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1

Central-Smoothing Hypergraph Neural Networks
for Predicting Drug–Drug Interactions
Duc Anh Nguyen , Canh Hao Nguyen , and Hiroshi Mamitsuka , Senior Member, IEEE

Abstract— Predicting drug–drug interactions (DDIs) is the problem ofpredicting side effects (unwanted outcomes) of a pair of drugs using drug
information and known side effects of many pairs. This problem can beformulated as predicting labels (i.e., side effects) for each pair of nodes in
a DDI graph, of which nodes are drugs and edges are interacting drugs
with known labels. State-of-the-art methods for this problem are graphneural networks (GNNs), which leverage neighborhood information in
the graph to learn node representations. For DDI, however, there aremany labels with complicated relationships due to the nature of side
effects. Usual GNNs often fix labels as one-hot vectors that do not reflectlabel relationships and potentially do not obtain the highest performancein the difficult cases of infrequent labels. In this brief, we formulate DDI
as a hypergraph where each hyperedge is a triple: two nodes for drugs
and one node for a label. We then present CentSmoothie, a hypergraphneural network (HGNN) that learns representations of nodes and labels
altogether with a novel “central-smoothing” formulation. We empiricallydemonstrate the performance advantages of CentSmoothie in simulations
as well as real datasets.

Index Terms— Drug–drug interactions (DDIs), hypergraphLaplacian, hypergraph neural networks (HGNNs), smoothing.
I. I NTRODUCTIONIn drug–drug interactions (DDIs), concurrent use of two drugs canlead to side effects, which are unwanted reactions in human bodies.
It is a very important task to predict DDIs to guide drug safety. Given
drug information and known side effects of many pairs of drugs,
one wishes to learn a model to predict side effects of all pairs of
drugs, which include new pairs of drugs without known side effects or
known pairs (to denoise or complete side-effect data). DDI is usually
represented as a graph with nodes for drugs, edges for drug pairsthat interact, with (binary vector) labels for (known) side effects [1].
The task is to predict labels of all pairs of nodes in the DDI graph.
Fig. 1(a) shows an example of a DDI graph, where the dotted edge
with question marks is the pair of drugs with labels to be predicted.
Recently, graph neural networks (GNNs) have emerged as a prominent approach for this task with high prediction performance [1], [2].
GNNs for predicting DDI have two steps: learning new representations of drugs from a DDI graph and using these representations for
Manuscript received 17 September 2021; revised 24 April 2022
and 4 August 2022; accepted 21 March 2023. The work of Duc Anh Nguyen
was supported in part by the Otsuka Toshimi Scholarship Foundation. The
work of Canh Hao Nguyen was supported in part by the Ministry of Education,
Culture, Sports, Science and Technology (MEXT) KAKENHI under Grant
22K12150. The work of Hiroshi Mamitsuka was supported in part by MEXT
KAKENHI under Grant 16H02868, Grant 19H04169, Grant 21H05027, andGrant 22H03645; and in part by the Artificial Intelligence in Physical Sciencesand Engineering Research (AIPSE) Program through the Academy of Finland.
(Corresponding author: Duc Anh Nguyen.)
Duc Anh Nguyen and Canh Hao Nguyen are with the Bioinformatics Center,
Institute for Chemical Research, Kyoto University, Kyoto 611-0011, Japan(e-mail: ducanh@kuicr.kyoto-u.ac.jp).
Hiroshi Mamitsuka is with the Bioinformatics Center, Institute for Chemical
Research, Kyoto University, Kyoto 611-0011, Japan, and also with the
Department of Computer Science, Aalto University, 02150 Espoo, Finland.
This article has supplementary material provided by theauthors and color versions of one or more figures available athttps://doi.org/10.1109/TNNLS.2023.3261860.
Digital Object Identifier 10.1109/TNNLS.2023.3261860

Fig. 1.
Illustrative examples of (a) traditional graph, (b) (proposed)
hypergraph for DDIs, and (c) central-smoothing assumption.

