Multiple Kronecker RLS fusion-based link propagation for drug-side effect prediction
Authors: Yuqing Qian
Ziyu Zheng
Prayag Tiwari
Yijie Ding
Quan Zou
Venue: Accepted by TMLR ()

Abstract: Drug-side effect prediction has become an essential area of research in the field of pharmacology. As the use of medications continues to rise, so does the importance of understanding and mitigating the potential risks associated with them. At present, researchers have turned to data-driven methods to predict drug-side effects. Drug-side effect prediction is a link prediction problem, and the related data can be described from various perspectives. To process these kinds of data, a multi-view method, called Multiple Kronecker RLS fusion-based link propagation (MKronRLSF-LP), is proposed. MKronRLSF-LP extends the Kron-RLS by finding the consensus partitions and multiple graph Laplacian constraints in the multi-view setting. Both of these multi-view settings contribute to a higher quality result. Extensive experiments have been conducted on drug-side effect datasets, and our empirical results provide evidence that our approach is effective and robust.

Published in Transactions on Machine Learning Research (06/2024)
Multiple Kronecker RLS fusion-based link propagation for drug-side effect prediction
Yuging Qian
ustapugginggian@gmal com Department of Mathematical Sciences, University of Nottingham Ningbo, P.R. China
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, P.R. R.CChina
Ziyu Zheng
smps:16@nnntiingham..d edu..cm
Prayag Tiwari*
prajag..Hwarrlieee..o
School of Information Technology, Halmstad University, Sweden
Yijie Ding*
WUEN dyj@ 1021163..omm com Yangize Delta Region Institade (Quzhou), University of Electronic Science and Technology of China, P.R. China
Quan Zou
zouquan wnclaa. net Institute of Fundamental and Prontier Sciences, University of Electronic Science and Technology of China, P. R.China
*Corresponding author.
Reviewed on OpenReview: https: //tp:/pppppe openreview. net/ forum? id= LdL
Abstract
Drug-side effect prediction has become an essential area of research in the field of pharma- cology. As the use of medications contimues to rise, so does the importance of understanding and mitigating the potential risks associated with them. At present, rescarchers have turned to data-driven methods predict drug-side effects. Drug-side effect prediction is a link pre- diction problem, and the related data can be described from various perspectives. To process these kinds of data, multi-view method, called Multiple Kronecker RLS fusion-based link propagation (MKronRLSF-LP)) is proposed. MKronRLSF-LP extends the Kron-RLS by finding the consensus partitions and multiple graph Laplacian constraints in the multi-view setting. Both of these multi-view settings contribute to a higher quality result. Extensive experiments have been conducted on drug-side effect datascts, and our empirical results provide evidence that our approach effective and robust.
1 Introduction
Pharmacovigglance is critical to drug safety and surveillance. The field of pharmacorigilance plays a crucial role in public health by continuously monitoring and evaluating the safety profile of drugs. Pharmacovigilance involves collecting and analyzing data from various sources, including health care professionals (Yang et al. 2016), patients, regulatory authoritics, and pharmaccutical companics. These data are then used to identify possible side effects and assess their severity and frequency (Da Silva & Krishnamurthy 2016 Galeano al. 2020). Traditionally, drug-side effects where health care professionals and patients reported adverse events to regulatory authoritics. However, this approach has limitations, such as underreporting and delayed detection.
primarily identified through spontaneous reporting systems,
To overcome these limitations, researchers have turned to data-driven methods to find drug-side effects. With the advent of electronic health rocords, largo-scale databases containing valuable information on modication usage and patient outcomes have become available. These databases have allowed researchers to analyze vast amounts of data to identify patterns between drugs and side effects.

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One of the most commonly used approaches to drug-side effects prediction is model-based methods. Model- based methods involve the use of advanced statistical and machine learning techniques to extract knowledge from large datasets. By analyzing patterns in the data, researchers can identify potential drug-side effects and their associated risk factors. In their work, (Pauwels et al.) 2011 predicted the side effects of drugs (Pau's method) by applying K-nearest neighbor (KNN), support vector machine (SVM), ordinary canonical correlation analysis (OCCA) and sparse canonical correlation analysis (SCCA) from drug chemical substruc- tures; furthermore, their experiment outcome suggests that SCCA performs the best. |Sayaa et al. (2012)
utilized SCCA to associate targeted proteins with side effects (Miz's method). Liu et al. (2012) predicted
drug side effects (Tiu's 's method) using SVM and multivariate information, such as the phenotypic character-
istics, chemical structures, and biological properties of the drug. Cheng et al. (2013) proposed a phenotypic network inference classifier to associate drugs with side effects (Cheng's hod). NDDSA models (Shabani- Mashcool et al. 2020) the diug-side effects prediction problem using a bipartite graph and applies a resource allocation mothod to find new links. MKI-LGG (Ding et al., 2018) integrates multiple kernels to describe the diversified information of drugs and side-effects. These kernels are then combined using an optimized linear weighting algorithm. The Local and Global Consistency algorithm (LGC) is used to estimate new potential associations based on the integrated kernel information.
Deep learning techniques Xu et al. 2022) have been increasingly used to predict drug side effects in recent years. These methods leverage the power of neural networks to analyze complex relationships between drugs, genes, and proteins. In SDPred (Zhao et al.] 2022). chemical-chemical associations, chemical substructure, drug target information, word representations of drug molecular substructures, semantic similarity of side effects, and drug side effect associations are integrated. To learn drug-side effect pair representation vectors from different interaction maps, SDPred uses the CNN module. Drug interaction profile similarity (DIPA) provided the most contribution. GCRS (Xuan et al. 2002)) builds complex deep-learning structure to fuse and learn the specific topologies, common topologies and pairwise attributes from multiple trug-side effect heterogencous graphs. Drug-side effect. heterogeneons graphs are constructed using drug-side effect associations, drug-disease associations and drug chemical substructures. Based on & graph attention network, Zhao et al. (202T) developed a prediction model for drug-side effect frequencies that integrated information on similarity, known drug-side effect frequencies, and word embeddings. The above deep learning- based method is kind of pairwise learning. To keep the sample balanced, this group selected the positive sample from trusted databases and the negalive sample by random sampling. Such a treatment results in cerlain loss of information and introduces noise to the label.
Drug-side effect prediction is a classic link prediction problem (Yuan et al. 2019 To solve this kind of
problem, many multi-view methods have been proposed in recent. years Ding et al. 2021| 2016 Cichonska ct al. 2018). Based on the information fusion at different stages of the training process, multi-view methods can roughly be divided into three categories: early fusion, late fusion and fusion during the training phase. Fig. illustrates our taxonomy of multi-view learning method literature.
In carly fusion techniques, the views are combined before training process is performed. Multiple kernel learning (MKL) (Wang et al. 2023b Cichonska et al. 2018 Nascimento et al. 2016) is a typical early fusion technique. For each view, it computes one or more kernels, and then learns the optimal kernel from the base kernels. For example, MKLL-KroneckerRLS (Ding et al.] 2019) combines diversified information using Contered Kernel Alignment-based Multiple Kernel Learning (CKA-MKIL). Based on the optimal kernel, Kronecker regularized least. squares (Kro-RLS) was used to classify drug-side effect pairs. It must. be noted that the performance of these methods relies heavily on the optimal view, which may be redundant miss some key information. In late fusion techniques, a different model for each view is scparately trained and later a weighted combination is taken as the final model. For instance, in Zhang et al. (2016). an ensemble model was constructed by integrating multiple methods, each providing a unique view. The model incorporates Liu et al. (2012), Cheng et al.] (2013), a Integrated Neighbour- Restricted Boltzmann Machine-based Method (RBMBM). Each model is trained independently, and the final partition is the average weighted average of the base partitions. Late fusion allows for individual modeling of inherently different views, providing fiexibility and advantage when dealing with díverse data. However, its drawback is the delayed coupling of information, limiting the extent to which each model can benefit from the information provided by other views.
