11institutetext: Institute of Information Science, Beijing Jiaotong
University, Beijing, China 22institutetext: Beijing Key Laboratory of Advanced
Information Science and Network Technology, Beijing, China
33institutetext: School of Information Science and Engineering, Hebei North
University, Zhangjiakou, China
33email<EMAIL_ADDRESS>
# Multi-modal Graph Learning for Disease Prediction

Shuai Zheng 1122 Zhenfeng Zhu 1122 Zhizhe Liu 1122 Zhenyu Guo 1122 Yang Liu
112233 Yao Zhao 1122

###### Abstract

Benefiting from the powerful expressive capability of graphs, graph-based
approaches have achieved impressive performance in various biomedical
applications. Most existing methods tend to define the adjacency matrix among
samples manually based on meta-features, and then obtain the node embeddings
for downstream tasks by Graph Representation Learning (GRL). However, it is
not easy for these approaches to generalize to unseen samples. Meanwhile, the
complex correlation between modalities is also ignored. As a result, these
factors inevitably yield the inadequacy of providing valid information about
the patient’s condition for a reliable diagnosis. In this paper, we propose an
end-to-end Multi-modal Graph Learning framework (MMGL) for disease prediction.
To effectively exploit the rich information across multi-modality associated
to diseases, a modal-attentional multi-modal fusion is proposed to integrate
the features of each modality by leveraging the correlation and
complementarity between the modalities. Furthermore, instead of defining the
adjacency matrix manually as existing methods, the latent graph structure can
be captured through a novel way of adaptive graph learning. It could be
jointly optimized with the prediction model, thus revealing the intrinsic
connections among samples. Unlike the previous transductive methods, our model
is also applicable to the scenario of inductive learning for those unseen
data. An extensive group of experiments on two disease prediction problems is
then carefully designed and presented, demonstrating that MMGL obtains more
favorable performances. In addition, we also visualize and analyze the learned
graph structure to provide more reliable decision support for doctor in real
medical applications and inspiration for disease research.

###### Keywords:

Multi-modal Disease prediction Graph learning Feature fusion

##  1 Introduction

A large amount of relational data exists in the biomedical field. As a general
description of relational data, graphs are facilitated to model a variety of
biomedical scenarios [21]. Recently, inspired by the excellent performance of
graph-based methods in machine learning, particularly graph convolutional
networks (GCNs) [17, 24, 9], they have also been applied to handle relational
data in various Computer Aided Diagnosis (CADx) tasks, such as Alzheimer
prediction [18], Autism prediction [5], and cancer prognosis prediction [20].

Figure 1: Architecture of three typical types of multi-modal feature fusion.
(a) Concatenation fusion, (b) Weighted fusion based on intra-modal attention
mechanism. (c) Our modal-attentional feature fusion. The (a) and (b) fusions
have only one interactive operation for different modal features, which
proceed at the end of a module. In contrast, our module has more interactive
operations for different modal features.

Most existing methods try to construct the patient relationship graphs from
existing features through pre-defined similarity measures, then apply GCNs to
aggregate patient features over local neighborhoods to give the prediction
results. These methods can be broadly classified into two categories: single-
graph-based methods and multi-graph based methods. Parisot et al. [19]
proposed to compute patient similarities from a set of meta-features such as
age and sex, thus constructing the adjacency matrix to apply GCNs. [13, 27]
employed the same graph construction rules and initially explored the effect
of graph structure on performance of the disease prediction through setting
different neighborhood sizes. These methods simply combine the imaging and
non-imaging modalities through graph construction and GCNs. However, they fail
to effectively mine the intrinsic information of each modality. Thus, several
recent works have proposed to construct multiple graphs in parallel, in which
each graph is built from different modality, then execute the integration of
the embeddings learned from different graphs for the prediction. As shown in
Fig.1(a), [8] concatenated the node embeddings directly, and both [12] and
[22] adopted attention-based fusion mechanism like Fig.1(b).