predictions. One drawback of this approach is the lack of learninglabel (i.e., side effect) representations. There are many side effects
with complicated relationships. For example, our largest dataset has
964 side effects, where the number of drug pairs for one side effect(positive samples in supervised learning) ranges from 288 to 22 520.
Previous methods represent each side effect as an independent onehot vector, potentially underutilizing the relationship among side
effects [1], [2], [3]. Considering the relationship between side effects
would be beneficial for predicting side effects, especially the ones
with only small numbers of positive samples (i.e., infrequent side
effects). Hence, it is desirable to learn the representations for bothdrugs and side effects, namely, both nodes and edge labels, together.
To this end, we propose to encode DDI data with a hypergraph [4].
A node in the hypergraph can be either a drug or a side effect.
A hyperedge is a triple of two drugs and a side effect that theycaused. Hence, a pair of drugs with multiple side effects (interactions) will result in many hyperedges in the hypergraph. Fig. 1(b)illustrates an example of a hypergraph corresponding to the DDIgraph in Fig. 1(a). The existing learning methods of hypergraphneural networks (HGNNs) are based on a smoothing assumption thatthe representations of nodes in a hyperedge should be close to eachother [5], [6]. However, this assumption is not necessarily appropriate
for our DDI problem, since each node representation should reflect
the (chemical or biological) properties of the corresponding drug, andinteracting drugs do not necessarily need to have similar properties.
We propose CentSmoothie, a central-smoothing HGNN thatuses our idea, central-smoothing assumption [see Fig. 1(c)] foreach hyperedge in the hypergraph for DDI. The idea is to learn
k-dimensional representation vectors for nodes in a hyperedge suchthat the following hold: 1) a drug node representation reflects theproperty of the corresponding drug and 2) a side-effect node representation reflects a combination of some properties of the two drugs
that cause the corresponding side effect [7]. To implement 2), we first
assume that a side-effect representation should be related to the
midpoint of the representations of the two interacting drugs, reflecting
the combination of the two drug properties. Furthermore, there might
have different side effects of the same two drugs, suggesting thateach side effect might be obtained by a partial combination of thetwo drug properties. Hence, we propose that the representation foreach side effect is learned to be close to a weighted midpoint of thecorresponding two drug representations.

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We formulate the above assumption, and then define thecentral-smoothing hypergraph Laplacian to be used in each layerof the HGNN with spectral convolution [5]. We also provide acomputational method with the complexity of O(n) for the proposed
hypergraph Laplacian.
We conducted extensive experiments to verify the performanceadvantages of CentSmoothie in both synthetic and real datasets. Our
experimental results demonstrated that CentSmoothie significantly
outperformed the existing spectral-based convolutional HGNNs in allcases. In particular, CentSmoothie achieved higher performances overbaselines for real datasets with more infrequent side effects, which
are more difficult to predict, justifying the benefit of learning label(side effect) representations.

function on a graph. Let sh(x, G) be a smoothness measure of x on
G, and ss(x, e) be a smoothness measure of x on hyperedge e. The
smoothness on the hypergraph usually has the following form [4]:II. R ELATED W ORKWhen T is a sum operator, the smoothness of a function on a
hypergraph can be found in the following form:XX
sh(x, G) =w(e)(3)(xu − xv )2 = x T L x