Method (INBM), and a
2

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View 1
View
View v
View
View
View V
View
View 2
View V
Information sharing
Fusion phase
Optimal view
Fusion phase
Model
Model
Model
Model
Model 2
Model V
Training independently
Training logether
Model
Fusion phase
Partition
Partition
Partition 2
Partition
Partition
Partition
Partition v
(a) Early fusion
(b) Late fusion
(c) Fusion during the training phase
Figure 1: Taxonomy of multi-view learning framework literature. Note: 'Partition" commonly refers to the
learned result. This concept more commonly found in classification and clustering tasks (Liu et al.) 2023 Bruno & Marchand-Ma Mailleet 2009 Wang al. (219)). (a) Early fusion: the views are combined before the training process is performed; (b) Late fusion: different model for each view is separately trained and then combination is taken as the final partition; (c) Fusion during the training phase: it has degree of
freedom to model the views differently but to also ensure that information from other views is exploited
during the training phase.
A third category is fusion during the training phase, which combines the benefits of both fusion types. fuses multiple views at the partition level and enables the model to explore all views while being allowed model one view differently. This framework has been applied classification models (Houthuys Suykens,
2021 Houthuys et al.) 2018; Qian et al.) 2022b Xie & Sun 2020) and clustering models (Lv et al., 2021 Houthuys et al. 2018 Wang el al. 2023a By exploring consensus complementarity information from multiple views, multi-view method can achieve better performance than single view method. The consensus principle pursues to achieve view-agreement among views. For instance, Wang et al. (2019) maximized the aligument between the consensus partition (clustering matrix) and the weighted combination of base partitions.
In this work, we apply this technique to the Kron-RLS algorithm. Due its fast and scalable nature. The proposed method is named Multiple Kronecker RLS fusion- based link propagation (MKronRLSF-LP)) Our work's main contributions are listed as follows:
(1) We extend Kron-RLS to the multiple information fusion setting by finding the consensus partition and multiple graph Laplacian constraint. Specifically, we generate multiple partitions by normal Kron-RI.S and adaptively learn weight for each partition to control contribution to the shared partitions. This work was conducted with the aim of fusing partitions while still allowing for some flexibility in modeling single information. Furthermore, multiple graph Laplacian regularization is adopted to boost the performance of semi-supervised learning. Both settings co-evolve toward better performance.
(2) To fuse the features of multiple information more reasonably, design iterative optimization algorithm to elfectively fuse multiple Kron-RLS submodels and obtain the final predictive model of drug-side effects. In the whole optimization, we avoid explicit computation of any pairwise matrices, which makes our method suitable for solving problems large pairwise spaces.
(3) The proposed method can address the general link prediction problem; it is empirically tested on four real drug-side effect datasets, which are more sparse. The results show that MIrOLRLSF-LLP can achieve excellent classification results and outperform other competitive methods.
The rest of this paper is organizod as follows. Section 2 provides description of the drug-side effect prediction problem. Section reviews related work about MKronR..FF-LPP Section comprehensively
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presents the proposed MKronRLSF-LP. After reporting the experimental results in Section we conclude this paper and mention future work in Section B
2 Problem description
Identification of drug-side effects is an example of the link prodiction problem, which has the aim of predicting how likely it is that there is a link between two arbitrary nodes in network. This problem can also be seen recommendation system (Jiang al. 2019 Fan et al., 2021 task.
Let the drug nodes and side effect nodes of network be ID {d1, d2,....dx)] and S {si, 82, ................................ SM), respectively. We denote the number of drug and side effect nodes by N and M, respectively.
We define an adjacency matrix E RNN M to represent the associations between drugs and side effects. Each element of F defined as F., 1 if the node pair (di, 8;) is linked and F., = otherwise.
The link prediction has the aim of predicting whether a link exists for the unknown state node pair (d,, s,) E D x S. Thus, it is classification problem. Most methods use regression algorithms to predict (ranging from 0-1), which we call the link confidence. Then, class of 0 1 is assigned to the predicted score by the threshold. Higher link confidence indicates a greater probability of the link existing, while lower values indicate the opposite. We define a new matrix F, which is estimated by the prediction model. Each of elements Fi, represents the predicted link confidence for the node pair (d,, 8z). Figure summarizes the link prediction problem discussed in this paper.
3
Related work
3.1 Regularized Least Squares
The objective function of Regularized Least Squares (RLS) regression is:
1 | 1I
+ A
arg min f
(K)
|
(1)
2
where À is a regularization parameter, prediction function and be defined as:
| denotes the RKHS norm Kailath 1971 of f())- (.) is the
f (K) Ka,
(2)
where a is the solution of the model, F is kernel matrix with elements
KiJ (d,, (i.j I.....N).
(3)
and & represents the kernel function.
By formulating the stationary points of Equation and elimination the unknown parameters a, the following solution is obtained
== K(K K
(4)
There is only one kind of feature space considered in this model. In the drug-side effect identification problem, there are two feature spaces: the drug space and the side effect space.
3.2 Kronecker Regularized Least Squares
Combining the kernels of the two spaces into single large kernel that directly relates drug-side effect pairs would be better option. Kronecker product kernel (Hue & Vert 2010) is used for this. Given the drug kernel Kp and side effect kernel Ks, then we have the kronecker product kernel
K Kg KD.
(5)
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where the @ indicates the Kronecker product (Laub 2004]. By applying the Kronecker product kernel to RLS, the objective function of Kronecker Regularized Least Squares (Kron-RIS) is botained:
A I1
arg min
2 live (F) (K)
(K)
(6)
where vec (+) is the vectorization operating function. By setting the derivative of Equation 6 w.r.t to zero, we obtain:
a a= (K + ANMM) vec (F).
Obviously, it needs calculating the inverse of (K NNMM) with size of NM NM, whose time complexity is O (N&M*) Thus, well-known theorem Raymond & Kashima 2010 Laub 2004 is proposed to obtain the approximate inverse.
It well known that the kernel (Liu et al. definite matrices, they can be eigen decomposed, KD = VDAD VB and Kg s VsAsVá. According to the theorem (Raymond Kashima, 2010: Laub 2004), the eigenvectors of the Kronecker product kernel K is the V Vs @ VD. Define the matrix A to be either A.J [Ask, x [Aplas' The eigenvalues of K is diag (vec (A)). The matrix K AINM has the same cigenvactors V, and cigenvalues diag (vec (A + X1)).
2023
Pekalska & Haasdonk
2008
matrices are positive semi-
Then, we can rewrile Equation as:
K(K AMNM) vec (F) Vddig((vec (A)) V diag(vec (A + A1)) VT 'VT 'vc (F).
Since VTV INM and diag(vec (A)) di)) (A + x1)) is also a diagonal matrix, we further simplify Equation
and get
K(K + ANNM) vec (F) Vdiag(vee (J)) vec (F),
(9)
where the matrix to be either
Aij Jtj Ai. X
(10)
Using the vec-tricks techniques ((A & B) vec (C) = vec (BCAT)), we further simplify Equation g Then, we get
F V= @ (V V/
(11)
where @ represents the Hadamard product. The computational time of this optimization method is O (N3 + M3), which is much less than O M33
3.3 Kronecker Regularized Least Squares with Multiple Kernel Learning
Kron-RLS is a kind of kernel method. It can be difficult for nonexpert users to choose an appropriate kernel.