Although the above methods have achieved remarkable performance, three key
issues remain to be further considered with respect to the application of GCNs
in disease prediction tasks, and even in some other biomedical tasks:

_(1) Insufficient inter-modal relationship mining._ Each modality provides
different information for the diagnosis of a disease, which is both
complementary and potentially redundant. However, concatenation [4, 8, 10] or
intra-modal attention mechanism [12, 22] adopted in previous studies are hard
to capture the latent inter-modal correlation, which may lead to the learned
features are biased towards a single modality. To solve this issue, we propose
a modal-attentional multi-modal fusion to mine the intrinsic relevance between
modalities while preserving the individuality of each modality.

_(2) Defining the graph adjacency matrix manually._ Existing single-graph-
based [19, 13, 25] and multi-graph-based methods [14, 8, 22] both construct
the graph through hand-designed similarity measures, which requires a careful
tuning and is thus difficult to generalize to downstream tasks. A better
approach is to learn a graph by the means of end-to-end, but less focus has
been put on the graph structure learning[26, 11], especially in the field of
medicine[4]. Meanwhile, sigmoid-based graph learning mechanism in [4] is prone
to causing gradient disappearance, which makes model training unstable. Thus,
we propose a learning-based adaptive approach for graph learning to learn the
graph structure dynamically. In fact, it provides a more feasible way for
downstream tasks and reveals the latent connections among samples.

_(3) Hard applicable to inductive learning._ For the approaches based on
spectral graph convolution like [10, 13, 19], it’s hard for them to generalize
to unseen samples. Besides, to accommodate inductive learning, it is also
essential but cumbersome for multi-graph-based methods [14, 8, 22] to measure
relationship of unseen samples on each graph. Unlike these approaches, our
MMGL can be flexibly extended to the scenario of inductive learning.

In this paper, we propose a novel Multi-modal Graph Learning framework (MMGL)
for disease prediction, and the main contributions can be highlighted in the
following aspects:

  * •

As a flexible modular inductive learning framework, the proposed MMGL provides
some substantial improvements and inspirations for the application of GCN in
disease prediction tasks.

  * •

Considering the correlation and complementarity between modalities, we propose
a modal-attentional feature fusion approach (MaFF) that exploits the inter-
modal relevance to integrate the multi-modal features.

  * •

To reveal the intrinsic connections among samples, a novel adaptive graph
learning mechanism (AGL) is proposed to achieves learnable graph construction,
thus obtaining the latent robust graph for downstream tasks.

  * •

The comparable even significant improvement compared to the state-of-the-art
methods indicates the advantages of our MMGL in terms of disease prediction
tasks.

##  2 Methodology

###  2.1 Problem Formulation

Let $X=\left[x_{1},x_{2},\cdots,x_{N}\right]\in\mathbb{R}^{d_{in}\times N}$
denote the $d_{in}$-dimensional multi-modal features of $N$ patients and
$Y=\left[y_{1},y_{2},\cdots,y_{N}\right]$ is the corresponding labels. Each
patient is represented by $M$ modalities, so the multi-modal features also can
denote as $X=\\{X^{1},X^{2},\cdots,X^{M}\\}$ and
$X^{m}=\left[x^{m}_{1},x^{m}_{2},\cdots,x^{m}_{N}\right]\in\mathbb{R}^{d_{m}\times
N}$, where $x^{m}_{i}$ represents the $d_{m}$-dimensional features of the
$m$-th modality of $x_{i}$ and $d_{in}=\sum_{m=1}^{M}d_{m}$. Given the multi-
modal features $X$, the issue we consider in this paper for multi-modal graph
learning is to achieve an optimal latent graph structure inference based on
multi-modal feature fusion considering inter-modal correlation, thus providing
reliable graph support to GCNs for disease prediction or the other biomedical
tasks.

As illustrated in Fig. 2, the overall framework of MMGL consists of three
modules. In feature fusion phase, the multi-modal features $X$ is integrated
into a fused single feature matrix
$H=\left[h_{1},h_{2},\cdots,h_{N}\right]\in\mathbb{R}^{d\times N}$ by modal-
attentional feature fusion module (MaFF). Then, in graph learning phase, the
adjacency matrix $A\in\mathbb{R}^{N\times N}$ characterizing the latent graph
structure is captured through a novel adaptive graph learning mechanism (AGL)
based on the multi-modal modal-fused features. Finally, according to the
learned adjacency matrix $A$ and fused feature matrix $H$, the disease
prediction results can be obtained by GCN.