The existing work in predicting DDI can be divided into two
approaches: non-graph-based and graph-based ones. In the nongraph-based approach, predefined feature vectors, indicating theexistences of chemical substructures and interacting proteins of drugs,
are used. The side effects can be predicted by using a model [forexample, a multilayer feedforward neural network (MLNN)], which
receives the feature vectors of two drugs as input and the vector
indicating the side effects of the two drugs as output [3], [8].
In the graph-based approach, topological information of graphs
is used to enhance the representations of nodes, leading to higher
performance than the non-graph-based approach. There are two
types of graphs that can be used: molecular graphs of drugs anda DDI graph. For a DDI graph where nodes are drugs and edges
are interactions between drugs, GNNs are applied to learn a new
representation of a drug node based on its neighbors. Recent results
show that GNNs for predicting DDI achieve the cutting-edge performance [1], [2]. An extension of a DDI graph can be a DDI
heterogeneous graph, where nodes are drugs, and side effects andedges are pairs of interacting drugs or drug-side effects [9]. However,the DDI heterogeneous graph cannot preserve triples of drug–drugside effects.
GNNs can be further divided into two approaches: spectral convolution and spatial convolution [10]. In the spectral convolution,
at first, the graph Laplacian is defined, and then, each GNN layer isconstructed from the graph Fourier transformation given the graphLaplacian [5], [11]. The spatial convolution approach uses nodespatial relation that a node is updated based on information fromneighbor nodes [9], [12].
Different from the existing work for predicting DDIs, we formulate
the DDIs in the form of a hypergraph and develop a new HGNN on
the DDI hypergraph.
In HGNNs, recent work has inherited the spectral convolution
approach on graphs to adapt to hypergraphs by defining the hypergraph Laplacian [5]. Once the hypergraph Laplacian is defined,
HGNNs can be constructed in the same manner as that for GNNs.
Another approach for HGNNs is the spatial convolution approachwith attention mechanisms [6].
III. BACKGROUND
In this section we briefly describe the hypergraph Laplacian being
derived from a smoothness measure [4]. Let G = (V, E) be a general
hypergraph, where V is the node set and E ⊂ 2V is the hyperedge
set. Let W = diag(w(e1 ), . . . , w(e|E| )) ∈ R|E|×|E| ≽ 0 be the diagonal
matrix that w(e) is the weight of hyperedge e. Let x ∈ R |V | be thevalues of nodes on the hypergraph that xu is the value of x at node u.
The hypergraph Laplacian is usually defined to be used in a similarmanner to the graph Laplacian: to evaluate the smoothness of ash(x, G) = Te∈E w(e)ss(x, e)(1)

where T is an aggregation operator, such as sum (the most commonlyused one), max, or l p norm [4]. Usual smoothing assumption on
hypergraphs is that nodes within a hyperedge should be close toeach other [5], [6], [13], and then, the smoothness measure on eachhyperedge is calculated byX
ss(x, e) =(2)(xu − xv )2 .
(u,v)∈ee∈E(u,v)∈ewhich has the quadratic form with L, and L is then called thehypergraph Laplacian of the hypergraph. In the next section, we willpropose a new smoothing assumption on hypergraphs and then define
a new hypergraph Laplacian.
IV. C ENT S MOOTHIE (C ENTRAL -S MOOTHING HGNN S )A. Problem Setting
We formulate the problem of predicting DDI as follows.
Input: Given a hypergraph of DDIs: G = (V, E), where the node
set V = VD ∪ VS consists of a drug node set VD and a side-effectnode set VS , a known hyperedge set E ⊂ VD × VD × VS (since two
drugs in a drug pair are unordered, two triples (u, v, t) and (v, u, t)(u, v ∈ VD and t ∈ VS ) are the same), and the feature vectors of
drugs: X D ∈ R |VD |×K 0 , where K 0 is the feature size. The feature
vectors of side effects are one-hot vectors.
Output: For each triple e = (u, v, t) ∈ VD × VD × VS , t is predicted
to be a side effect of u and v if the score of the triple is larger thana threshold.