To address such limitations, Multiple Kernel Learning (MKL) (Gönen & Alpaydm 2011 is proposed. Since
kernels in MKL can naturally correspond to different views, MKL has been applied with great success
cope with the multi-view data (Wang al.) [2021] Xu al. 2021 Guo al. 2021 Qian al. 2022a Wang
et al. 2023b) by combining kernels appropriately.
Given predefined base kernels { (Kblen and K j-1 from drug feature space and side effect feature space,
respectively. These kernels can be built from different types or views. The optimal kernel can be combined by a linear function corresponding to the base kernels:
Σ
w K
(12)
Usually, an additional constraint is imposed on the corresponding combination cocfficient w to control its structure:
P
Σ
w = 1, w² 20, 1,...
(13)
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vo (vec() I-II KH KIt
IK S
K
Kronether product
Side effects kemels
Multiple graph Laplacian
Drag kemels
Constrain F
(veo(F) Kaa (eatt)-Kaa'' aa K'
Sharing information
(o)(F) Σ Emraaa 7
(oo(FF - Kal. 2 K'Ka'
K
A daptive weights
Consensus partitions
(oo(F) Karl -urr - Kaa
K K-KK S.K.
Pairwise kertells
Multiple partitions
Framework diagram of MKronRLSF-LP. MKronRLSF-LP allow the multiple partitions have a degree of freedom to model the single information and introduce a multiple graph Laplacian regularization into consensus partition.
Figure 2:
The optimal side effect kernel Kgg is omitted.
Based on MKL method, Ding et al. (019 and Nascimento et al. (0166) developed Kron-RLS based MKL methods, called Kron-RLS with CKA-MKL and Kron-RLS with selfMKL, respectively. Kron-RLS with CKA-MKL combines diversified information using Centered Kernel Alignment-basen Multiple Kernel Learn- ing (CKA-MKL). In Kron-RLS with selfMKL, the weights indicating the importance of individual kernels are calculated automatically to select the more relevant kernels. The final decision function of both methods is given by:
(
(Kgr
ATNas) -1 vec (F).
(14)
4 Proposed method
Existing multi view fusion methods based on Kron-RLS all follow MKL framework. These mothods optimize the optimal pairwise kernel as a linear combination of a set of base kernels. Prior to training, all views are fused, and information not shared during training phase. This typical carly fusion tochnology. Our proposal addresses this limitation by fusing multi-view information in consensus partition. Compared with MKL framework, the advantage of the proposed method is that it allows sub partitions to have certain degree of freedom to model the single information. Further, multiple graph Laplacian regularization is introduced into the consensus partition to boost performance. Fig. 2 illlustrates the main procedure of MKroRRLST-LP.
4.1 The construction of kernel matrix
Kron-RLS a kind of kernel method. We construct drug kernels using five different kinds functions. Gaussian Interaction Profile (GIP):
(GIP.Dli exp (->lld,-d))
(15)
where 7 is the gaussian kernel bandwidth and 1.

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Cosine Similarity (COS):
df dj [Kcos,Dis [di] [dp]
(16)
Correlation coefficient (Corr):
Cov (dg dg)
[Koorn = /Var (d,) Var (dz)
(17)
Normalized Mutual Information (NMI):
Qdd, KNMI.DI.J VH H (d,)
(18)
where Q (d,, d,) the mutual information of di and dj. 1 (d,) and H (dj) are the entropies of de and dj. respectively. Neural Tangent Kernel (NTK):
[KTKKDkk = Eaow [fNTK (0, , fNTK (9.d,)l,
(19)
where JNTK is a fully connected neural network and 0 is collection of parameters in this network. Similarity, we construct the side effect kernels (Karp,s, Kcos,s, KCorss KNMISS, KNTK,S) in side effect space.
4.2 The MKronRLSF-LP model
Let us define sets of base kernel sets separately:
K {K) D: ................................ Kb}
(20a)
Ks K ...... K2}
(20b)
where P and Q represents the numbers of drug and side effect kernels, respectively. Based the Kd and Ks, can get set of pairwise kernels:
K
= K K K. KV = K
(21)
where denotes the numbers of base pairwise kernels. Obviously, V is equal to P x Q.
By using multiple partitions, can manipulate multiple views in partition space, which enhances the robustness of the model. The following ensemble KronRLS model is obtained
Ao a" K'a') Σ { ||vee (F) K" K"aal1
arg min a
(22)
2
In multi-view methods, the consensus principle establishes consistency between partitions from different views. However, it's essential to find that these partitions deliver varying degrees of importance to the final prediction, unlike fusion without discrimination. To facilitate this, we introduce a consensus partition, denoted by F. Tt is a weighted línear combination of partitions F, from multiple distinct views. A variable w. is introduced for view which characterizes its importance, which is calculated based on the training error. To prevent sparse situations, we employ 11.11/ to smooth the weights. Then, we have the following optimization problem
arg min F.a",w
1
vec FF)
Σ
w K" a
+ p
Xo We ||vee (F) K"a" aa" K"aa) 3 1|l12
1
2
(23)
V
8.t.
w.
= 1, w.
2 0, 0, L...., V.

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observe that the consensus partition F fits to adjacency matrix F by indirect path. As described in section 2 false zeros represent unobserved links in the network. Hence, we must avoid overfitting the observed matrix F. Inspired by manifold scenarios, the Laplacian operator adeptly mitigates overfitting and noise, preserving the original data structure and keeping nodes with common labels closely associated. This approach is simple, and empirical evidence confirms its effective performance (Pang & Cheung 2017 Chao & Sun, 2019 Jiang et al. (023).. Here, we apply multiple graph Laplacian regularization Equation 23 which can effectively explore multiple different views and boost the performance of F. Specifically, the Kronecker product Laplacian matrix is calculated from the optimal drug and side effect similarity matrix, which are weighted linear combinations of multiple related kernel matrices. The weight of each kernel can be adaptively optimized during the training process and reduce the impact of noisy or less relevant graphs. The optimization problems for MKromRLST-LP can be formulated as:
In Equation 23
arg min F.a" nn 0g
(F)
Σ
w. k"a
>
Wv
| (F) K"Ka"aa 11 K"aa"l
1 3/1121 X" a" K'aa) +
2
oveo (F) Lvec (F)
Σ w. 1, w. 0, L.....V.
(24)
INM
(Hs" K3H 0.3) & (HP HrH
Q
K3
[ss Ks KD Σ Opl Kb.
P
Σ [0s]. = 1, 1,,0s, 2 2
Q. Σ [0p) = 1,,[0,, 2 2,1 I,...,
where L a normalized laplacian matrix, Hs and HD are diagonal matrix with the jth diagonal elements Σx [Kā and Σ, [, respectively. And, 1, guaranteeing each graph has particular contribution to the Laplacian matrix.
Due to the lack of space, we present optimization algorithm of the Equation 24 in Appendix Section A.1
5 Experiments
In this section, the performance of MKronRLSF-LP shown, and we make comparisons with bascline methods and other drug-side effect predictors.
5.1 Dataset
Table 1: Summary of the real drug-side effect datasets.
Name
Drug
Side effect
Associations
Sparsity
Reference
Liu
832
1385
59205
94.86%
(Cheng et al. 2013
Pau
888
1385
61102
95.03%
Pauwells et al. 201
Miz
658
1339
49051
94.43%
Sayaka et al 2012
Luo
708
4192
80164
97.30%
[Luo et al. 2017
Four real drug-side effect datascts are used to assess the effectiveness of our proposed method. Pau dataset is derived from the SIDER database (Kuhn el al. 2010)) which contains information about drugs and their recorded side effects. Miz dataset includes information about trug-protein interactions and drug-side effect interactions, obtained from the DrugBank (Wishart al. (2066) and SIDER database, respectively. There were 658 drugs with both targeted protein and side effect information. Additionally, Liu al. mapped drugs in SIDER to DrugBank 3.0 (Knox et al. 2010), resulting in final dataset of 832 drugs and 1385
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side effects. Luo dataset has large mumber of side effects and was extracted from the SIDER 2.0. Table summarizes information about the datasets. We can see that these four datasets are sparse. In other words, there are fewer positive samples than negative samples. Thus, drug-side effect prediction can be viewed as a classification problem with extremely imbalanced data.
