as the degree
of temporal correlation between regions of the brain computed using time
series of BOLD signals, and rs-fMRI FC provides a comprehensive view of the
brain’s intrinsic organization (Lee et al. (2012)). Indeed, FC between the
default mode network and frontoparietal network have been validated to
contribute to individual differences in cognitive ability (Hearne et al.
(2016)).

While the majority of intelligence prediction approaches involve linear
regression methods, some studies have applied non-linear approaches including
polynomial kernel SVR (Wang et al. (2015)), and kernel ridge regression (He et
al. (2020)) methods and deep neural networks (He et al. (2020); Fan et al.
(2020); Li et al. (2023)). In recent years, Graph Neural Networks (GNNs) have
gained great interest and have evolved rapidly for end-to-end graph learning
applications. GNNs are considered the state-of-the-art deep learning methods
for solving graph-structured data analysis problems, as they specify a neural
network to fit into the graph structure with nodes and edges, and embed node
features and edge features with structural information in the graph. Various
studies have investigated the effectiveness of GNNs in different applications
such as social networks, protein networks, and neurological biomarkers (Kim
and Ye (2020); Kazi et al. (2023); Nandakumar et al. (2021)). Given the
network-structured nature of the brain, modeling brain connectome via GNNs has
been implemented. Most brain GNN studies utilize the FC graph from rs-fMRI
(Ktena et al. (2018); Škoch et al. (2022); Wu et al. (2021); Ma et al. (2018))
and classify a particular phenotype of the subjects, such as gender (Arslan et
al. (2018); Kazi et al. (2021)) or specific disease status (Kazi et al.
(2021); Ma et al. (2018)), while its predictive power for intelligence is yet
to be investigated.

Most GNNs assume that the nodes learn embeddings in an identical way
throughout the whole graph, which is problematic for brain connectome due to
the sub-network nature of the brain (Parente and Colosimo (2020)). Recently,
BrainGNN (Li et al. (2021)) proposed a new GNN architecture that tackled this
limitation by proposing a clustering-based embedding method in the graph
convolutional layer, which allows nodes in different clusters (representing
different brain networks) to learn embeddings differently. Inspired by
BrainGNN, we present a novel GNN model, Brain ROI-aware Graph Isomorphism
Networks (BrainRGIN ), for intelligence prediction. Firstly, we make use of a
graph isomorphism network (GIN) (Xu et al. (2018)) to improve the expressive
power of GNNs, which is designed to approximate the power of the Weisfeiler-
Lehman (WL) graph isomorphism test. Similar to BrainGNN, we also tackle the
limitation of node identical learning mechanism by introducing cluster
representation of the region of interest (ROI). By combining these two
architectures, our model can effectively capture both local and global
relationships between brain regions. Furthermore, we validate various
aggregation and read-out functions including attention-based readout methods.
As far as we are aware, this is the first study that uses graph neural
networks to uncover the patterns of the brain for intelligence prediction
using resting state fMRI data. We evaluate the performance of our proposed
model on a large dataset and demonstrate its effectiveness in predicting
individual differences in intelligence.

##  2 Theory and related work

###  2.1 Graph Neural Networks

Let $G=(V,E)$ denote a graph, where V represents the node set and E represents
the edge set of the graph G. Nodes are initialized with input feature vectors
$X_{v}$ for $v\in V$. GNNs use the graph structure and node features $X_{v}$
to learn the latent representation vector of each nodes, $h_{v}$. In some
cases, edges are also defined by vectors that can also be learned. There are
many variants of GNN, such as graph convolutional network (GCN) (Kipf and
Welling (2016)), graph attention network (Veličković et al. (2017)), and
inductive graph (Hamilton et al. (2017)). We focus on GCN and extension of
GCNs, and our research interest here is graph prediction, where, given a set
of graphs ${G_{1},...,G_{N}}\subseteq G$ and their labels
${y_{1},...,y_{N}}\subseteq Y$, we aim to learn a latent representation vector
$h_{G}$ of a graph, that predicts the label of an entire graph,
$y_{G}=g(h_{G})$.

Right after the introduction of the GCN model (Kipf and Welling (2016)), a new
extension, relational GCN (RGCN) (Schlichtkrull et al. (2017)) was proposed
that uses the neighborhood aggregation strategy similar to GCN but extends it
to handle relational data by incorporating the edge type in (Schlichtkrull et
al. (2017)) into the aggregation function. The RGCN model calculates the
forward propagation of node representation as:

$h^{(l)}_{i}=\text{ReLU}\left(W^{(l-1)}_{0}\cdot h^{(l-1)}_{i}+\sum_{j\in
N^{(l)}(i)}W^{(l-1)}_{r}(e_{i,j})\cdot h^{(l-1)}_{j}\right)$ (1)

where $h^{(l)}_{i}$ denotes the features for the $i$-th node in the $l$-th
layer, and $N^{(l)}(i)$ is the set of indices of neighboring nodes of node
$i$, $W^{(l)}$ denotes the model parameters to be learned. Specifically,
$W^{(l)}_{r}$ is the parameters learned specific to $e_{ij}$, the edge type
associated with the edge from node i to j. Thus, RGCN achieves improved
performance on tasks that require explicit modeling based on the edge
features.