Figure 2: Architecture overview of our MMGL. MMGL consists of three modules:
Modal-attentional feature fusion module, adaptive graph learning module, and
prediction module.

###  2.2 Modal-attentional Feature Fusion

In a real diagnostic scenario, medical experts always need to analyze various
multi-modal data of the patient to make a reliable decision, since the single-
modal data lacks of providing enough information for an accurate diagnosis.
Similarly, reliable Computer Aided Diagnosis (CADx) also requires to be
capable of leveraging the complementarity of multi-modal data [15]. To capture
inter-modal relevance and complementarity for efficient information
integration, we propose a transformer-style [23] modal-attentional feature
fusion module named MaFF, which fuses the features of each modality while
preserving rich information.

Given the query vectors $Q^{m}$ of current modality and key-value pairs of the
others (i.e., $K$-$V$), the inter-modal attention score can be calculated. In
practice, considering the problems of space-efficiency and parallelization,
the scaled dot-product is chosen as attention function [23]. Since each modal
feature has different dimension, as shown in Fig. 1(c), we first use the
projection matrices (i.e., $W_{Q}$, $W_{K}$, $W_{V}$) with fixed dimension
$d_{f}$ to translate $X$ to $Q$, $K$, and $V$, which facilitates the
computation of attention scores in the same dimensional space. For a specific
patient $x$, we can obtain the corresponding query matrix
$q=\\{q^{m}\\}^{M}_{m=1}$, key matrix $k=\\{k^{m}\\}^{M}_{m=1}$, and value
matrix $v=\\{v^{m}\\}^{M}_{m=1}$. Then, the inter-modal attention score map
$P$ for $x$ is computed as:

$P_{ij}=\frac{\mathrm{exp}[(q^{i})^{\top}\cdot
k^{j}/\tau]}{\sum_{i=1}^{M}\mathrm{exp}[(q^{i})^{\top}\cdot k^{j}/\tau]}$ (1)

where $P_{ij}$ denotes the attention score between modality $i$ and $j$.
$\tau$ is the scaling factor to control the hardness of attention, which is
set to $\sqrt{d_{f}}$ like in [23]. After that, we perform cross-modal
aggregation of the value vectors of each modality based on the calculated
inter-modal correlations $P$, thus the integrated feature $h$ of patient $x$
could be computed as:

$h=W_{h}^{\top}\cdot
Concat(\hat{v}^{1},\hat{v}^{2},\cdots,\hat{v}^{M}),~{}\mathrm{where}~{}\hat{v}^{m}=W_{m}^{\top}\cdot(v^{m}+\sum_{j=1}^{M}P_{mj}~{}v^{j})$
(2)

where $W_{h}$ and $W_{m}$ are projection layers. Besides, the implementation
of residual connection between $\sum_{j=1}^{M}P_{m,j}~{}v^{j}$ and the initial
value vector $v^{m}$ can effectively avoid the gradient vanishing problem
during training process.

Compared to the fusion module in [12, 4, 8], the modal-attentional fusion puts
concerns on inter-modal correlation through a multi-modal attention mechanism.
As a consequence, it tend to optimally combine the complementary information
from different modalities. It’s worth noting that the multi-modal attention
map $P$ is patient-specific, which is also applicable to inductive learning.
And we could obtain global-level inter-modal correlation map by averaging $P$
over all patients. Besides,the proposed multi-modal attention mechanism can
also be scalable to multi-head version easily.

###  2.3 Adaptive Graph Structure Learning

Based on existing graph structures, GCNs in [17, 24, 6] learn node
representations for downstream tasks through neighborhood aggregation or
spectral convolution. However, it’s no trivial to obtain the available graph
for some specific tasks in biomedical field. Therefore, the graph learning
problem often needs to be considered for applying GCNs in biomedical tasks.