5.2 Parament setting
In this paper, the objective function 24 contains the following regularization parameters: μ, 3, 0, e and V. To find the right combinations of the regularization parameters of MKroORLSF-LPP to give the best performance, the grid search method is performed on the Pau dataset. The optimal parameters with the best AUPR are selected.
We first select \² l...., V by the relative pairwise kernel with a single view Kron-RLS model. For cach parameter X", we select it in the range from 2- to 2 with step 2 The optimal parameters X are shown in Table [ According to a previous study et al. 2019), the performance is not affected by parameter e, so set 2. Then, we fix X", v I...., V at the best values and tunc μu, B, a from within the range 2-10 to 2 with step 2 The optimal regularization parameters are μ = 2-7, B = 20 and = 2-
5.3 Baseline methods
In this work, compare MKrroRLSF-LLP
with the following baseline methods: BSV ( Due to the lack of space, we present details of these baseline methods in Appendix Section A.3 For a fair comparison, the same input as our method fed into these
Comm R & Cooper
1995
et al. 2019), Kron- Kron-RIa self-MKLL Nascimento et al. 2016). MvGRLP (Dng
RLS (tt.wiiseeKKCCiihsssssa et al.
2018
et a.. 2021 and MyGCN et al.
2022)
bascline methods. To achieve the best performance, we also adopt 5-fold CV on the Pau dataset to tune
the parameters.
5.4 Threshold finding
Because the MKronRLSF-LP and baseline methods only output the value of regression, we apply threshold finding operation. For certain validation set in the five-fold cross-validation (5-fold CV) procedure, we collect the labels and their corresponding predicted scores. Then, we obtain the optimal threshold by maximizing the Fscore on the predicted scores and labels from this validation sets. trend of Fscores Recall and Precision with different thresholds over four datasets shown in Fig. 6 While the threshold of prediction rises, the values of Recall rising. Oppositely, Precision falling. The Fscore is the harmonic mean of the Recall and Precision. It thus symmetrically represents both Recall and Precision in one metric. Here, find the optimal threshold under maximizing the value of Fscore- Table 5 summarizes the thresholds of different baseline methods on different datasels.
5.5 Comparison with baseline methods
We conduct the 5-fold CV to evaluate the performance of our method versus the baseline method. To further provide a fair and comprehensive comparison, each algorithm is iterated 10 times with different cross index, and then the mean values and standard deviations are reported Table 3. The best single view is KGIP,D KNTK,S, which selected by 5-fold CV on Pau datasct.
First, observe that the proposed method has the best AUPR and Fscore all datasets. Especially, the proposed method has higher AUPR and Facore than BSV on datasets. This indicates the improvement in using multiple views. The simple coupling frameworks BSV and Comm perform well on the Pau datasct. However, BSV and Comm cannol perform as well on other datasets, which indicates that the simple fusion schemes are sensitive to the dataset and not robust. Furthermore, Kron-RLS+ - pairwiseMK. achieves the highest AUC of 95.01%. %, 95.02% 02% and 94.70% on the Liu, Pau and Miz datasets, respectively. This shows slight improvements of 0.23%. 0.21% and 0.23% over our method, respectively. As we discussed in Section 5.1 drug-side effect prediction is extremely imbalanced classification problem. The AUC can be considered

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the probability that the classifier will rank randomly chosen positive instance higher than randomly chosen negative instance. Therefore, the AUC is not an important metric for predicting drug side effects.
Another interesting observation is that MKronRLSF-LP outperforms other MKL strategy methods in com- parison. For example, it exceeds the best MKL method (CKA-MKL) by 2.1%, 2.32%, 1.43%, 2.51% in terms of AUPR on Liu, Pau, Miz and Luo dataset, respectively. These results verify the effectiveness of the consensus partition and multiple graph Laplacian constraint.
For more thorough analysis and reliable conclusions, we use post-hoc test statistics to statistically assess the different metrics shown in Table 3 Fig. 3 shows the results of these tests visualized as Critical Difference diagrams. These results show that MKromRLSF-LP is significantly better ranked than all methods in terms of AUPR, Recall and Fscore- In addition, MKrroRLST-LP is only inferior than Kron-RLSSpairviseee. and
in terms of AUC and Precision, respectively. Besides, MvGCN is worse ranked than our method. Another point worth mentioning is that there is no sufficient statistical evidence to support that MvGCN performs better than model-based methods. MvGCN uses shallow GCN to avoid over-smoot.ing. The shallow GCN (Miao et al.) 2021) can only capture local neighbourhood information of nodes, but the global features of the network have not been fully explored. A result of this is inaccurate embedding vectors.
In summary, the above experimental results demonstrate the superior prediction performance of MKronRLSF-LP to other baseline methods. We attribute the superiority of MKronRLSF-LP as three aspects: (1) The consensus partition is derived through joint fusion of weighted multiple partitions; (2) MKronRI.FF-LP utilizes the multiple graph Laplacian regularization to constrain the consensus predicted value F, which makes the consensus partition is robust; (3) Unlike existing MKL methods, the proposed MKronRLST-LP fuses multiple pairwise kernels at the partition level. It is these three factors that contribute to the improvement in prediction performance.
5.6 Ablation study
To validate the benefits of jointly applying the consensus partition and multiple graph Laplacian constraint, we conduct an ablation study by excluding particular component. First, we construct a Kron-RLS based on each pairwise kernel separately. Each partition learns independently, so it can be regarded as an ensemble Kron-RLS, and its objective function is Equation 22 The results should be consistent for each view, and heterogeneous views have varying degrees of importance in the final prediction. Therefore, we set. a consensus partition F, which is a weighted linear combination of base partitions (as shown in Equation 23). To further improve the performance and robustness of the model, we apply multiple graph Laplacian constraints to the consensus partition. Finally, the objective function 24 of MKrooRLST-LP is obtained. The results of the ablation study are shown in Fig. 4 It can be observed that the consensus partition and the multiple graph Laplacian constraint is helpful for MKronRLSF-LP to achieve the best results.
5.7 Comparisons of computational speed
In order to demonstrate the effectiveness of M.rOORTSF-LPP, we are now comparing it to different baseline methods in terms of computational speed. Except MvGCN, other methods are performed on a PC equipped with an Intel Core 17-13700 and 16GB RAM. Because MvGCN is a deep learning- based method, it is performed on a workstation equipped with NVIDIA GeForce RTX 3090 GPU. For all baseline methods, we tested 10 times to report the mean running time. The results are shown Table The results do not include the kernel calculation time.