Similarly, a more expressive graph neural network, GIN (Xu et al. (2018)) was
proposed in 2018, which approximates the WL graph isomorphism test to achieve
better graph discrimination and incorporates the global structure of a graph
while learning node representations. GINs also make use of a permutation
invariant readout function to compute the final representation of the graph,
ensuring that the model’s output is independent of the ordering of the nodes.
The forward propagation of GINs can be represented as:

$h_{i}^{(l)}=MLP^{(l)}\left(\left(1+\epsilon^{(l)}\right)h_{i}^{(l-1)}+\sum_{j\in\mathcal{N}^{(l)}(i)}h_{j}^{(l-1)}\right)$
(2)

where $\epsilon^{(l)}$ is a trainable parameter that helps to avoid the over-
smoothing problem, and $MLP^{(l)}$ is a 2-layered multi-layer perception to
update the final feature representation for the $i$-th node in the $l$-th
layer. The output of the graph is then computed as:

$h_{G}=READOUT\left({h_{i}^{(l)}}_{v\in G}\right)$ (3)

where $h_{G}$ is the final representation of the graph and $READOUT$ is a
permutation invariant function that aggregates the node representations to
produce a single output vector. GINs have been shown to outperform other
state-of-the-art GNNs on various graph classification tasks, demonstrating
their power and effectiveness in learning representations of graph-structured
data (Xu et al. (2018)).

##  3 Proposed Architecture

Figure 1:  Overall Architecture of BrainRGIN . The static FNC matrix is
extracted from a resting state fMRI time series data. Three blocks of
BrainRGIN are used with attention-based readout functions followed by a fully
connected layer for prediction.

The architecture presented in Fig. 1 depicts the overall working mechanism of
the BrainRGIN . As the initial step, we create a functional connectivity graph
using functional relations between ROIs of the brain. After creating the FC
graph, a three-layer RGIN (ROI-aware graph isomorphism network) block is
established, where each block encompasses a sequence of RGIN convolutions,
succeeded by a TopK Pooling layer. The output of RGIN is subject to an
Attention-Based Readout block either with a Squeeze-Excitation Readout (SERO)
function or a Graph Attention Readout (GARO) function. Finally, a single-layer
fully connected neural network serves to compute the intelligence score.

###  3.1 Functional connectivity graph creation

The initial phase involves the processing of input from fMRI time series data
to create a static FC matrix or static functional network connectivity (sFNC)
matrix. The difference between FC and FNC lies in how ROIs are generated:
regions selected based on an atlas lead to an FC matrix, while regions
generated by independent component analyses (ICA) lead to an FNC matrix. The
brain is spatially divided into N ROIs. In this study, we employed ICA ROIs
resultant static FNC matrix. Using ROIs time series, Pearson’s correlation
between ROIs is used to create a FNC matrix. The resulting FNC matrix is used
to construct an undirected graph denoted by the tuple $G=(V,E)$ with an
adjacency matrix $A\in R^{N*N}$. Each ROIs represents graph nodes indexed by
the set $V=1,...,N$. The input node features, $x_{i}$, are formed using
Pearson’s correlation coefficients between node i and all other nodes. An edge
set $E$ represents the functional connections between ROIs with each edge
$e_{ij}$ linking two nodes $(i,j)\in E$.

The Adjacency matrix $A_{k}\in R^{N\times N}$ is formed as in Equation 4,
where $e_{i,j}$ is the thresholded element of FNC matrix to achieve either
fully connected or sparse graph.

$A_{i,j}^{k}=\left\\{\begin{array}[]{ll}0,&i=j\\\
e_{i,j},&\text{otherwise}\end{array}\right.$ (4)

####  3.1.1 RGIN Convolution

We present RGIN convolution, an approach to effectively capture both node and
edge features in the graph by merging RGCN and GIN. Similar to BrainGNN,
within the context of brain function, the type of edge relation reflects the
different functional clustering of brain networks. In other words, nodes in
the brain are divided into functional clusters, and different brain clusters
form unique types of edge relations. Without fixing cluster assignments for
ROIs, the proposed model also learns cluster formation such that a group of
nodes in the same cluster works together (update together) to achieve the best
performance for the task. GIN is incorporated for learning node embeddings for
its better graph discriminative expression.

In RGIN, we replace the aggregation function of GIN with that of RGCN,
allowing the model to learn different mechanisms for different clusters. The
motivation behind using this design is twofold: 1) GIN utilizes Multilayer
Perceptrons (MLPs) to learn the injective functions to adapt to the complexity
of brain connectivity. 2) RGCN is able to model the sub-network clustering
nature of brain connectivity. The forward propagation function of RGIN is
defined as follows:

$h_{i}^{(l)}=\text{MLP}^{(l)}\left((1+\epsilon^{(l)})\cdot W_{i}^{(l)}\cdot
h_{i}^{(l-1)}+\sum_{j\in N^{(l)}_{(i)}}W_{j}^{(l)}\cdot e_{i,j}^{(l-1)}\cdot
h_{j}^{(l-1)}\right)$ (5)

While in regular GNN models, including GIN and RGCN, $W_{i}$ and $W_{j}$ are
learnable weight matrices, we define them as the function with parameters
subject to cluster assignment of nodes to make it ROI aware convolution layer.
Then, RGIN is trained in an end-to-end fashion with a 2-layered MLP.
$\epsilon^{(l)}$ here is a learnable parameter that determines the importance
of node $i$ compared to its neighbors $j$. In addition, multiplying node
features by the edge weights, similar to the graph convolution operations in
(Gong and Cheng (2018)), created a greater impact for neighbors connected by
stronger edges.