B. Central-Smoothing Hypergraph LaplacianThe key idea is a central-smoothing assumption: each hyperedge iscalled central smooth if a weighted version of the midpoint of drug
node representations is close enough to the representation of the sideeffect node. It is motivated by biological research that a side effect ofa pair of drugs is caused by a combination of properties of the two
drugs [7]. Assuming that representations reflecting all properties ofdrugs are obtained in a k-dimensional space, the combination containing properties of the two drugs should reflect the corresponding side
effects. We show that among commonly used combination operators:
average, concatenation, max pooling, and min pooling, the average(also the midpoint) is a good option. First, our operator for combining
two drug properties for side effects needs to satisfy the following two
criteria: 1) order invariance in the k-dimensional space, since thedrug pair has no order and 2) effects of both positive and negativeembedding values must be kept to cover the whole embedding space.
We can see that the following hold: 1) concatenation violates and2) max pooling and min pooling violate, but the average (midpoint)
satisfies both criteria. In addition, a weighted midpoint, which in theideal case, would contain properties from each drug and represents a
specific combination of the properties, potentially reflecting the causeof a side effect.

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1) Central-Smoothing Measure on a Hyperedge: In the embedding
space of K -dimension, considering dimension k with the embeddingof nodes: X k ∈ R|V | that X k,u ∈ R is the embedding of node u ∈ V .
Given a hyperedge e = (u, v, t), a weight Wk,t ∈ R+ is a parameter
indicating the relevance of side effect t on dimension k. We assign
the weight of side effect t to the hyperedge (wk (e) = Wk,t ), andlet Wk = diag(wk (e1 ), . . . , wk (e|E| )) be the diagonal matrix of thehyperedge weights. The central-smoothing measure on dimension kof the hyperedge is defined as follows:ssc (X k , e) = Wk,t

X k,u + X k,v− X k,t
2

2

.

(4)

2) Central-Smoothing Measure on the Hypergraph: For hypergraph G, the central-smoothing measure on dimension k isdefined as the sum of the central-smoothing measures on all
hyperedges
shc (X k , G) =

X


Wk,t

e∈E

X k,u + X k,v− X k,t
2

2

.

(5)

3) Central-Smoothing Hypergraph Laplacian: Since shc (X k , G) is
a nonnegative quadratic form, there exists an Lk ∈ R|V|×|V| , suchthat shc (X k , G) = X kT Lk X k . We call Lk as the central-smoothing
hypergraph Laplacian, which can be derived as follows.
Let H ∈ R|V |×|E| be a weighted oriented incidence matrix of G
that for a hyperedge e ∈ E, Hu,e = Hv,e = 1/2, and Ht,e = −1,
we have2X
X k,u + X k,v
shc (X k , G) =Wk,t
− X k,t2e∈Edef= X kT H Wk H T X k = X kT Lk X k .

(6)35) Non-Weighted Version: In our experiments, we will examine
the need for the weight of each side effect. So, we here show anon-weighted version of central-smoothing hypergraph Laplacian,called CentSimple, by fixing Wk to be an identity matrix, where thecentral-smoothing hypergraph Laplacian in (7) becomes L̃k = H H T .
C. Central-Smoothing HGNNs
1) Transforming Input Features to Latent Spaces: We first transform the input feature vector of drugs and one-hot vector ofside effects to the K -dimension latent space by using a two-layer
feedforward neural network for drugs, and a one-layer feedforward
neural network (as an embedding table) for side effect, respectively,
as follows:
(0)
X (0)
D = f D (X D ); X S = f S (X S )where X D ∈ R|K 0 |×|VD | is the drug input features with feature size K 0 ,K ×|V D |,X S ∈ R|VS |×|VS | is the one-hot vector of side effect, X (0)
D ∈ R
(0)
K ×|VS |XS ∈ R, and f D and f S are the corresponding feedforward
neural networks.
2) Convolution Layers on the Latent Spaces: We adapt HGNN
layers [5] using Lk at dimension k. Given hypergraph Laplacian Lk ,we have the normalized adjacency matrix with a self-loop at each
−1/2
−1/2
node: Ãk = 2I − dLk Lk dLk , where dLk is the degree matrix,
corresponding to Laplacian Lk and I is the identity matrix.
Let D̃ k be the corresponding degree matrix of Ãk , and each layerof central-smoothing HGNNs has the following form:X (l+1) = σ X̃ (l+1) 2(l)(9)
where X̃ (l+1) = [x̃ (l+1), . . . , x̃ (l+1)] and x̃ (l+1)= D̃ k Ãk D̃ k xk(l) ,
K
k
1
(l)
K ×K
2 ∈R
is the parameters for the transformation from layer (l)to layer (l + 1), and σ is an activation function.
−1/2