For graph learning, it is usually modeled as two kinds of forms: (i) learning
a joint discrete probability distribution on the edges of the graph [7], (ii)
learning a similarity metric of nodes. Since the former is non-differentiable
and hard applicable to inductive learning, we take the graph learning problem
in consideration from the perspective of similarity metric learning of nodes.
Some previous methods have adopted radial basis function (RBF) kernel [22,
27], cosine similarity [10], or threshold-based metric(for discrete feature)
[19, 13] as the similarity metric. However, these approaches still require
careful manual tuning to construct a meaningful graph structure for downstream
GCNs. Therefore, as illustrated in Fig 2, we propose a simple but effective
learnable metric function, which could be jointly optimized with the
downstream GCNs:

$\hat{A}_{ij}=Sim(h_{i},h_{j})=\cos(W_{A}^{\top}h_{i},~{}W_{A}^{\top}h_{j})$
(3)

where $W_{A}$ is a learnable weight matrix and $\hat{A}_{ij}$ is computed as
weighted cosine similarity between patient $i$ and $j$. Since there are few
uni-directional effects between patients except for epidemics, thus the
learned adjacency matrix $\hat{A}$ is symmetric that is also in accordance
with the expectations of realistic population graph of patients.

Commonly, a realistic adjacency matrix is usually non-negative and sparse.
However, since $\hat{A}$ is a fully connected graph that is computationally
expensive and the element $\hat{A}_{ij}$ is ranging in [-1,1], we capture a
non-negative sparse graph $A$ from $\hat{A}$ by applying the ReLU function,
i.e., setting negative value elements in $\hat{A}$ to zero. Finally, the
latent graph $A$ is obtained for downstream tasks.

###  2.4 Model Optimization

Graph Regularization Due to the sensitivity of GCNs to the graph structure,
graph learning has a significant impact on the performance of GCN in
downstream tasks. Furthermore, the constraint on the sparsity, connectivity,
and smoothness of the learned graph is also important for adaptive graph
learning [3]. Here, the Dirichlet energy is used to measure the smoothness of
a set of graph signals $\\{h_{1},h_{2},\cdots,h_{N}\\}$:

$\mathcal{L}_{smooth}=\frac{1}{2N^{2}}\sum_{i,j=1}^{N}A_{ij}\left\|h_{i}-h_{j}\right\|^{2}$
(4)

It can be seen from Eq. 4 that the smaller the distance between $h_{i}$ and
$h_{j}$, the larger $A_{ij}$ will be. Hence, the smooth loss
$\mathcal{L}_{smooth}$ is intended to making connections between similar
nodes, which means to enforce smoothness of the graph signals on the learned
graph $A$.Essentially, $L_{smooth}$ simultaneously serves to control the
sparsity of A [11]. However, only utilizing $L_{smooth}$ may lead to the
trivial solution (i.e., $A=0$). To avoid it, two additional regularization
terms following [11] are imposed on $A$:

$\mathcal{L}_{con}=\frac{-1}{n}\mathbf{1}^{\top}\log(A\mathbf{1})~{}~{}~{}\mathrm{and}~{}~{}~{}\mathcal{L}_{r}=\frac{1}{n^{2}}\|A\|_{F}^{2}$
(5)

where the first term $\mathcal{L}_{con}$ uses logarithmic barrier to control
the connectivity of $A$, and the second term $\mathcal{L}_{r}$ is a
regularization term to avoid the excessive sparseness caused by
$\mathcal{L}_{smooth}$. The total graph regularization loss is defined as
$\mathcal{L}_{g}=\mathcal{L}_{smooth}+\alpha\mathcal{L}_{con}+\beta\mathcal{L}_{r}$.

####  2.4.1 Loss Function

Based on the integrated feature matrix $H$ and learned sparse graph $A$, we
use GNNs to give the predicted results $\hat{Y}=GCN(H,A)$ of the patients.
Unlike [4, 10] which optimize the graph structure directly based on task-aware
prediction loss, we use a joint loss function to guide the optimization of all
three modules of MMGL simultaneously:

$\mathcal{L}=\mathcal{L}_{t}(Y,\hat{Y})+\lambda\mathcal{L}_{g}(H,A)$ (6)

where $\mathcal{L}_{t}$ and $\mathcal{L}_{g}$ denote the task-aware loss and
the graph regularization loss respectively, $\lambda$, $\alpha$, and $\beta$
are hyper-parameters to balance the three loss terms. For the disease
prediction task treated as classification problems, $\mathcal{L}_{t}$ is set
to cross-entropy loss.