As given in Equation 6, ${W}^{(l)}_{i}$ is defined as a function to
incorporate the position encoding $r_{i}$, with parameters $\theta_{1}$ and
$\theta_{2}$ defined to learn the clustering specific parameter for nodes.
ReLU is the rectified linear unit activation function. and $\textbf{b}^{(l)}$
is the bias term.

$\textbf{W}^{(l)}_{i}=\theta_{2}^{(l)}\cdot\text{relu}(\theta_{1}^{(l)}\textbf{r}_{i})+\textbf{b}^{(l)}$
(6)

In the same way as BrainGNN (Li et al. (2021)), we allow RGIN to learn
different update learning parameters for different clusters conditioned on the
ROIs. We represent each node’s location information by a vector
$\textbf{r}_{i}$, using one-hot encoding instead of coordinates, assuming that
the ROIs are aligned in the same order for all the brain graphs.

We assume that $\theta^{(l)}_{1}$ =
$[\alpha^{(l}_{1},......,\alpha^{(l}_{N^{(l)}}]$, where $N^{(l)}$ is the
number of ROIs in the $l^{th}$ layer,
$\alpha^{(l)}_{i}=[\alpha^{(l)}_{i1},\ldots,\alpha^{(l)}_{iK(l)}]\in\mathbb{R}^{K(l)},\forall
i\in\\{1,\ldots,N^{(l)}\\}$, where $K(l)$ is the number of clusters in
$N^{(l)}$ ROIs, and $\alpha^{(l)}_{i}$ is the non-negative assignment scores
of ROI $i$ to clusters. Assume
$\mathbf{\theta}_{2}^{(l)}=[\beta^{(l)}_{1},\ldots,\beta^{(l)}_{K(l)}]$ with
$\beta^{(l)}_{u}\in\mathbb{R}^{d(l+1)\times d(l)}$, $\forall
u\in\\{1,\ldots,K(l)\\}$. $\beta^{(l)}_{u}$ is a basis matrix. Then, we can
rewrite equation (6) as:

$\textbf{W}^{(l)}_{i}=\sum_{u=1}^{K(l)}{\alpha}_{iu}^{(l)}\beta^{(l)}_{u}+\textbf{b}^{(l)}$
(7)

This reduces the number of learnable parameters while still allowing a
separate embedding kernel for each ROI. The final forward propagation function
of RGIN Convolution can be written as:

$\begin{split}h_{i}^{(l)}=\text{MLP}^{(l)}\Biggl{(}&(1+\epsilon^{(l)})\cdot\left(\sum_{u=1}^{K(l)}\alpha_{iu}^{(l)}\beta^{(l)}_{u}+\textbf{b}^{(l)}\right)\cdot
h_{i}^{(l-1)}\\\ &+\sum_{j\in
N^{(l)}_{(i)}}h_{j}^{(l-1)}\cdot\left(\sum_{u=1}^{K(l)}\alpha_{ju}^{(l)}\beta^{(l)}_{u}+\textbf{b}^{(l)}\right)\cdot
e_{i,j}^{(l-1)}\Biggr{)}\end{split}$ (8)

####  3.1.2 Pooling Layers

Via RGIN convolution, node-wise representation are generated. However, for the
prediction task discussed in this paper, which requires graph-level prediction
instead of node-level, these node-wise representations must be collected or
pooled together. We apply ROI-aware TopK Pooling as it improves
interpretability for rsfMRI data, by keeping the most indicative ROIs and
removing the noisy and uninformative nodes (Li et al. (2021)), along with
enforcing sparsity on the network. To select the most indicative ROIs, the
choice of which nodes to drop is determined based on the scores of nodes
obtained by projecting the node features to 1D via a learnable projection
vector $\omega^{(l)}\in\mathbb{R}^{d^{(l)}}$. The pooled graph
$(V^{(l+1)},E^{(l+1)})$ is computed as follows:

  1. 1.

Calculate the scores of nodes $s^{(l)}$ with node feature matrix as follows:

$\displaystyle s^{(l)}=\frac{{H}^{(l)}w^{(l)}}{\|w^{(l)}\|_{2}}$ (9)

  2. 2.

Normalize the score $s^{(l)}$ by subtracting its mean and dividing by its
standard deviation, yielding final scores $\tilde{s}^{(l)}$:

$\displaystyle\tilde{s}^{(l)}=\frac{(s^{(l)}-\mu(s^{(l)}))}{\sigma(s^{(l)})}$
(10)

  3. 3.

Find the top $k$ elements in the normalized score vector $\tilde{s}^{(l)}$
with $k$\- largest values and get their indices as $i$:

$\displaystyle i=\text{topk}(\tilde{s}^{(l)},k)$ (11)

  4. 4.

