1 Graph Regularized Probabilistic Matrix Factorization for Drug-Drug Interactions Prediction

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Graph Regularized Probabilistic Matrix

Factorization for Drug-Drug Interactions Prediction

Stuti Jain, Emilie Chouzenoux, Senior Member, IEEE, Kriti Kumar, Member, IEEE

and Angshul Majumdar, Senior Member, IEEE

Abstract—Co-administration of two or more drugs simultane-

ously can result in adverse drug reactions. Identifying drug-drug

interactions (DDIs) is necessary, especially for drug development

and for repurposing old drugs. DDI prediction can be viewed

as a matrix completion task, for which matrix factorization

(MF) appears as a suitable solution. This paper presents a novel

Graph Regularized Probabilistic Matrix Factorization (GRPMF)

method, which incorporates expert knowledge through a novel

graph-based regularization strategy within an MF framework.

An efﬁcient and sounded optimization algorithm is proposed to

solve the resulting non-convex problem in an alternating fashion.

The performance of the proposed method is evaluated through

the DrugBank dataset, and comparisons are provided against

state-of-the-art techniques. The results demonstrate the superior

performance of GRPMF when compared to its counterparts.

Index Terms—Matrix factorization, Probabilistic matrix fac-

torization, Graph regularization, Drug-drug interaction predic-

tion

I. INTRODUCTION

Drug-Drug Interaction (DDI) refers to the effects of a given

drug when taken together with another drug, at the same

time. Co-administration of two or more drugs simultaneously

can affect the pharmokinetics and/or pharmacodynamics of

one or more drugs, which can cause unexpected and even

adverse drug reactions [1]. These effects can cause severe

injuries to the patients and even be responsible for deaths.

Thus, it is necessary to know the DDI for the drugs used

in the market, for clinical safety. Knowledge of DDI is also

vital for developing new drugs, as well as for repurposing

old drugs from clinical and public health perspectives. Pre-

clinical identiﬁcation of DDIs is an ill-posed problem as

clinical testing (e.g., in vitro, in vivo, and in populo) is

usually conducted on a small group of drugs. Such a process

is time and cost intensive. Thus, DDI prediction employing

computational approaches that are implementable on a large

scale has become a popular research topic in recent years [2].

Computational approaches for DDI prediction can be

broadly divided into two categories: (i) Similarity-based ap-

proaches, that are based on the similarity of drug infor-

mation (e.g., chemical structure [3], targets [4], side-effects

[5], and (ii) knowledge-based approaches, that employ text

S. Jain and E. Chouzenoux are with CVN, Inria Saclay, Univ. Paris Saclay,

91190 Gif-sur-Yvette, France. e-mail: (emilie.chouzenoux@centralesupelec.fr,

stuti.jain@inria.fr).

A. Majumdar and K. Kumar is with Dept. of ECE, IIIT - Delhi, India,

110020. e-mail: (angshul@iiitd.ac.in, kritik@iiitd.ac.in).

This work received support from the Associate Team COMPASS between

Inria and IIIT Delhi. E.C. and S.J. acknowledge support from the European

Research Council Starting Grant MAJORIS ERC-2019-STG-850925.

mining from scientiﬁc literature [6], electronic medical record

database [7] and the FDA Adverse Event Reporting System [8]

to predict DDI. Note that the latter group of approaches do not

perform learning per se, as it is mostly a tool to mine clinical

ﬁndings. Although different machine learning and artiﬁcial

intelligence models have been used to address the problem [9],

DDI prediction remains a challenging problem to address.

In this work, the DDI prediction task is formulated as

a matrix completion problem, involving a symmetric matrix

with rows/columns corresponding to drugs. We adopt a matrix

factorization paradigm, when the sought matrix is deﬁned

as the product of two latent factors satisfying some prior

knowledge. Our contribution lies in the construction of an

original prior well suited to DDI prediction. It incorporates

expert knowledge on the DDIs within a graph-based regular-

ization term similar to [10], with the aim to favor expected

(dis)similarities between drug pairs. This formulation results

in the so-called Graph Regularized Probabilistic Matrix Fac-

torization (GRPMF) method, for which we also propose a

sounded optimization algorithm relying on modern proximal

methods. We evaluate the performance of our method on the

DrugBank dataset, and present comparisons against state-of-

the-art techniques.

The paper is organized as follows. Section II discusses

related works on DDI prediction. Section III provides a brief

overview of various MF-based methods. Section IV presents

our main contribution, that is the proposed GRPMF formula-

tion and the optimization algorithm to resolve it. Section V

presents our experimental results and comparisons with the

state-of-the-art methods, and ﬁnally, Section VI concludes the

work.

II. RELATED WORKS

Clinical trials are time and money consuming. Many DDIs

thus remain unknown, mostly because not tested during trials.

Machine learning-based methods have been widely inves-

tigated to predict the unobserved DDIs. A heterogeneous

network-assisted inference (HNAI) method is proposed in

[11], gathering ﬁve prediction models (naive Bayes, decision

tree, k-nearest neighbor, logistic regression, and support vector

machine) to perform DDIs prediction from drug phenotypic,

therapeutic, structural, and genomic similarities. The work

in [12] presents a neural network (NN) based method that

proposes a heuristic selection of several drug similarity scores

integrated with a nonlinear similarity fusion strategy to obtain

abstract features for DDI prediction. Another work [13] pro-

poses a semi-supervised learning method for DDI prediction,

arXiv:2210.10784v1 [q-bio.QM] 19 Oct 2022

that uses drug chemical, biological, and phenotype data to

calculate the feature similarity of drugs using a regularized

least square score minimization.