##  3 Experimental Results and Analysis

In this section, we evaluate the performance of MMGL on two biomedical
datasets. We first detail our experimental protocol, and then present the
comparison results of MMGL with the state-of-the-art methods in disease
prediction tasks.

###  3.1 Datasets and Preprocessing

TADPOLE [18]: As a subset of the Alzheimer’s Disease Neuroimaging Initiative
(ADNI) database (adni.loni.usc.edu), TADPOLE dataset contains features
extracted from multi-modalites, which include MR, PET, cognitive tests,
cerebro-spinal fluid (CSF) biomarkers, risk factors, clinical examinations and
demographic information. For Alzheimer’s Disease prediction, we select 685
patients with 366-dimensional multi-modal features from TADPOLE, divided into
245 normal, 360 Mild Cognitive Impairment (MCI) and 80 Alzheimer’s Disease
(AD) patients, respectively. Then, we divide the features according to the
corresponding modalities and use the means of features for missing value
filling.

ABIDE [1]: The Autism Brain Imaging Data Exchange (ABIDE) collected 1000
resting-state functional magnetic resonance imaging (R-fMRI) data with
corresponding phenotypic data from 20 different sites. For Autism disease
prediction, we select 871 patients, which are divided into 468 normal and 403
Autism Spectrum Disorder (ASD) patients. Then, for a fair comparison, we
follow the preprocessing step as in [19].

####  3.1.1 Implementation details

Without loss of generality, the standard GCN [17] is adopted as the prediction
module, which can also be replaced by other GCNs. To stabilize the training
process, we use a modular iterative training strategy, where a complete
training epoch is performed by jointly training MaFF and AGL once, and then
jointly training AGL and GCN once. The model uses Adam [16] as the optimizer
and is implemented on the PyTorch platform. For hyper-parameters tuning, we
set 4 attention heads of MaFF, and the other hyper-parameters are tuned
through hyperopt [2].

###  3.2 Performance Comparisons

####  3.2.1 Baselines.

To evaluate the performance of MMGL, we choose to compare with several
baselines, especially those that have achieved the state-of-the-art results in
disease prediction tasks recently. Both PopGCN [19] and InceptionGCN [13] are
single-graph-based methods and two of the earliest works to use GCNs for
disease prediction tasks. Multi-GCN [12] is a multi-graph-based method. In
addition, we also compared with LGL [4] and EV-GCN [10] which are the most
related state-of-the-art works in disease prediction tasks.

Table 1:  Quantitative comparisons over two benchmark datasets.$(\%)$ Methods | TADPOLE | ABIDE
---|---|---
ACC$(\%)$ |  AUC$(\%)$ |  ACC$(\%)$ |  AUC$(\%)$
PopGCN [19] |  $82.11\pm 5.45$ |  $80.32\pm 4.90$ |  $69.80\pm 3.35$ |  $80.32\pm 3.90$
InceptionGCN [13] |  $74.39\pm 1.24$ |  $81.17\pm 1.60$ |  $72.69\pm 2.37$ |  $72.81\pm 1.94$
Multi-GCN111Due to the source code is not publicly available, the reported results here are our re-implementation of the original algorithms. [12] |  $84.11\pm 5.22$ |  $89.34\pm 5.38$ |  $69.24\pm 5.90$ |  $70.04\pm 4.22$
EV-GCN [10] |  $86.90\pm 2.37$ |  $90.71\pm 2.55$ |  $85.90\pm 4.47$ |  $84.72\pm 4.27$
LGL111Due to the source code is not publicly available, the reported results here are our re-implementation of the original algorithms. [4] |  $91.14\pm 1.77$ |  93.92$\pm$1.61 |  $84.69\pm 4.19$ |  $84.46\pm 4.33$
MMGL |  93.73$\pm$1.70 |  $93.81\pm 1.80$ |  86.95$\pm$3.88 |  86.74$\pm$3.77