Create the pooled node features $H^{(l+1)}$ by element-wise multiplying the
original node features $H^{(l)}$ with the sigmoid of the normalized scores and
selecting only the elements indexed by $i$:

$\displaystyle H^{(l+1)}=(H^{(l)}\odot\text{sigmoid}(\tilde{s}^{(l)}))_{i:}$
(12)

  5. 5.

Create new adjacency matrix as the new pooled graph $E^{(l+1)}$ by returning
the edges between selected nodes $i$ from previous edge matrix $E^{(l)}$

$E^{(l+1)}=E^{(l)}_{i,i}$

In this description, $\|\cdot\|_{2}$ represents the L2 norm, $\mu$ and
$\sigma$ are functions that calculate the mean and standard deviation of a
vector, TopK identifies the indices of the largest $k$ elements in a vector,
$\odot$ denotes element-wise multiplication, and $(\cdot)_{i,:}$ selects
elements in the $i^{th}$ row and all columns.

####  3.1.3 Readout

The conventional READOUT function of GNN can be thought of as a fixed decoder
that decodes whole-graph features from the node features with no learnable
parameters. We address this issue by incorporating attention to the READOUT
function. The attention here refers to the scaling coefficient across the
nodes learned by the model. Therefore, we make use of attention-based readout
functions called GARO and SERO (Hu et al. (2017)) as proposed in STAGIN (Kim
et al. (2021)).

GARO function is inspired by the key-query embedding-based attention mechanism
of the Transformer (Vaswani et al. (2017)). The key embedding
$\mathbf{K}\in\mathbb{R}^{D\times N}$ is computed from node feature matrix
$\mathbf{H}\in\mathbb{R}^{D\times N}$, $D$ is the dimension of node feature
and $N$ is a number of nodes. The query embedding
$\mathbf{q}\in\mathbb{R}^{D}$ is computed from the vector of unattended graph
representation $\mathbf{H}_{\phi{mean}}$, where ${\phi{mean}}$ represents the
global average of node feature matrix $H$. $zspace$ is the final attention
vector.

$\displaystyle\mathbf{K}$ $\displaystyle=\mathbf{W}_{key}\mathbf{H},$ (13)
$\displaystyle\mathbf{q}$
$\displaystyle=\mathbf{W}_{query}\mathbf{H}{\phi_{mean}},$ (14)
$\displaystyle\mathbf{z}{space}$
$\displaystyle=\sigma\left(\frac{\mathbf{q}^{\top}\mathbf{K}}{\sqrt{D}}\right),$
(15)

where $\mathbf{W}_{key}\in\mathbb{R}^{D\times D}$,
$\mathbf{W}_{query}\in\mathbb{R}^{D\times D}$ are learnable key-query
parameter matrices, $\sigma$ is the sigmoid function. The GARO function uses
the attended key matrix to compute the final graph representation as follows:

$\displaystyle\mathbf{h}_{\mathrm{GARO}}$
$\displaystyle=\mathbf{H}\mathbf{z}_{space}.$ (16)

The GARO function allows the graph neural network to effectively capture
dynamic brain connectome by attending to the important nodes.

On the other hand, the SERO function applies the squeeze and excitation
operations to enhance the relevant features. Originally, the squeeze
excitation module was shown to increase the performance of CNN models (Roy et
al. (2019)). As we have a fixed number of nodes similar to (Kim et al.
(2021)), we applied the SERO module. It is important to note that the SERO
activation does not scale the channel dimension, but the node dimension. The
squeeze operation computes the global information of the node features using
the global average pooling, followed by the excitation operation which models
the dependencies between different nodes. Specifically, we first apply a
linear transformation to the squeezed feature vector and pass it through the
sigmoid function to obtain the importance scores for each nodes. These
importance scores are then multiplied with the original feature vector to
obtain the final readout feature vector. Given a set of node features
$\mathbf{H}$ with dimensionality $D$, the SERO function outputs the feature
vector $\mathbf{h_{SERO}}$ of dimensionality
$\mathbb{D^{\prime}}\in\mathbb{R}^{N\times D}$ as:

$\displaystyle z$ $\displaystyle=\mathbf{H}{\phi_{mean}}$ (17)
$\displaystyle{z}{space}$
$\displaystyle=\sigma(\mathbf{W}_{2}\delta(\mathbf{W}_{1}z))$ (18)
$\displaystyle\mathbf{h}_{SERO}$ $\displaystyle=\mathbf{H}\mathbf{z}_{space}.$
(19)

where $\sigma$ is the sigmoid function, $\delta$ is the ReLU activation
function, $\mathbf{W}_{1}\in\mathbb{R}^{D\times D}$,
$\mathbf{W}_{2}\in\mathbb{R}^{N\times D}$ are learnable weight matrices. The
first equation computes the global information of the node features using
global average pooling, and the second equation models the channel-wise
dependencies by learning the feature importance scores. The third equation
combines the original feature vectors with the computed importance scores to
obtain the final readout feature vector.