−1/2

D. Predicting DDIs

Then
Lk = H Wk H .
T(7)4) Computing the Central-Smoothing Hypergraph Laplacian: The
central-smoothing hypergraph Laplacian Lk in (7) can be computedwith the time complexity of O(|E|). Concretely, each element Lk,i, j
can be computed by
X
Lk,i, j =wk (e)Hi,e H j,e .
(8)e∈E|i, j∈e

We have four cases as follows.
P
1) Lk,i, j = Lk, j,i = 1/4 t∈Vs |(i, j,t)∈E Wk,t if i! = j ∈ VD .
2) Lk,i, j = Lk, j,iP= −1/2n d (i, j)Wk, j if i ∈ VD , j ∈ VS .
3) Lk,i,i = 1/4 t|t∈VS m d (i, t)Wk,t if i ∈ VD .
4) Lk,i,i = q(i)Wk,i if i ∈ VS .
where n d (i, j) = |{(u, v, j) ∈ E|u = i ∨ v = i}|, m d (i, t) =|{u|(i, u, t) ∨ (u, i, t) ∈ E}|, and q(i) = |{(u, v, i)|(u, v, i) ∈ E}|.
a) Complexity analysis: Given N convolution layers, the computational complexity for all central-smoothing hypergraph Laplacianis O(N · K · |E|). Each Lk can be computed with a complexityof O(|E|) by iterating over all hyperedges in E once, and foreach hyperedge, the side-effect weight is added to the corresponding
elements in Lk , and we have N · K Laplacian matrices to compute.
We note that K here is referred to the size of latent features,and this is not the original input features. In practice, even if thesize of the original input features is very large, the number oflatent features can be very small (≤200), which is computationallytractable.

Assuming that X ∗T ∈ R|V |×K is the final node representation withlearned weights W ∗ = {Wk∗ |k = 1 . . . K }. For all e = (u, v, t), t
is predicted to be a side effect of u and v if the representation oft is close enough to the weighted midpoint of the two drug node
representations (computed by score function p(e, X ∗ , W ∗ )). First,
we compute smoothness measures ssa(e, X ∗ , W ∗ ) of (u, v, t) on all
dimensions
 ∗
2
K
∗
X
X k,u + X k,v∗∗ssa(e, X ∗ , W ∗ ) =Wk,t− X k,t
.
(10)
2
k=1
Then, the prediction score is defined to bep(e, X ∗ , W ∗ ) =1.
1 + ssa(e, X ∗ , W ∗ )(11)

If p(e, X ∗ , W ∗ ) > h, a predefined threshold, then t is predicted to
be a side effect of u and v.
E. Objective Function of CentSmoothie
Let Ē = VD × VD × VS \ E be complement of the hyperedge set.
The objective function to train CentSmoothie is to maximize the scorep(e, X ∗ , W ∗ ) of the known hyperedges and minimize the score of thecomplement set Ē ∗ . Then, the objective function can be defined asfollows:X
min ∗ f (X ∗ , W ∗ ) =(12)(1 − p(e, X ∗ , W ∗ ))2∗

W ≥0,Xe∈E+λXp(e, X ∗ , W ∗ )2e∈ Ē

where λ is a hyperparameter.