####  3.2.2 Quantitative Results.

We evaluate MMGL and other baselines on both the TADPOLE and ABIDE datasets
using 10-fold stratified cross validation strategy, and the mean scores and
standard errors of Area Under Curve (AUC) and accuracy are reported. As shown
in Table. 1, it can be concluded that, (i) compared to single-graph-based
methods which are simply using meta-features and imaging features, the further
use of multi-modal features can effectively improve the performance of the
model; (ii) our MMGL outperforms Multi-GCN [12] by about 10.0% and 17.5% on
TADPOLE and ABIDE datasets respectively, which just verifies that the
effectiveness of MaFF to integration of multi-modal features; (iii) the
approximate 2.2% improvement of our MMGL on ABIDE dataset over LGL that is the
state-of-the-art method is achieved, which demonstrates that our AGL may more
effective compared to the graph learning in LGL.

|  |  |
---|---|---|---
(a) | (b) | (c) | (d)
Figure 3: Visualization of the kNN graph and the learned graph on ABIDE and
TADPOLE. Colors indicate different node labels. (a) kNN graph of ABIDE; (b)
learned graph of ABIDE; (c) kNN graph of TADPOLE; (d) learned graph of
TADPOLE.

####  3.2.3 Qualitative Results.

We visualize the kNN graphs and graph structures learned by MMGL, where the
kNN graphs are constructed by the fused features. As illustrated in Fig. 3,
the kNN graph and the learned graph have overall similarity and form subgraphs
corresponding to the patient classes, reflecting the differences between
classes, which demonstrates the effectiveness of MaFF. Furthermore, compared
to kNN graph, graph structure learned by AGL is more sparse between different
classes of patients, indicating that AGL is better able to learn intra-class
similarity while capturing inter-class differences. Thus, although the
groundtruth graph does not exist, we can still see the superiority of AGL
compared to kNN graph construction.

###  3.3 Ablation study

To validate the effectiveness of modal-attentional feature fusion (MaFF) and
adaptive graph learning mechanism (AGL), we replace MaFF with MLP and
concatenation operation respectively, and replace AGL with kNN graph
construction based on RBF kernel and construction method of popGCN
respectively. Table. 2 shows the ablation study results on different modules
in our models. Specifically, the performance of the constructed graph of
popGCN is the worst, especially on the ABIDE dataset, indicating that hand-
constructed graphs are indeed not a desirable choice. Besides, AGL achieves
favorable performance despite the absence of MaFF, which again validates the
effectiveness of adaptive graph learning. More importantly, it can be observed
that the combination of MaFF and AGL achieves a performance that far exceeds
other combinations.

Table 2:  Quantitative evaluation of ablation studies on the TADPOLE and ABIDE datasets. | TADPOLE | ABIDE
---|---|---
ACC$(\%)$ |  AUC$(\%)$ |  ACC$(\%)$ |  AUC$(\%)$
MMGL |  93.73$\pm$1.70 |  93.81$\pm$1.80 |  86.95$\pm$3.88 |  86.74$\pm$3.77
MLP+AGL |  89.42$\pm$2.22 |  90.30$\pm$2.34 |  85.07$\pm$4.68 |  83.36$\pm$4.64
Concat+AGL |  85.97$\pm$2.06 |  88.17$\pm$2.48 |  83.70$\pm$2.64 |  83.70$\pm$2.68
MaFF+popGCN |  85.39$\pm$3.37 |  87.91$\pm$2.78 |  69.27$\pm$4.45 |  69.30$\pm$4.33
MaFF+kNN |  87.97$\pm$3.69 |  89.67$\pm$2.65 |  84.19$\pm$3.83 |  83.91$\pm$4.07

##  4 Conclusion

In this paper, we propose a novel multi-modal graph learning framework named
MMGL for disease prediction. For better integration of complementary
information of multi-modalities, we propose a modal-attentional feature fusion
module (MaFF) to achieve feature fusion considering inter-modal correlations.
Furthermore, based on fused features, a lightweight adaptive graph learning
mechanism is proposed to reveal the intrinsic connections among samples,
constructing the optimal graph structure for downstream tasks. We have carried
out extensive experiments on two disease prediction problems, and the results
demonstrate the obvious superiority of our MMGL over currently available
alternatives. More importantly, as a high modular inductive framework, MMGL
provides a baseline that different variants of MMGL can be easily implemented
to perform scenario-specific multimodal adaptive graph learning. Our ongoing
research work will extend our MMGL to adaptive unified graph learning for more
biomedical tasks.

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