Furthermore, as the effectiveness of the mean and max element-wise pooling
operation is proven (He et al. (2020)), we compare the attention-based readout
function with the mean and max element-wise pooling readout method. For a
network, $G$ with $l$ convolution and respective pooling layers, the output
graph of the $l^{th}$ pooling block is summarized using a mean and max pooling
operation element-wise on $H(l)=[h(l)_{i}:i=1,...,N(l)]$. The resulting vector
is obtained by concatenating both the mean and max summaries. To obtain a
graph-level representation, the summary vectors from each layers of RGIN block
are concatenated together.

####  3.1.4 Loss Functions

We primarily use the SmoothL1Loss function as a criterion to train the model.
SmoothL1Loss is preferred over Mean Squared Error (MSE) Loss as it provides a
more robust and less sensitive measure of distance between predicted and
target values, with a less steep gradient around zero that makes it less
sensitive to outliers and noise, leading to better model convergence and
improved performance. It is defined as:

$L_{\text{smoothL1}}(x,y)=\begin{cases}0.5\cdot(x-y)^{2},&\text{if }|x-y|<1\\\
|x-y|-0.5,&\text{otherwise}\end{cases}$

Here, $x$ represents the predicted value and $y$ is the target value.

Furthermore, we also add the Unit Loss and TopK pooling loss (Li et al.
(2021)) for interpretation. Unit Loss is important because we use a learnable
vector $\mathbf{\omega}$ to represent nodes, but this vector can be scaled in
different ways without affecting the results. To solve this issue, we add a
rule that the vector must have a fixed length of 1, and we use a loss function
to ensure that this rule is followed, which is Unit Loss. The loss is
formulated as:

$L_{\text{unit}}(v)=||\omega||_{2}-1$

Here, $\omega$ represents the learnable vector representing a node, and
$||\omega||_{2}$ is the L2 norm of the vector. The goal is to minimize this
loss, which effectively encourages the learnable vectors to have a fixed
length of 1. This helps in finding meaningful and unique values for the vector
while accounting for different scaling factors.

Furthermore, using TopK Pooling loss ensures that top K selected indicative
ROIs should have significantly different scores than those of the unselected
nodes. It helps in identifying the most relevant ROIs. In order to achieve the
desired behavior in our model, where selected nodes should exhibit scores
close to 1, while unselected nodes should approach a score of 0, we employ a
training strategy as in (Li et al. (2021)). This strategy involves ranking the
sigmoid-transformed scores, $\tilde{s}^{(l)}_{m}$, in descending order for
each instance $m$, resulting in
$\hat{s}^{(l)}_{m}=[\hat{s}^{(l)}_{m,1},\ldots,\hat{s}^{(l)}_{m,N^{(l)}}]$. To
introduce diversity in these ranked scores across all $M$ training instances,
we employ a specific constraint. In practice, we define the TPK loss using
binary cross-entropy, given by:

$\displaystyle L^{(l)}_{\text{TPK}}$
$\displaystyle=-\frac{1}{M}\sum_{m=1}^{M}\left(\frac{1}{N^{(l)}}\sum_{i=1}^{k}\log(\hat{s}^{(l)}_{m,i})+\sum_{i=1}^{N^{(l)}-k}\log(1-\hat{s}^{(l)}_{m,i+k})\right)$
(20)

This loss encourages the scores of selected ROIs to be higher ensuring that
they stand out from the rest of the nodes.

The total loss $L_{\text{total}}$ is a combination of these individual loss
components:

$L_{\text{total}}=L_{\text{smoothL1}}+\sum_{l=1}^{L}L^{(l)}_{\text{unit}}+\lambda_{1}\sum_{l=1}^{L}L^{(l)}_{\text{TPK}}$

Where $L$ represents the number of layers in the model, and $\lambda_{1}$ is a
hyperparameter that balances the contribution of the TopK Pooling loss. This
combination of loss components helps in training the model to achieve good
convergence, meaningful node representations, and relevant ROIs selection.

Overall with the architecture above, our proposed model for resting state fMRI
data prediction using staticFNC could bring several benefits:

  * •

By replacing the aggregation function of GIN with that of RGCN, the resulting
RGIN model takes advantage of both permutation invariant update function and
aggregation functions.

  * •

We tackle the limitation of all brain ROIs learning embeddings in an identical
manner by incorporating a clustering-based embedding method in the
convolutional layer of the graph.

  * •

Instead of using conventional READOUT methods of GNNs, we make use of
attention-based readout function which effectively captures the information by
obtaining the importance scores for each node.

