Predicting drug-target interactions via sparse learning
Ratha Pech1 , Hao Dong1,2∗ , Maryna Po3 , Zhou Tao1,2∗

arXiv:1706.01876v1 [cs.LG] 6 Jun 2017

1

CompleX Lab, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
2
Big Data Research Center, University of Electronic Science and Technology of China,
Chengdu 611731, People’s Republic of China and
3
Department of Chemistry and Biochemistry, George Manson University, Virginia 22030, U.S.A
Drug-target interaction (DTI) prediction plays a very important role in drug development. Biochemical experiments or in vitro methods to identify such interactions are very expensive, laborious
and time-consuming. Therefore, in silico approaches including docking simulation and machine
learning have been proposed to solve this problem. In particular, machine learning approaches have
attracted increasing attentions recently. However, in addition to the known drug-target interactions, most of the machine learning methods require extra information such as chemical structures,
genome sequences, binding types and so on. Whenever such information is not available, they may
perform poor. Very recently, the similarity-based link prediction methods were extended to bipartite
networks, which can be applied to solve the DTI prediction problem by using topological information only. In this work, we propose a sparse learning method to solve the DTI prediction problem,
which does not require extra information and performs much better than similarity-based methods.
We compare the proposed method with similarity-based methods including common neighbor index,
Katz index and Jaccard index on the DTI prediction problem over the four renowned and benchmark
datasets. The proposed method performs remarkably better. The results suggest that although the
proposed method utilizes only the known drug-target interactions, it performs very satisfactorily.
The method is very suitable to predict the potential uses of the existing drugs, especially, when
extra information about the drugs and targets is not available.
Keywords: drug-target interaction, drug discovery, link prediction, low-rank matrix, sparse matrix, similarity
index

BACKGROUND

Developing a new drug to the market is very costly and
takes too much time [1, 2]. Therefore, in order to save
time and cost, scientists have tried to identify new uses of
existing drugs, known as drug repositioning. Moreover,
predicting these interactions between drugs and targets
is one of the most active domains in drug research since
they can help in the drug discovery [3, 4], drug side-effect
[5, 6] and drug repositioning [7–10]. Currently, the known
interactions between drugs and target proteins are very
limited [11, 12], while it is believed that any single drug
can interact with multiple targets [13–15]. However, laboratory experiments of biochemical verification on drugtarget interactions is extremely expensive, laborious and
time-consuming [16–18] since there are too many possible interactions to check. From the current capability of
large-scale chemical and protein data collecting, storing
and processing, in silico prediction of the interactions
between drugs and target proteins is an effective and efficient tool for discovering the new uses of existing drugs.
The prediction results provide helpful evidences to select potentially novel drug-target interaction candidates
for further biochemical verification, which can reduce the
costs and risks of failed drug development [19].
There are two major approaches in in silico prediction,
including docking simulation and machine learning [20].
Docking simulation is the common method in biology,
but it has two major limitations. Firstly, this method requires three-dimensional structures of targets to compute
the binding of each drug candidate [21–23], but such kind
of information is usually not available [24, 25]. Secondly,

it is very time-consuming. Therefore, in the last decade,
many efforts have been made to solve the DTI prediction problem by machine learning approaches [20, 26, 27].
Most known machine learning methods [28–30] treat DTI
prediction as a binary classification prediction in which
the drug-target interactions are regarded as instances and
the characteristics of the drugs and target proteins are
considered as features. To train the classifier, machine
learning methods require label data, e.g., positive samples of truly existing interactions and negative samples
of noninteractive pairs. Normally, the positive samples
are available, but the negative samples are not known.
Although similarity-based methods are simple, sometimes they do not perform well since common neighbor
and Jaccard indices utilize only local information of the
networks [32]. Katz index also performs unsatisfactorily
(will show later) since the large decay factor will bring
redundant information [34], while the small decay factor
makes Katz index close to common neighbor index or
local path index [35, 36].
To overcome the limitations of machine learning methods and similarity-based methods, we propose a matrixbased method, namely sparse learning method (SLM).
On one hand, SLM does not require extra information
about the characteristics of drugs and target proteins or
negative samples. On the other hand, SLM performs
much better than similarity-based methods on the four
renown datasets. The proposed method can help selecting the most likely existing interactions for further
chemical verifications, especially when the prior knowledge about the characteristics of drugs and targets is not
available. In a word, SLM can reduce cost and failure in

2
drug development, and thus advance drug discoveries.

Firstly, we decompose A as follows,
A = AX + E.