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMSIn practice, as | Ē| is too large, we randomly sample a subsetof  ⊂ Ē, || = |E| to replace Ē in the objective function
to reduce the computational cost (a CentSmoothie implementation
available at https://github.com/anhnda/CentSmoothieCode). To keep
the non-negative constraint on W ∗ , we used a projected gradientdescent [14].
V. E XPERIMENTS
We conducted experiments to evaluate the performance of our
proposed method, CentSmoothie, a HGNN with a central-smoothing
assumption, in two scenarios: 1) a synthetic dataset and 2) three
real DDI datasets. On the synthetic dataset, we aimed to validatethat CentSmoothie could achieve higher performances than traditional
HGNNs, by using the data generated from the central-smoothing
assumption. On the real DDI datasets, we examined the performanceof CentSmoothie in comparison with baseline models, to prove thatthe central-smoothing assumption is suitable for DDI data.
For both scenarios, we used 20-fold cross validation using themean area under the ROC curve (AUC) and the mean area under the
precision–recall curve (AUPR) with standard deviations, to validate
the prediction performances [1].
For graph and HGNNs, the numbers of layers and the embedding
sizes were in [1, 2, 3] and [10, 20, 30], respectively. The activation
function was rectified linear unit (ReLu). The hyperparameter λ was
fixed: 0.01. The results obtained were the highest performances with
the number of layers of 2 and the embedding size of 20 for all
methods. All experiments were run on a computer with Intel Core
I7-9700 CPU, 8-GB GeForce RTX 2080 GPU, and 32-GB RAM.
A. Synthetic Data
1) Generation: We generated a synthetic dataset with the idea thateach drug has several groups of features, and the combination of twogroups of features leads to a side effect of the drugs. We fixed thenumber of drugs D = 500, the number of side effects: S = 45,
and changed the maximum number of groups of drug features from
1 to 6. The detail of the generation process can be found in the
Supplementary Material.
2) Comparing Methods: For the synthetic dataset, we used thecentral-smoothing HGNNs CentSmoothie, the non-weighted centralsmoothing HGNNs CentSimple, and the existing spectral-based
HGNN, pairwise smoothing hypergraph neural network (HPNN) [5].
3) Results: Fig. 2 shows the AUC and AUPR of each comparedmethod, obtained by changing the maximum number of groups offeatures for drugs. We could easily see that CentSmoothie achieved
the highest AUC and AUPR scores for all values of x-axis, followed
by CentSimple and then HPNN. In particular, the AUC scores of
CentSmoothie were always higher than 0.95, while those of HPNN
decreased when drugs are more complex with larger numbers ofgroups drugs features. This clearly showed that CentSmoothie could
correctly capture the patterns generated by the central-smoothing
assumption, particularly for larger numbers of groups of drug features. Similarly, the AUC scores of CentSimple decreased with higher
number of maximum number of groups of features, e.g., around0.75 at 6. The pattern for AUPR scores was also similar to thatof AUC scores. This result showed that CentSmoothie could learn
different side effects for drug pairs more effectively than CentSimple,
implying the significance of using a weight for each side effect in
CentSmoothie.
B. Real Data
1) Data Description: We used three real DDI datasets: TWOSIDES, CADDDI, and JADERDDI. TWOSIDES is a public dataset

Fig. 2.

Synthetic data performance comparison. (a) AUC. (b) AUPR.