##  4 Experiments

####  4.0.1 The ABCD (Adolescent Brain Cognitive Development) Dataset

ABCD is a large ongoing study following youths from age 9-10 into late
adolescence to understand factors that increase the risk of physical and
mental health problems. Participants were recruited from 21 sites across the
US to represent various demographic variables. Data used in this study were
from 8520 children aged 9–10 at baseline, including resting state fMRI image
and fluid intelligence, crystallized intelligence, and total composite scores.
Data were split into training (n = 5964), validation (n = 1278), and test (n =
1278) subsets. There were 4430 male and 4089 female subjects in this study.
Age and site effects were regressed out from the intelligence scores to make
sure that only the relevant intelligence features are captured by our graph
model.
We conducted preprocessing on the raw resting-state fMRI data utilizing a
combination of the FMRIB Software Library (FSL) v6.0 toolbox and Statistical
Parametric Mapping (SPM) 12 toolbox within the MATLAB 2019b environment. The
preprocessing encompassed several key steps, namely: 1) correction for rigid
body motion; 2) distortion correction; 3) removal of dummy scans; 4)
standardization to the Montreal Neurological Institute (MNI) space; and 5)
application of a 6 mm Gaussian kernel for smoothing. Subsequently, we employed
a fully automated spatially constrained independent component analysis
framework to extract 53 robust intrinsic connectivity networks (ICNs) using
the Neuromark_fmri_1.0 template. These ICNs were categorized into seven
functional domains based on their anatomical locations and functional
characteristics, which included subcortical, auditory, visual, sensorimotor,
cognitive control, default mode, and cerebellar domains. Functional network
connectivity (FNC) was computed as the Pearson correlation between the time
courses of these intrinsic connectivity networks.

Table 1: Comparison of different BrainRGIN architectures for intelligence
prediction

Aggregation | Readout | Fluid Intelligence | Crystallized Intelligence | Total Composite Scores
---|---|---|---|---
MSE | Corr | MSE | Corr | MSE | Corr
Sum | Attention Based Readout (SERO) | 263 | 0.23 | 295.95 | 0.27 | 261 | 0.31
Mean |  | 269 | 0.21 | 295 | 0.27 | 268.58 | 0.29
Sum | Attention Based Readout (GARO) | 274.69 | 0.20 | 263.7 | 0.30 | 291 | 0.29
Mean |  | 270.05 | 0.20 | 268.7 | 0.28 | 267.01 | 0.29
Sum | Mean + Max Readout | 300 | 0.19 | 299.81 | 0.27 | 271.37 | 0.30
Mean | 298 | 0.19 | 298.30 | 0.27 | 289.93 | 0.30

###  4.1 Experimental Setup

The neural network architecture depicted in Fig. 1 was implemented using
Pytorch (Paszke et al. (2019)), and Pytorch Geometric (Fey and Lenssen (2019))
for the specific graph neural network components. The number of nodes was 53
(corresponding to NeuroMark (Du et al. (2020)) ICA Components), and the number
of node features per each node was the number of pairwise correlations between
each other nodes (i.e., 53). The performance of the BrainRGIN architecture was
evaluated using the ABCD dataset for predicting fluid intelligence,
crystallized intelligence, and total composite scores. We created three
different variations of BrainRGIN for various intelligence prediction tasks.
The number of edges depends on the threshold percentage used to retain only
the strongest correlations, which was selected to be 100% for all the
prediction tasks. The model architecture for all intelligence prediction tasks
was implemented with 3 RGIN layers with node sizes 32, 128, and 256
respectively followed by pooling layers as shown in Fig. 1 and attention-based
readout functions for each layer. The pooling ratio from hyperparameter tuning
was set to be 0.38 from fluid intelligence, 0.46 for crystallized intelligence
and 0.78 for total composite scores. The number of clustered communities is
set to 7, and the motivation for this comes from the seven functional networks
defined by (Yeo et al. (2011)), because these 7 networks show key brain
functionality relevance. The majority of these settings were fixed with the
hyperparameter search. We also tested the BrainRGIN architecture with a
variety of aggregation (Sum, Mean) and readout (SERO, GARO and Mean+Max)
architectures to identify how different choices affect the performance of the
model. We first identified the best BrainRGIN architecture compared with a
variety of graph convolution, pooling and readout architectures for predicting
intelligence. Finally, the best architecture was used for comparison with
baseline models.

We compared the performance of BrainRGIN with some baseline models. The
baseline models includes BrainGNN (Li et al. (2021)), Support Vector
Regression (SVR), Logistic Regression (LR), and Ridge Regression (Ridge). We
particularly excluded reporting the performance of other baseline models like
GCN (Kipf and Welling (2016)), GAT (Veličković et al. (2017)), GraphSage
(Hamilton et al. (2017)) because of proven BrainGNN superior performance over
these models. For BrainGNN, we performed multiple sweeps to identify the best
performance. Based on performance, setting the learning rate of both BrainRGIN
and BrainGNN initially to 0.001 and reducing every 30 epochs achieved the best
performance for all prediction tasks. For BrainGNN, we used two convolutional
layers of size 32, as presented in the original paper (Li et al. (2021)), with
a fully connected layer of size 512. For the other baseline methods, we used
Polyssifier (https://github.com/sergeyplis/polyssifier). This tool is widely
used to perform baseline model comparisons and has a feature to automatically
perform hyperparameter search and identify the best parameters of the model
for the highest performance. For the evaluation metrics, we considered Mean
Squared Error (MSE) and Correlation. The results were reported using a
separate holdout testing set (n=1278) and the average scores of experiments
using four different seeds are reported for every intelligence prediction
task.