Some works address the DDI prediction problem as an

edge detection (i.e., link prediction) problem where the edges

to infer represent connections between drugs. The work in

[14] presents both unsupervised and supervised techniques

for link prediction using binary classiﬁers such as tree, k-

nearest neighbors, support vector machine, random forest,

and gradient boosting machine based on topological and

semantic similarity features to estimate the drug interactions.

Another work [15] proposes two methods based on NNs and

factor propagation over graph nodes, namely, adjacency matrix

factorization (AMF) and adjacency matrix factorization with

propagation (AMFP) for link prediction for discovering DDIs.

The superior performance of deep learning (DL) techniques

across different domains has triggered the interest in such

techniques to estimate drug interactions. The work in [16]

presents a biomedical resource LSTM (BR-LSTM) that com-

bines biomedical resources with lexical information and entity

position information together to extract DDI from the biomed-

ical literature. Note that this model is not DDI prediction

per se, but only an automatic tool for mining of information

from clinical literature. The work in [17] proposes a convo-

lutional mixture density recurrent NN model that integrates

convolutional neural networks, recurrent NNs, and mixture

density networks for DDI prediction. An autoencoder-based

semi-supervised learning algorithm for feature extraction from

FDA adverse event reports to identify potential high priority

DDIs for medication alerts is presented in [18]. Another work

[19] employs autoencoders and a deep feed-forward network

trained on structural similarity proﬁles (SSP), Gene Ontology

(GO) term similarity proﬁles (GSP), and target gene similarity

proﬁles (TSP) of known drug pairs to predict the effects of

DDIs. Due to the black-box nature of the DL models, some

work has been done on seeking for explainable DL-based DDI

techniques. A comprehensive review of the explainable AI-

based techniques to promote the trust of AI models for the

critical task of DDI prediction is presented in [20].

Recently, some works have utilized Matrix Comple-

tion/Factorization (MC/MF) techniques to predict DDIs. Here,

given the partially observed DDI matrix, the task is to compute

the unobserved interactions between the drugs. Some of the

popular generic (not tailored for DDI) MF techniques are (i)

singular value decomposition (SVD) [21], (ii) non-negative

matrix factorization (NMF) [22] and, (iii) probabilistic matrix

factorization (PMF) [23]. We will present the two later ap-

proaches in detail in our next section, as MC/MF constitutes

the core of our contribution.

In addition to the conventional binary DDI prediction,

the work in [24] presents an NMF-based approach utilizing

drug features for comprehensive DDI prediction. Here, the

comprehensive DDI matrix is a signed binary matrix with

+1 for enhancive drugs, −1for degressive drugs, and 0

for no drug interactions, respectively, which is rather useful

to predict the (positive/negative) behaviors of the interacting

drugs. The work in [25] presents an attribute supervised

learning model probabilistic dependent matrix tri-factorization

(PDMTF) approach for adverse DDI prediction. They utilized

two drug attributes, molecular structure, side effects, and

their correlation to compute the adverse interactions among

drugs. The work in [26] introduces a manifold regularized MF

(MRMF) technique to predict DDIs using drug similarities

based on drug features like substructures, targets, enzymes,

transporters, pathways, indications, side effects, and off side

effects.

The publicly available large structured biomedical databases

has enabled the use of knowledge graph (KG) based ap-

proaches for different applications in the biomedical domain.

KGs are used to synthesize large biomedical graphs that map

similar drug-related entities in the drug database. The work

in [27] uses KGs embeddings, namely, RDF2Vec, TransE,

TransD, and machine learning algorithms for DDI prediction.

A KG NN method (KGNN) that captures the drug and its

potential neighborhoods by mining their associated relations

in KG for DDI prediction is proposed in [28]. This method

utilizes the drugs’ topological structures in KG for potential

DDI prediction. Another work [29] utilizes KGs combined

with DL techniques for estimating DDIs. This work considers

the DDI matrix and KG in the form of learned embed-

dings (like ComplEx, TransE, RDF2Vec, etc.) as input to the

Convolutional Neural Networks (CNN) and Long-Short Term

Memory (LSTM) model to predict DDIs.

In this work, we focus on the MC/MF based framework, as

it presents the advantage of being non supervised and highly

interpretable. Our contribution is to incorporate expert knowl-

edge within this family of approach, so as to take advantage

of the aforementioned progressed in database availability.

III. BACKGROUND

This section presents an overview of MF techniques for

MC. We choose here to remain in a generic setting where the

matrix to complete is real-valued and rectangular. Note that,

for the DDI task, the sought matrix is square symmetric and,

in most cases, binary valued, which might lead to simpliﬁed

formulations.

A. Matrix Completion Problem

Let us consider the problem of a full matrix R∈RN×M

to recover from partially known matrix Y∈RN×M. Let

D={i∈ {1, . . . , N}, j ∈ {1, . . . , M}s.t. (i, j)is observed}.

Non observed entries are typically set to zero. The masking of

the indexes outside the set Dis modeled through a Hadamard

product with a matrix B∈ {0,1}N×M, such that Bij = 1

if (i, j)∈ D, and Bij = 0 otherwise. The partially known

matrix Ycan be expressed as:

Y=BR. (1)

The task of matrix completion amounts to recovering the

entries of Rthat do not belong to the set of observed

indexes D.

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1GraphRegularizedProbabilisticMatrixFactorizationforDrug-DrugInteractionsPredictionStutiJain,EmilieChouzenoux,SeniorMember,IEEE,KritiKumar,Member,IEEEandAngshulMajumdar,SeniorMember,IEEEAbstractCo-administrationoftwoormoredrugssimultane-ouslycanresultinadversedrugreactions.Identifyingdrug-druginter...

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1 Graph Regularized Probabilistic Matrix Factorization for Drug-Drug Interactions Prediction

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