for DDI extracted from the FDA adverse event reporting system(U.S. database) [15]. To the best of our knowledge, TWOSIDES
is the largest and commonly used benchmark dataset for DDI [1],[8], [16]. In a similar manner as in [15] of TWOSIDES, we usedsignificant tests to generate two new DDI datasets: CADDDI from
Canada vigilance adverse reaction report (Canada database, from1965 to February 2021) [17] and JADERDDI from The JapaneseAdverse Drug Event Report (Japanese database, from 2004 to March
2021) [18]. We only selected small molecular drugs appearing in
DrugBank [19]. Each drug feature vector was a binary vector withthe size of 2329, indicating the existences of 881 substructures and1448 interacting proteins [20]. The statistics of the final datasets isshown in Table I.
2) Comparing Methods: On the real datasets, we compared
our proposed methods to baselines: none-graph-based, graph-based,
and hypergraph-based methods. For the none-graph-based method,
we used an MLNN [8]. For GNNs, on the drug molecular graphs,
we used multiresolution GNN (MRGNN) [16] with the recommended
hyperparameter settings. On the DDI graph, we used Decagon [1],a spatial convolution, the spectral convolution graph neural networks(SpecConv) [11], and a heterogeneous GNN (HETGNN) [9]. For
HGNN, we used the existing spectral convolution HGNN, HPNN [5].
We also showed the results of CentSimple to see the effect of central
smoothing without having weights for side effects.
3) Results: Table II shows the AUC scores and AUPR scoresof all methods. We could see that again CentSmoothie achieved
the highest AUC and AUPR scores in all three datasets. For
TWOSIDES, CentSmoothie achieved 0.9348 in AUC and 0.8749 in
AUPR, followed by CentSimple (0.9242 and 0.8638), HPNN
(0.9044 and 0.8410), HETGNN (0.9113 and 0.8267), SpecConv(0.8785 and 0.8256), Decagon (0.8639 and 0.8094), MRGNN(0.8452 and 0.8029), and MLNN (0.8372 and 0.7919).
For CADDDI and JADERDDI, CentSmoothie had the highest
performances with AUC and AUPR: (0.9845 and 0.8230) and(0.9684 and 0.6044), respectively. The second and third best methods
were CentSimple and HPNN, respectively.
In particular, in AUC, there existed two clear performance gaps.
The first one was between hypergraph-based methods (CentSmoothie,
CentSimple, and HPNN) and non-hypergraph-based methods(HETGNN, SpecConv, Decagon, MRGNN, and MLNN). The second
one was between CentSmoothie and (CentSimple and HPNN). The
first gap showed the advantage of using the hypergraph-based method
for predicting DDI. The second gap showed the advantage of central
smoothing over regular smoothing. In addition, we could see theimportance of learning weights for each side effect to improve theprediction performance.
In AUPR, there was a clear gap between CentSmoothie and theremaining methods. This again showed the advantage of learning
weights under the central-smoothing assumption for predicting DDI.

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5

TABLE IS TATISTICS OF THE T HREE R EAL DATASETSTABLE IIC OMPARISON OF P ERFORMANCES OF THE M ETHODS ON THE R EAL DDI DATASETS

training data. Fig. 3 shows the AUC (left) and AUPR (right) scoresof the methods on the subset of most infrequent side effects, obtainedby starting with the most infrequent side effect and adding the next
infrequent side effects to the subset. From both AUC and AUPR
scores in Fig. 3, we could see that CentSmoothie achieved the best
performances for all values of x-axis (the rightmost point of x-axis
corresponds to using all side effects), being followed by CentSimple
and HPNN.
VI. C ONCLUSION
We have presented CentSmoothie, an HGNN, for predicting DDIs,
to learn representations of side effects together with drug representations in the same space. A unique feature of CentSmoothie
is a new central-smoothing formulation, which can be incorporated into the hypergraph Laplacian, to model DDIs. Our extensive
experiments using both synthetic and three real datasets confirmed
clear performance advantages of CentSmoothie over existing hypergraph and GNN methods, indicating that CentSmoothie could learn
representations of drugs and side effects simultaneously with thecentral-smoothing assumption. Furthermore, CentSmoothie kept highperformance on the infrequent side effects for which the performancesof other methods dropped significantly, indicating that CentSmoothie
allows leveraging the relationships among side effects to help the
difficult cases of less frequent side effects. For future work, it isinteresting to extend the central-smoothing assumption into moregeneral cases not limited to three-uniform hypergraphs. In addition,
learning adaptive ratios to replace the constraint of the midpoint might
be considered.
R EFERENCES

Fig. 3. Performance comparison [AUC (left) and AUPR (right)] on (a) TWOSIDES, (b) CADDDI, and (c) JADDERDDI.

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