##  5 Results

The results of the experiment are shown in Table 1 and Table 2. As can be seen
from Table 1, the BrainRGIN architecture achieved the best performance for
predicting fluid intelligence with a mean squared error (MSE) of 263 and a
correlation of 0.23 with RGIN convolution and SERO readout method. It also
achieved the best performance for predicting crystallized intelligence with an
MSE of 263.7 and a correlation of 0.30 with the RGIN convolution and SERO
readout method. In the case of total composite scores, the GARO attention-
based readout function with the RGIN Graph model attained the best scores with
an MSE of 261 and a correlation of 0.31. Additionally, BrainRGIN also
outperformed all baseline models and achieved better results than SVR, LR, and
Ridge, with lower MSE and higher correlation values for all fluid
intelligence, crystallized intelligence, and total composite scores. These
findings highlight the superior performance of RGIN aggregation and attention-
based readout methods over the BrainGNN model and other baseline models in
predicting intelligence scores. Furthermore, we conclude that attention-based
readout methods outperform other readout methods, and were found to contribute
significantly to the architecture’s success in predicting intelligence scores.

Table 2: Comparison of BrainRGIN With Baseline Models

Models | Linear | Fluid Intelligence | Crystallized Intelligence | Total Composite Scores |
---|---|---|---|---|---
MSE | Correlation | MSE | Correlation | MSE | Correlation |
SVR | No | 275 | 0.20 | 307 | 0.24 | 307 | 0.24 |
LR | Yes | 326 | 0.19 | 354 | 0.22 | 345 | 0.23 |
Ridge | Yes | 325 | 0.19 | 353 | 0.22 | 349 | 0.23 |
BrainGNN | No | 264 | 0.22 | 288.29 | 0.28 | 294.12 | 0.29 |
BrainRGIN | No | 263 | 0.23 | 263.7 | 0.30 | 261 | 0.31 |

Table 3: Effect of edges threshold selection in model prediction

Edge Threshold | MSE
---|---
Fluid | Crystallized | TotalComp
100% | 263 | 263.7 | 261
80% | 269.22 | 276.12 | 272
60% | 271.35 | 278.38 | 269.24
50% | 288.12 | 281.06 | 283
40% | 290.05 | 297.12 | 288

These findings underscore the importance of carefully selecting appropriate
graph neural network components for predicting intelligence scores from rsfMRI
data and provide a valuable foundation for future research in this area.

###  5.1 Hyperparameter Study

We also analyzed how changing the edges threshold affected the performance of
the model. Interestingly, as can be seen from Table 3, we saw that using 100%
of edges gave a superior performance for prediction for all intelligence
prediction tasks. Besides, inspired by BrainGNN (Li et al. (2021))
hyperparameter study for TopK Loss regularizer, we fixed the regularizer
$\lambda 1$ to 0.1 to partially force the network to select the same top nodes
and also make sure that the selected nodes have different scores than those of
the unselected nodes.

###  5.2 Interpretation of brain regions and networks

To identify the top ROIs for the intelligence prediction tasks, we first
extracted the pooled ROIs after passing through the first layer of TopK Pool
layer of a fully trained model using a holdout test set. We then selected the
ROIs with highest frequency across each of the samples for all the
intelligence scores. For fluid intelligence, we selected two ROIs (Middle
Temporal Gyrus, and Middle Frontal Gyrus) (Fig 2(a)) with 90% frequency
threshold. Similarly, for crystallized intelligence, middle frontal gyrus and
caudate were selected with a frequency threshold of 90% (Fig 2(b)). For total
composite scores, as the pooling ratio from hyper-parameter tuning was higher
(0.78), we were able to extract 21 brain regions for 95% frequency. We
categorized the selected regions into seven connectivity networks and plotted
them independently in Fig. 3.

##  6 Discussion and Conclusion

In this research study, a novel technique called Brain ROI-Aware Graph
Isomorphism Networks, BrainRGIN , was proposed to predict intelligence using
static FNC matrices derived from resting-state fMRI data. BrainRGIN integrates
the expressive power of GIN and clustering-based GCN and also incorporates
attention-based readout function, in the hope of better representing brain
networks and improving model prediction. Specifically, by replacing the
aggregation function of GIN with that of RGCN, the model leverages the
powerful representation learning capability of GIN, while still capturing the
edge strength and edge type represented by a clustering-based embedding
method. Another notable aspect of the proposed architecture is the use of
attention-based readout functions instead of conventional readout methods,
which is proven to be very effective as can be seen from Table 1. The
attention mechanism assigns importance scores to each node, effectively
capturing spatial relevance information for prediction. Using attention-based
readout functions not only improved the overall prediction of the model but
also validated the theory that different brain regions contribute in a
different manner to intelligence prediction.