As expected, learning from multiple views takes more time than learning from only one view (BSV). Also, since RLFFLLS fuses multiple views at the partition level, it requires more running time than TTon-RLLSCKA-MKKJ and Kron-RLSS+sel--KLL Another observation is that MKronRLST-LP is much faster than Kron-RLS- Roan-RLS-paaaee RLS--parrisMMKLL This can be explained by looking at the time complexity of MKKroRLSF-LLP and Kron-RI.s - plexity of both methods. In our optimization algorithm, we use eigendecomposition techniques to compute the approximate inverse. The time complexity of our method is O(PP Iterr (Q + ).)) Dif-
The inverse of pairwise kernels dominates the time com-
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AUPR 9.0
0.2
04
0.6
0.8
1.0
1.2
550)
MyGALP
Kram-HLLS--sel-000 sel--LL 02.422)
Kien-lLs CKK-NLL
Mysich [0.447]
[0.463] Gorven Kron-HLS
AUC
0.6
0.8
1,5
1.2
CKA (555
00.76] Miron
Comm (ron
MyGCN
[0.547]
[0.597] MYGRUP
Recall
0.2
0.4
0.5
1.0
40
4
0.715) KLS palwsotta
Mycah jd [.431]
[0 (..55] MyGRLP
Kor--RLLS-saff-RKL (2.472]
[0.503] Gorver Kron-HLS
Precision
0.8
1.2
Comm fron 458)
MyGALPP
MvOCh
Kion RLS--sel-MO
Escore
palin
0.553] MKCORRLFF
MyCOK (53)
10,509] KronALS-sell
Figure 3: Critical difference diagram of average ranks. A crossbar is over each group of methods that do not show statistically significant difference among themselvvs.
70
65
AUPR(%)
60
Ensemble Kron-RLS
Ensemble Kron-RLS
Consensus partition
55
Ensemble Kron-RLS
+ Consensus partition
multiple graph Laplacian constraint
dataset
Pau dataset
Miz dataset
Luo dataset
Figure 4: Ablation study of the consensus partition and multiple graph Laplacian constraint on four datasets.
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Table 2: Mean running time (in seconds) of baseline methods on four datasets.
Methods
Pau
Liu
Miz
Luo
BSV
0.79
0.83
0.68
5.84
Comm Kron-RLS
19.38
20.95
18.39
148.60
Kron-RLS CKA-MKL
2.69
2.18
2.36
13.13
1583.67
14
1364.21
Kron-RI.
12.21
13.05
12.09
155.85
MvGRLP
8.94
8.37
7.23
58.53
MvGCN
305.44
329.43
343.50
MKrOORI.SF-LPP
50.55
43.9
35.83
280
represents that the method took more than 2 hours to run.
solves the system with the conjugate gradient approach that iteratively improves the result by performing matrix-vector products. Hence, Kron-RLS K paiisiseeKiiiK is carried out in PQQ M N2)).. When MvGCN deal with Luo datasct, running time exceods hours. This is because MvGCN utilizes a self-supervised learning strategy based on deep graph infomax (DGI) to initialize node embeddings. Whenever there are many nodes in bipartite network, DGI takes very long time to implement.
ferently, Kron-RLS Kron-KL.S+pairvisstte +airwiseMKL
5.8 Comparison with other drug-side effect predictors
A comparison of the proposed drug-side effect prediction method with state-of-the-art methods also pro- vided. Tables and present the results of 5-fold CV in terms of AUPR, AUC, Recall, Precision and Facore on the four datasets, respectively. We have highlighted the best results in bold and underlined the second-best results.
Obviously, MKronRLSF-LP achieves the highost AUPR and Facore on all datascts. In the problem of drug-side effects prediction, AUPR and Fecore more desirable metrics (Ezzat et al. 2017, Li et al., 2021
Therefore, we conclude that our method outperforms the other assessed methods. GCRS (uuan et al. 2022) and SDPred (Zhao al.] (202)) are deep learning- based methods. GCRS construets multiple heterogeneous graphs and multi-layer convolutional neural networks with attribute-level attention to predict drug-side effect pair nodes. SDPred fuses mult side information (including drug chemical structures, drug target, drug word, side effect semantic similarity, side effect word) by feature concatenation and adopts CNN and MLP for prediction tasks. However, on Luo dataset, GCRS and SDPred perform poorly; this is probably because they are pairwise learning methods and randomly negative sampling to construct the training set. The randomly negative sampling method cannot be guaranteed due to the reliability and quality of negative sample pairs, which results in a certain loss of information ensemble model ZZang et al. 2016) combine Liu's method {Liu et al. 2012), Cheng's method (Cheng al., 2013), INBM and RBM by the average scoring rule. It is obvious that the results of the ensemble model are significantly improved than the results of the sub-model on four datascts.
et al., 2015 Ali & Aittokallio, 2019). The
6 Conclusion
This paper presents MKronRLSF-LP for drug-side effect prediction. The MKrroRLSF-LPP method solves the general problem of multi-view fusion-based link prediction by utilizing the consensus partition and multiple graph Laplacian constraint. MKromRLSF-LP allows for some degree of freedom to model the views differently and combination weights for cach view to find the consensus partition. Each view's weight is dynamically learned and plays a crucial role in exploring consensus information. It is found that the use of Laplacian regularization enhances semi-supervised learning performance, so a term of multiple graph Laplacian regularization is added to the objective function. Finally, we present an efficient. alternating optimization algorithm. The results of our experiments indicate that our proposed methods are superior in terms of their classification results to other baseline algorithms and current drug-side effect predictors.
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Acknowledgments
This work is supported in part by the National Natural Science Foundation of China (NSFC 62172076. 62250028 and U22A2038), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY23F020003), and the Municipal Government of Quzhou (Grant No. 2023D036).
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A Appendix
A.1 Optimization
It difficult and timo-consuming solve the Equation 24 bocause it contains multiple variables and large pairwise matrices. In this section, we divide the original problem into five subproblems and develop an iterative algorithm to optimize them. And, avoid explicit computation of any pairwise matrices in the whole optimization, which makes our method suitable for solving problems in large pairwise spaces.
F-subproblem: we fix a", w, Op and Os to optimize variants F. Let A = H 0.5 K 0.5 B
H 0.5 K; KHH,U and vee (r)) = K" Then, the optimizatiin model of P as follows:
w. vec ( + ovec (F) (F)*La Lvee (f)
arg min
vec
2
(25)
F
P=1
s.I.L
INM A B.
Let the derivative of Equation
25 w.r.t t F to zero, the solution of F can be obtained:
vec ()) ((1 + + NNM aA B) B)
Σ w. vec (F.) (Fx))
(26)
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Notice that the inverse matrix the right-hand side of Equation 26 needs too much time and memory. Therefore, use eigen decomposed techniques to compute the approximate inverse. Let VAAAVA VÁ and VBABVB be the eigen decomposition of the matrices A and B, respectively. Define the matrix U to be U = [A,,, x [A By the theorem [Raymond & Kashima 2010), the kronecker product matrix &
can eigendecomposeel as (VA @ VB) diag (vec (VA) 8 VB) Then substituting it in Equation 26 can write the inverse matrix in Equation 26 as
we
((1 (1+ INM aA B) B) (11 (1+ (Vi & VB) diag (vec (U)) (VA 0 Vn)")
(27)
Since, it holds that (Va VB) (VA @ VB) T INM. Equation 27 can be transformed into
((1+0) σA B) (VA (B) + + INM odiag (vee (U))) (Va (Va&VB)".
(28)
Notice that the inverse matrix in Equation 28 is a diagonal matrix whose value can be calculated as the matrix W
Wis -1+0-oUt--)
(29)
So, further rewrite the Equation 26
E -== vec (
F (VA X VB)diag (vec (V
(30)
Taking out the vec-tricks operation, we can obtain the solution
w. F va) ) V
F = VB o o V
(31)
w-subproblem: we fix all the variants except w. The formula is as follows:
1
wy
Full?)) rr) + 2 ||
arg min
F
W.
2
2
F
(32)
V
s.t.
w. = 1, w. 2 0, v I...., V.
1=1
Problem 32 can be simplified as standard quadratic programming problem (Nocedal & Wright 2006)
arg min w" Gw w h
w
V
(33)
s.t.
w.