METHODS
Datasets

In this work, we implement the proposed method
as well as similarity-based methods on four benchmark
and renown datasets namely MATADOR [33], enzyme
[26], ion channel [26] and G-protein-coupled receptors
(GPCR) [26]. The manually annotated target and drug
online resource (MATADOR) (May 2017) dataset is a
free online dataset of chemical and target protein interactions. There are 13 columns in the dataset, however,
we utilize only two columns, including Chemical ID and
Protein ID, to construct the adjacency matrix. Enzyme,
ion channel and GPCR (May 2017) are the drug-target
interaction networks for human beings. The statistics of
the four datasets are presented in Table I.
TABLE I: The statistics of the four datasets.
MATADOR enzyme ion channel GPCR
# drugs
# targets
# interactions
Sparsity of A

801
2901
15843
0.007

445
664
2926
0.010

210
204
1476
0.034

223
95
635
0.030

Sparse learning method

First of all, we construct the adjacency matrices of the
drug-target interactions in the four datasets. Mathematically, the adjacency matrix is define as
(
1, if drug i interacts with target j
Aij =
. (1)
0, otherwise
Then we obtain A ∈ Rm×n , where m is the number of
drugs and n is the number of target proteins.
The real data are normally far from perfect, meaning
that, a portion of the drug-target links in the real data
would be incorrect or redundant, and also some other
drug-target links would be missing from the real data.
Therefore, the adjacency matrix A can be decomposed
into two parts. The first part is a linear combination of
A, which is essentially a projection from the noisy data
A into a more refined and informative data. The second
part can be considered as the noise or the outliers, which
is strained off from the original data A and represented
by a sparse matrix with most entries being zeros. The
method seeks the lowest-rank matrix among all the candidates which is further utilized to construct the score
matrix that estimates the likelihoods of the potential interactions.

(2)

Obviously, there are infinite many solutions of Eq. (2).
However, since we wish X to be of low rank, where rank
of a matrix is the maximum number of linearly independent column (or row) vectors in the matrix, and E to be
sparse, we can enforce the nuclear norm or trace norm
on X and sparse norm on E. Mathematically, Eq. (2)
can be thus relaxed as
min ||X||∗ + α||E||2,1
X,E

s.t. A = AX + E,

(3)

P
where ||A||∗ = pi σi (i.e., σi is the singular values of A),
Pn
Pn
2
||E||2,1 = j=1
i=1 (Eij ) is the noise regularization
strategy and α is a positive free parameter taking a role
to balance the weights of low-rank matrix and sparse matrix. Minimizing the trace norm of a matrix well favors
the lower-rank matrix, meanwhile the sparse norm is capable of identifying noise and outliers.
Eq. (3) can also be regarded as a generalization of the
robust PCA [37, 38] because if the matrix A in AX in
the right side of Eq. (3) is set as identity matrix, then
the model is degenerated to the robust PCA. Eq. (3) can
be rewritten into an equivalent problem as,
min ||J||∗ + α||E||2,1

X,E,J

s.t. A = AX + E, X = J. (4)

Eq. (4) is the constraint and convex optimization problem which can be solved by many off-the-self methods,
e.g., iterative method (IT) [39], accelerated proximal gradient (APG) [40], dual approach [41], and augmented Lagrange multiplier (ALM) [42]. In this work, we employ
Inexact ALM method by firstly converting Eq. (4) to
an unconstraint problem, then minimize this problem by
utilizing augmented Lagrange function such that

L = ||J||∗ + α||E||2,1 + tr Y1T (A − AX − E) +
 µ

tr Y2T (X − J) +
||A − AX − E||2F + ||X − J||2F ,
2
(5)
where µ ≥ 0 is a penalty parameter. The Eq. (5) is unconstraint and can be solved by minimizing with respect
to J, X and E, respectively, by fixing the other variables
and then updating the Lagrange multipliers Y1 , Y2 . The
detailed explanation of how to solve Eq. (5) is shown in
Table II.
We denote the solution of Eq. (5) as X∗ and E∗ . If
Aij represents the interaction drug i and protein j, then
X∗ ∈ Rn×n can be considered as a similarity matrix that
describes similarities proteins. While if Aij represents
the interactions between protein i and drug j (as the
transposition of the adjacency matrix in Eq. (2)), then
X∗ ∈ Rm×m describes similarity between drugs. After
obtaining X∗ , the solution of Eq. (5), we can compute
the score of interactions between each pairs of chemicals
and proteins by projecting the adjacency matrix onto the
lower-dimensional space as
S = AX∗ .

(6)

3
Known interactions
Drug

Decomposition

Predicted interactions

Low-rank matrix X*

Target

Drug

Target

1

1

2

2

3

3

4

m×n

5

4

..
.

m

..
.

Score matrix S=AX*

Adjecacency matrix A∈

Sparse matrix E*

6

..
.

n

..
.

FIG. 1: The illustration of the proposed method. Firstly, the known drug-target interactions are utilized to construct the
adjacency matrix A. Secondly, A is decomposed into a low-rank matrix X∗ and a sparse matrix E∗ , which can be used to
depict the hidden pattern and the noise in the original data. Finally, the score matrix is computed by projecting the adjacency
matrix onto a lower-dimensional space via the low-rank matrix X∗ .