(a)  Middle frontal gyrus and Middle temporal gyrus

(b) Middle frontal gyrus and Caudate

Figure 2: Regions Significant in Fluid and Crystallized Intelligence
Prediction

(a) Cognitive Control Network

(b) Default Mode Network

(c) Sensorimotor Network

(d) Subcortical Network

(e) Visual Network

(f) Cerebellar Networks

Figure 3: Significant regions expressed as Connectivity Networks for Total
Composite Scores

The top two regions contributing to fluid intelligence are the middle frontal
gyrus and the middle temporal gyrus. In fact middle frontal gyrus contributes
to all three intelligence scores, and its overall significance in predicting
intelligence is in line with the literature. In particular, the dorsolateral
prefrontal cortex in the middle frontal gyrus is well known to play a crucial
part in many domains of cognitive processes, including working memory (Barbey
et al. (2013)), attention control (Knight et al. (2020)), executive function
(Nejati et al. (2021)), and decision making (Patterson et al. (2007)), etc (Yu
et al. (2022)). Given its multi-domain involvement in cognition, this region’s
engagement substantiates its relevance in all intelligence scores. The
function of the middle temporal gyrus is relatively more specific to language
relevant (Turken and Dronkers (2011)), such as semantic processing (Binder et
al. (2009)), syntactic comprehension (Yu et al. (2022)), language
comprehension, decoding intelligible speech. Its role in fluid intelligence
prediction could be attributed to its contribution to information decoding and
integration. In the context of crystallized intelligence, besides the middle
frontal gyrus, caudate plays the most remarked contribution. The caudate’s
association with learning (Choi et al. (2020)) and memory consolidation
(Müller et al. (2017)) aligns with crystallized intelligence’s reliance on
acquired knowledge and experience (Grazioplene et al. (2014)). The combined
involvement of middle frontal gyrus and caudate suggests a cooperative
engagement in translating stored knowledge into practical problem-solving
skills, a hallmark of crystallized intelligence.

The diverse set of brain regions identified as relevant for total composite
score reflects the intricate and distributed nature of cognitive processes, as
well as the general and broad attribute of ’intelligence’. These regions cover
six relatively separate brain networks. Sensorimotor network (postcentral
gyrus) and visual network(middle/inferior occipital gyri, calcarine cortex,
cuneus, fusiform) involve basic functions of various sensory inputs (J;Tadi )
and further integration of inputs (BrainMadeSimple (2022)). The cognitive
control network covers particularly frontal-parietal regions (superior/middle
frontal gyri, supplementary motor area, insula, hippocampal) and participates
in various higher-order cognitive processes (Jacques et al. (2018)), such as
executive function, attention, working memory, and planning (Tanji and Shima
(1994)). The default network comprises the anterior cingulate cortex,
posterior cingulate cortex, and precuneus and reflects the brain’s intrinsic
activity in contrast to task-oriented controls (Zanto and Gazzaley (2013)).
Their functions are linked to self-referential thinking (Raichle (2015)),
introspection, and episodic memory retrieval (Gusnard et al. (2001)).
Subcortical network, precisely caudate as discussed before has a role in
learning and memory and has been shown to be able to predict IQ (Vincent et
al. (2006)). Last but not the least is the cerebellum. Its function is well
recognized to be beyond motor function, but subserving cognition (Koziol et
al. (2011)), and recently cerebellum has been partitioned to echo the 7
cortical networks (King et al. (2019)). In summary, the interplay of these
diverse brain regions likely contributes to the complexity of cognitive
processes that manifest as Total Composite Scores. The extensive network of
regions suggests that intelligence is not confined to a single brain area but
rather emerges from the collaboration of numerous interconnected regions, each
contributing its unique specialization to overall cognitive performance.

In conclusion, the BrainRGIN architecture presented in this study offers
several advantages for intelligence prediction using resting-state fMRI data.
It effectively captures the local and global relationships between brain
regions, incorporates edge information, utilizes attention-based readout
functions, and addresses the variability among brain ROIs. The superior
performance of BrainRGIN over baseline models highlights its potential for
predicting intelligence and provides valuable insights into the relationship
between brain function and cognitive processes. Future research can explore
the application of this architecture to other types of fMRI data, such as
task-based fMRI, to further advance our understanding of brain functioning.

## Acknowledgements

This study was funded part by NIH grant R01DA049238 and NSF grant 2112455. We
thank the Adolescent Brain Cognitive Development (ABCD) participants and their
families for their time and dedication to this project. Data used in the
preparation of this article were obtained from the Adolescent Brain Cognitive
Development (ABCD) Study (https://abcdstudy.org), held in the NIMH Data
Archive (NDA). This is a multisite, longitudinal study designed to recruit
more than 10,000 children aged 9-10 and follow them over 10 years into early
adulthood. The ABCD Study is supported by the National Institutes of Health
and additional federal partners under award numbers U01DA041048, U01DA050989,
U01DA051016, U01DA041022, U01DA051018, U01DA051037, U01DA050987, U01DA041174,
U01DA041106, U01DA041117, U01DA041028, U01DA041134, U01DA050988, U01DA051039,
U01DA041156, U01DA041025, U01DA041120, U01DA051038, U01DA041148, U01DA041093,
U01DA041089, U24DA041123, U24DA041147. A full list of supporters is available
at https://abcdstudy.org/federal-partners.html. A listing of participating
sites and a complete listing of the study investigators can be found at
https://abcdstudy.org/consortium_members. ABCD consortium investigators
designed and implemented the study and/or provided data but did not
necessarily participate in analysis or writing of this report. This manuscript
reflects the views of the authors and may not reflect the opinions or views of
the NIH or ABCD consortium investigators.

## Code Availability

The code is made available at https://github.com/bishalth01/Brain-ROI-Aware-
Graph-Isomorphism-Networks-BrainRGIN-

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