1, 0,0 - 1,..., V.
where G E VVV with the element as
T Fj
1/4 trace
Fr
if
G
(34)
T
2 trace
Fi
F
+ 3,
if i-
h is a vector with
h: trace (5T
pm
f
(35)
The optimization method for Equation 33 is the interior-point optimization algorithm
(Byrd et al.
1999
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i p-subproblem: With the fixed all the variants except pD, the formula can be written
1 o (F)² Lvve (F)
arg min
Op 2
s.t. L INM - (H5 KiHH 0.0)
(HD* KbHD ".
(36)
Kb Σ Op)] Kb: Σ Opp, 1, 1p]. 20, L......
Let A K3 and B HD
0.5 Kb H
0.5
Then substituting L in Equation 36 with A and B
D
the objective function 36 can be written as
arg min Pp
1 govec (F)
Σ
(A & B') vec (F)
2
1=1
(37)
P
8.8.
0D); = (p]] 2 0, = I.
Further, introduce the Lagrange multiplier & and the objective function 37 can be converted to a Lagrange function:
P
P
Lag (0p, - avec Σ
A 2 B¹) B') vec ( -
Σ 10p) -1
(38)
Based on setting the derivative of Equation 38 solution
w.r.l I. On and & to zero respectively, we have the following
00d), vec
(F) T (A & B*)
(+)
(F) +t
(F)
(A B*) vec F (F)) +t
(39)
By using the vec-tricks operation, we can describe the solution as
10pl = trace (FTB'AA))
+
P trace
T (TT'PAT)*
(40)
O--suprroblem solution of Os is similarity 0p. Here, the optimization process omitted and we directly give the solution
trace FT (FT))())))) +
O0s, trace 5 BF
(41)
where B = H= 0.5 HH and A' H K H
a" o--subproblem: By dropping all other irrelevant terms with respect a", we have
arg min 1
X" a= K'a²) Wy l|vec (F) K" K"a"13
vec
F
w. K a'
+ 1
(42)
2
It can be observed from the objective function 42 that when training the parameter a", other views K; with weight w; were taken into consideration. Therefore, each partition's 's training is not completely separate, but involves information sharing.
Based on setting the derivative of problem
42 w.r.l a to zero, we get
K
d
INM
a"
vec F
Σ 1=1,8
w. K'a + vec (F)
(43)
1 +
1 + paw
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V Σ F + F, the Equation 43 can be writlen as i=1,8f
Let W- = --
X
a" 1 pmw
K" +
IN
voc (W).
(44)
1+ pame
We can observe that the form of Equation techniques and the vec-trick operation to effectively compute a².
44 similar to Equation
Therefore, we use eigen decomposod
We summarize the complete optimization process for problem 24 in Algorithm
Algorithm 1: Optimization for MKronRLST-LP.
Input:
The link matrix F; The regulation parameters 14, 8, 0, and X², u V; The predicted link matrix F;
Output:
Compute two sets of base kernel sets Kp and Kg by Equation 20a and 20b
Initialize a"; -- 1, V by single view Kron-RI.S; w, = 1 1/V, 1, I.....V.................... 0 = 1/P,i 1,..., Q;
0's 1== while Not converyence do Update F by solve the subproblem
25
Update w by solve the subproblem
32
Update Op by solve the subproblem
36
Update Og by Equation 41
for i = to V do
Update a' by solve the subproblem
42
end 10
end
A.2 Measurements
Considering that drug-side effect prediction is an extremely imbalanced classification problem and we do not want incorrect predictions to be recommended by the prediction model, we utilize the following evaluation parameters:
TP
Recoll
(45a)
TP FN
TP
Precision TP + FP
(45b)
Precision X Recall
F Pacore 2 x Precision Recall'
(45c)
where TP, FN, FP and TN are the number of true-positive samples, false-negative samples, false-positive samples and true-negative samples, respectively. The area under the ROC curve (AUC) and area under the precision recall curve (AUPR) is also used to measure predictive accuracy, because they are the most commonly used evaluate metrics in the biomedical link prediction. The precision-recall curve shows the tradeoff between precision and recall at different thresholds. Fscore is calculated from Precision and Recall. The highest possible value of Fscore is indicating perfect precision and recall, and the lowest possible value is 0, if either precision or recall zero. AUC can be considered as the probability that the classifier will rank randomly chosen positive instance higher than randomly chosen negative instance (Li et al.
2021
Therefore, we consider AUPR and Fscore more desirable metrics (Ezzat et al. 2017
Li et al. 2021
A.3
Baseline methods
Best single view (BSV): Applying Kron-RLS the best single view. The one with the maximum AUPR is chosen here.
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Published in Transactions on Machine Learning Research (06/2024)
Committee Aron-RLS (Comm Kron-RLS) (Perrone & Cooper 1995): Each view is trained by Kron- RLS separately, and the final classifier is weighted average.
Kron-RLS with Centered Kernel Alignment- based Multiple Kernel Learning (Kron-RLA) -ainnRRL++KKKS MKT. (Ding et al. 2019): Multiple kernels from the drug space and side effect space are linearly weighted by the optimized CKA-MKL. Finally, Kron-RLS is employed optimal kernels.
Kron-RLS with pairwise Multiple Kernel Learning (Kron-RLS ( (eannkL(CCCCccsssi Ciihhonska et al, 2018): First, constructs multiple pairwise kernels. Then, the mixture weights of the pairwise kernels determined by CKA-MKT. Finally, it learns the Kron-RLS function based the opti- mal pairwise kernel.
Kron-RLS with weightei multiple kernel learning - (ascimento et al, 2016): The optimal drug and side effect kernels are lincarly weighted based on the multiple basc kernel. The proper weights assignment each kernel is performed automatically.
Multi-view graph regularized link propagation model (MyGRLP) (Ding et al. 2021 ): This is an extension of the graph model (Zha et al. 2009). To fuse multi view information, multi-view Laplacian regularization is introduced constrain the predicted values.
Multi-view graph convolution network (MvGCN) (Fu et al., 2022 This extends the GCN (Zhang et al. 2019) from a single view to multi-view by combining the embeddings of multiple neighborhood information aggregation layers each view.
A.4 Code and Data Available
The code and data available at htttp:///githbb https/haw.ccc///hhhghg/ttltalaaa
A.5
Figures
A.6 Tables
20

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Published in Transactions on Machine Learning Research (06/2024)
The links between drugs and side offects
Drugs
Side effects
d
Unknoown links
d
nown Tinks
Represents by matrix
cl
links
Unkmown links
cl
cl
F
The adjacenicy maktix I
Predict
S
cl
High confidence
cl
confiiance
d
Figure 5: Visualization of drug-side effect association problems.
Liu dataset
Pau dataset
Miz dataset
Luo dataset
1.0
0.8
0.6
Optimal threshold:01177
Max Fa 631
0.6
Optimal Opeishi threshole...100
Max Faze: 0.632
Score
0.6
Max Facm:: 6.66
Optimal thresholc.0.119
0.6
Hax F 605
Optimal threshois0.0 0.34
0.2
Feure Preciston
Funes
Fawe Fresbrion
Fawe Precision
Precition Recal
Recall
Recal
Recal
0.0
0.0
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.6
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
D.
0.8
1.0
0.0
0.2
0.4
0.5
0.8
1.0
Throdhold
Thrushald
Thrushald
Threshald
Figure 6: Results (MKrOnRLSFFLLP) for F Fscores Recall and Precision of different throsholds.
21

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Published in Transactions on Machine Learning Research (06/2024)
Table Prediction performance comparison baseline methods on four datasets.
Dataset
Methods
AUPR(%)
AUC(%)
Recall(%)
Precision(%) (%)
Pecore (%)
BSV
60.12+1.12
93.22++..60
58.77+0.33
0..09
58.52+0.23
Comm Kron-RLS
65.63+1.95
94.11=1.44
61.63++0.3
61.9++1.77
61.57+1.65
Kron-RLS
65.92+0043
92.51+0.08
62.11+0.43
63.09+0.56
62.59++0.41
+CKA-MKL
Liu
Kron-RLS
62.03:10.44
95.01=0.006
65.39=2022
54.46=0.30
59.43:10.21
+pairwiscMKL
Kron-RLS
65.02+00.47
92.1++0110
60.97+0.57
63.1220.61
62.03+00.2
+self-MKL
MvGRLP
66.32=0.45
94.29=0.08
63.56=0.46
60.87=0.62
62.18=0.39
MyGCN
62.69+1181
94.01+0.87
60.81+0.37
60.33+1.31
60.48+1.15
MKronRISF-IP
68.02:10.44
94.78+00133
65.18+0.93
61.27+1.08
63.02=00.3
BSV
65 65.26=0.98
94.57=0.34
62.54=0.5
60.77+1.27
60.65+0.73
Comm Kron-RLS
65.63++0.36
94.78+-0.13
64.01+00388
60.05++0.49
61.01++0.27
Kron-RLS
65.49-10.37
92.3910.133
61.65:0.40
63.22:10.51
62.42:10.27
+CKA-MKL
Pau
Kron-RLS
63.48-0.39
95.02:1.007
78.1
45.01
57.11
+pairwiseMKL.
Kron-RLS
64.11
91.94L0.25
62.37-10.29
6..97
61.65
+self-MKL
MvGRLP
66.17
94.42=0007
02.18
61.95
62.06:10.22
MvGCN
63.51+1.43
94.08
63.21+0.69
57.94+1.34
60.4+1.78
MKronRLST-LP
0.38
94.81
65.72+3.58
60.65
62.87
BSV
56.58+2..33
90.71+2.06
6..76+0.69
53.94+2.31
55.39+22.3
Comm Kron-RLS
58.08+1.07
91.36+1.25
62.37+0.81
55.16+1.99
36.54
Kron-RLS
66.92+00.44
92.58+0.14
0.56
64.3::0.46
61.45++0.44
+CKA-MKL
Miz
Kron-RLS
62.13:00.9
94.70=10.11
63.78+0.47
56.26=10442
59.79++0.30
+PL
Kron-RLS
65.84+0.43
92.06+0.16
63.6310.48
6..7
60.68:10.33
+self-MKL
MvGRLP
66.68=00.35
94.10+0.11
63.46+0.43
61.82+0.30
62.63+0.29
MyGCN
62.17+11.90
93.35+1.73
59.54+0.43
60.74+1.78
59.76+1.955
MKronRLSF-LL
68.35-00.3
94.47+0.09
65.15+2.77
62.1013.19
63.45+10.53
BSV
60.40=0.40
94.40=0.11
58.2840.41
58.6810.46
38.48+00.9
Comm Kron-RI.S
54.19+1.36
91.92+4.01
57.61+2.46
53.16+1.97
52.99+1.54
Kron-RLS
60.87110.6
92.03+0.115
55.55+0.34
64.15:10.46
59.544
+CKA-MKL
Luo
Kron-RLS
50.29+0.29
94.37+0.11
55.66+00.9
45.97+00.99
50.35++031
+PIirwiseMKI.
Kron-RLS
22.29-11.57
79.74+1.62
56.62+1..77
2..91
28.2
+Kelf-MKL
MvGRLP
61.76+10.45
94.08+00.07
58.70+0.40
60.05+0061
58.37+0.42
MvGCN
61.1810.41
94.54+0.11
57.94+0.37
61.26
51.07+0.38
MLSOLL
63.32-10.58
94.07-L0.14
59.43+40.95
60.47
22

---

Published in Transactions on Machine Learning Research (06/2024)
Table 4: The optimal parameters X" obtained with the single view Kron-RLS model (based on the relative pairwise kernel).
KaIPS
KGIPS
KGIPS
KGIPS
KarPs
KGIP,D
2
2
2
2
2
ioos,D
22
23
23
22
2-2
C
23
23
24
2
24
KMLD
2
21
21
20
2-1
K KTT.D
2
24
23
2
2
Table 5: Summary of the threshold of baseline methods on four datasets.
Methods
Liu
Pau
Miz
Luo
BSV
0.145
0.146
0.142
0.128
Comm Kron-RLS
0.205
0.204
0.192
0.183
0.100
0.106
0.099
0.102
Kron-RLS
0.149
0.159
0.101
0.107
Kron-RL.S+selIMKKI
0.119
0.116
0.113
0.129
MyGRLP
0.090
0.091
0.094
0.085
MVGCN
0.225
0.237
0.208
0.197
MKronRLSF-LP
0.177
0.168
0.179
0.149
Table 6: Prediction performance comparison of other drug-sie side effect predictors on Liu datasets.
Methods
AUPR(%)
AUC(%)
Recall
Precision
Fscore (V6)
Liu's method
28.0
90.7
67.5
34.0
45.2
Cheng's method
59.2
92.2
59.0
55.7
56.9
RBMBM
61.6
94.1
61.5
57.4
59.4
INBM
64.1
93.4
60.7
60.4
60.6
Ensemble model
66.1
94.8
62.3
61.1
61.7
MKL-LGGC*
67.0
95.1
NDDSA with sschem
60.5
94.1
57.9
56.4
57.1
NDDSA without sschem
60.4
94.0
57.4
56.8
57.1
MKronRLSF-LP
68.2
94.7
63.8
62.5
63.1
represents not available; the bold and underlined values represent the best. and second performance measure in each column, respectively; and represents the results are derived from (Ding al. 2018 and (Shabani-Masie el al. 2020), respectively.
23

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Published in Transactions on Machine Learning Research (06/2024)
Table 7: Prediction performance comparison of other drug-side effect predictors on Pau datascts.
Methods
AUPR(%)
AUC(%)
(ecall(%)
Precision(%)
F Sscore (%))
Pau's m
38.9
89.7
51.7
36.1
42.5
Liu's method
34.7
92.1
64.6
40.0
49.5
Cheng's method
58.8
82.3
58.3
55.0
56.6
RBMBM
61.3
94.1
60.8
57.7
59.2
INBM
64.1
93.4
60.8
60.5
60.7
Ensembel model
66.0
94.9
62.4
61.2
61.6
MKL-LGC*
66.8
95.2
NDDSA with sschem
60.3
94.2
59.3
54.9
57.0
NDDSA without sschem
60.3
94.1
58.2
55.9
57.0
MKronRLSF-LP
67.9
94.7
63.4
62.9
63.2
represents not available; the bold and underlined values represent the best and second performance measure each column, respectively;
a, b and c represents the results are derived from (Zhang al. 2016 (Ding and (Shahani-Mashcooll et. al. 2020 respectively.
2018
Table 8: Prediction performance comparison of other drug-side effect predictors Miz datasets.
Methods
AUPR(%)
AUC(%)
Recall(%)
Precision
Fscore (%)
Miz's "
41.2
89.0
52.7
38.7
44.6
Liu' method
36.3
91.8
64.0
41.5
50.5
Cheng's ' method
56.0
92.3
58.4
56.8
57.6
RBMBM
61.7
93.9
60.5
58.8
59.6
INBM
64.6
93.2
61.6
60.5
61.1
Ensemble model
66.6
94.6
62.4
61.9
62.2
MKL-LGC*
67.3
94.8
NDDSA with sschem
60.6
93.9
58.8
56.3
57.5
NDDSA without sschem
60.7
93.6
60.0
55.5
57.6
MKronRLSF-LP
68.5
94.5
63.0
64.2
63.6
represents not available; the bold and underlined values represent the best and sccond performance measure in each column, respectively;
a, b and e represents the results are derived from (Zhang et al. 2016 and Mashhooll et al. 2020), respectively.
(Ding et al. 2018
Table 9: Prediction performance comparison of other drug-side effect predictors on Luo datasets.
Methods
AUPR(%)
AUC(%)
Recall(%)
Precision
Fscore (%)
Liu's method
39.4
93.5
59.6
48.3
53.3
Cheng's method
53.2
90.9
53.1
52.3
52.7
RBMBM
55.1
93.5
56.1
54.3
55.1
INBM
57.3
91.7
55.8
56.7
56.2
Ensemble model
58.6
93.9
46.1
68.4
55.1
MKL-LGC
61.7
94.6
NDDSA with "
53.1
94.2
47.6
57.3
52.0
NDDSA without sschem
44.5
93.7
44.7
47.8
46.2
GCRSb
27.2
95.7
SDPred
22.6
94.6
MKronRLSF-LP
63.5
94.1
59.2
61.9
60.5
represents not available; the bold and underlined values represent the best and second performance measure in each column, respectively; b represents the results are derived from Silabani-Mashee et al. 2020 and Xuan et al.
2022 respectively.
24


Reviews:
[{"review_id": "EA19XZJiu9", "reviewer": "Reviewer_HTZM", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths\n- Introduce a novel late fusion technique, including various optimization steps, and contrast that to early fusion methods.\n- The methodology and rationale are presented comprehensively, facilitating understanding.\n- Comparative analysis with multiple Kron-based techniques and other multi-view graph approaches, as well as deep learning based approaches, strengthens the study's contextualization.\n\n## Weaknesses\n- There's a lack of clarity on how potential overfitting is mitigated and how the approach is fairly evaluated.\n- Certain claims may be somewhat exaggerated or require more substantiation.\n- A thorough proofreading pass would enhance the manuscript's clarity and readability.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors propose to extend the Kronecker regularized least squares (Kro-RLS) technique to classify drug-side effect. Their proposal focuses on late fusion by finding a consensus partition, applying multiple graph Laplacian regularizations. To accomplish this, they introduce an optimization algorithm and subsequently contrast their approach with various baseline methods.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "## Majors requests\n- The proposed technique aims to determine the optimal threshold by maximizing the F-score, which is also one the main metrics used for comparing with alternative approaches. However, the absence of a validation or test split raises concerns about potential overfitting.\n\n- Various methods listed in Tables 4, 5, and 6, such as \"RBMBM,\" \"MKL-LGC,\" and \"NDDSA,\" are not previously introduced in the manuscript. Providing brief descriptions for these methods would enhance the reader's understanding and facilitate a more informed assessment.\n\n- In Section 6, the final paragraph appears disconnected from the preceding content: \"MKronRLSF-LP uses L2 loss to measure the quality of approximation. However, the L2 loss function measure is sensitive to outliers and the interaction matrix contains false zeros. Thus, feature work contain replaces the quadratic form of residues by robust loss, such as LINEX lossTang et al. (2021) and p-power lossChen et al. (2017)\".\n\n- In Section 5.6, the following sentence seems to be exaggerated given that AUC results are reported yet not considered: \"Obviously, MKronRLSF-LP achieves the best prediction results for all datasets (the highest AUPR and Fscore score on all datasets)\".\n\n\n## Minor requests\n- There are numerous typos and oversights present in the manuscript: \"Based on MKL method, Ding et al. Ding et al. (2019) and Nascimento et al. Nascimento et al. (2016)\", \"Psecision\".\n\n- The description of the datasets is nearly absent, which could hinder readers' understanding of the data used in the study.\n\n- In Table 1, \"Zero of rates\" appears to be nonsensical and may require clarification or correction.", "broader_impact_concerns": "There are no ethical concerns associated with the release of this work. However, providing a model card would facilitate the method's proper utilization.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "8QTKmnmbCb", "reviewer": "Reviewer_rgQm", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The main issue with the current paper is in the 1) presentation, 2) justification and 3) validation.\n1. the authors never explain the notion of partition or consensus, which is the main contribution of the approach. This prevents the reader from understanding what is the gist of the proposal and why this particular approach should yield an advantage. \n2. The authors very briefly mention at page 7  that  \"the node pair sharing the same labels should be kept close together. This means any two pair nodes with same labels have a higher similarity. That is, the pair node labels with stronger correlations are assumed to be closer to each other in the original space. This is analogous to the Laplacian operator on manifolds\". This is the only justification for the introduction of the laplacian regularisation offered to the reader. No justification is offered for the partition notion (which is not explained).\n3. a more thorough empirical validation should be offered: a) an ablation experimental design should be employed to show the relative importance of the partition notion and the laplacian regularisation; b) a significance test is missing, so we do not know if the improvement reported is statistically significative (please use a post-hoc analysis and a critical differences diagram); c) the author says that \"we avoid explicit computation of any pairwise matrices, which makes our method suitable for solving problems in large pairwise spaces\", but do not offer an efficiency comparison with other approaches; d) the authors should use an artificial problem where the difficulty of the problem is controlled by design and show the regime when the proposed approach works and when it stops working (e.g. when the number of missing links is above a certain threshold w.r.t. the size of the network, etc)", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors propose to tackle the problem of drug-side effect prediction which is a link prediction problem or a recommendation problem. They propose to use a multiple kernel approach. They start from a Kronecker regularised least square formulation and add two contributions: a notion of consensus partition and a regularisation via a multiple graph Laplacian constraint.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please address the previous issues:\n1. explain the notion of partition and consensus (perhaps adding a visual support) in plain English before using any formal notation \n2. justify intuitively the reasoning on why these changes (partition and Laplace smoothing) should in principle help here and how these ideas could be useful in related problems (explain which are the characteristics that these problems should have to benefit from your approach) \n3. provide a) an ablation study, b)  critical differences diagrams, c) efficiency comparisons,  d) artificial problem", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "4zu1XvZh1b", "reviewer": "Reviewer_8TLU", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. This paper focuses on an important problem.\n2. The method is computationally efficient.\n3. This paper achieves good performance on the given benchmarks.\n\nWeakness:\n1. This work seems combine the previous method such as Kronecker regularized least squares (Kron-RLS) and Multi-view graph regularized link propagation model (MvGRLP), etc. Based on the results, they are incremental improvements on the previous method. \n2. The presentation and citation should be improved.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a new multi-view learning method called MKronRLSF-LP for predicting drug-side effects, which is an important problem in pharmacovigilance. The method extends the Kronecker regularized least squares (Kron-RLS) framework by learning a consensus partition from multiple views. It also incorporates multiple graph Laplacian regularization to enhance the performance. An efficient optimization algorithm is developed to fuse the multiple Kron-RLS submodels and make predictions without explicitly computing large pairwise matrices. Experiments on datasets demonstrate the good performance of MKronRLSF-LP compared to various baseline methods and state-of-the-art approaches.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. This paper should carefully discuss the compare the results with the previous graph neural network based method.\n\n2. The authors should improve the overall presentation of the paper. This includes ensuring proper citation formatting throughout the manuscript, improving the grammar and sentence structures.\n\n3. The discussion of experiments are also weak. The authors should provide more understandings and ablation studies of proposed methods.", "broader_impact_concerns": "I didn't see any potential concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: All reviewers were supportive of accepting the paper. The Authors improved the work significantly during the rebuttal phase, in particular by adding several clarifications and the ablation study. The emphasized strengths of the paper included novelty of the model and the comprehensive evaluation.
Decision: Accept (poster)