TABLE II: The illustration of the Inexact ALM algorithm

TABLE III: The illustration of the SLM algorithm

Algorithm 1: Solving problem (5) by Inexact ALM

Algorithm 2: The algorithm of the proposed method

Input: Given a dataset A parameters α, β
Output: X∗ and E∗

Input: Given an adjacency matrix A
1. compute the low-rank coefficient or weighting
matrix X∗ and sparse noise E of Eq. (5) by using
algorithm 1 as shown in table II
2. compute the similarity matrix S by Eq. (6)
3. set the entries of S corresponding to nonzero entries
of A to zero, i.e., ignore the known interactions
4. sort the remaining scores in S in descending order
Output: The highest scores are the most likely potential
interactions

Initialize: X = 0, E = 0, Y1 = 0, Y1 = 0, µ = 10−4 ,
maxµ = 1010 , ρ = 1.1,  = 10−8
while not converged do
1. fix the other and update J by
J = arg min µ1 ||J||∗ + 12 ||J − (X + Y2 /µ)||2F
2. fix the other and update X by
X = (I + AT A)−1

AT A − AT E + J + (AT Y1 − Y2 )/µ
3. fix the other and update E by
E = arg min µλ ||E||2,1 + 12 ||E − (A − AX + Y1 /µ)||2F
4. update the multiplier
Y1 = Y1 + µ(A − AX − E)
Y2 = Y2 + µ(X − J)
5. update parameter µ by
µ = min(ρµ, maxµ )
6. check the convergence condition
||A − AX − E||∞ <  and ||X − J||∞ < 
end while

After obtaining S, we remove the known interactions by
setting the entries of S corresponding to nonzero entries
in A to zeros and sort the remaining scores in descending
order. The drugs-target pairs with highest scores are the
most likely unknown interacting pairs. The full process
of the proposed method is illustrated in Fig. 1. Table III
illustrates the detailed procedure of the proposed SLM
algorithm.

Evaluation

We adopt a cross validation technique and two popular metrics to test the proposed method as well as previous benchmarks. We apply the 10-fold cross validation [20, 31], which divides the total known interactions
between the chemicals and proteins into 10 sets with approximately the same size, and then utilize 9 sets as training data and keep the remaining set as testing data. We
repeat it for ten times where each set has one chance to
be the testing set. In the simulation, we independently
run the 10-fold cross validation for five times and report
average values accordingly.
We consider the two popular metrics, including the
area under the receiver operating characteristic (ROC)
curve (AUC) and the area under precision and recall
curve (AUPR), to evaluate the performances of the proposed method and the benchmarks. ROC is the diagnostic ability of a binary classifier with regarding to different
thresholds [43], while AUC curve displays true positive
rate (sensitivity) versus false positive rate (1-specificity)
at different values of thresholds. The sensitivity is the
percentage of the test samples with ranks higher than a

4

Precision

MATADOR

Enzyme

1

1

0.8

0.8

0.6

0.6
CN

CN

0.4

0.4

Katz
Jaccard

0.2

Katz
Jaccard

0.2

SLM

SLM
0

0

0.2

0.4

0.6

0.8

1

0

0

0.2

0.4

Ion Channel

0.6

0.8

1

GPCR

1

1

0.8

0.8

0.6

0.6

Precision

CN
Katz
Jaccard
SLM

CN
Katz

0.4

0.4

Jaccard
0.2
0

0.2

SLM
0

0.2

0.4

0.6

0.8

1

Recall

0

0

0.2

0.4

0.6

0.8

1

Recall

FIG. 2: The precision and recall curves of the four methods on the four datasets.

given threshold, whereas, specificity is the percentage the
test samples that fall below the threshold.

RESULTS

When there are many fewer positive elements in the
testing data comparing to the total number in testing
data, AUC may give overoptimistic results of the algorithms [27, 44–46]. Therefore, utilizing only AUC may
mislead our conclusion. In such case, AUPR can give
better evaluation, especially in biological significance.

We compare SLM with the similarity-based methods,
e.g., common neighbor index (CN), Katz index and Jaccard index since these methods also utilize only the
known information of drug-target interactions. We do
not compare the proposed method with the preferential
attachment (PA) index since it is reported in [31] that PA
produces the lowest performance among all the similarity
indices.
The PR curves of SLM and similarity-based methods
are illustrated in Fig. 2. Obviously, SLM performs much
better than the other three benchmarks for all the four
datasets. Table IV reports AUC, AUPR and precision
of the four datasets. We set K = N , so that precision
equals recall. As shown in Table IV, SLM remarkably
outperforms all similarity-based methods under consideration and among the three similarity indices, Jaccard
index is slightly better than common neighbor and Katz
index in term of AUPR and precision on MATADOR and
enzyme, meanwhile it performs approximately the same
as CN and Katz indices on ion channel and GPCR.
In the proposed method, there is a free parameter α
that balances the weights of low-rank matrix and sparse
matrix as shown in Eq. (3). When α is set too large, the
sparse norm will compress most of the entries of matrix
E to zeros, while if α is very small, most of the entries
of A will be small but not zeros. In this work, we obtain the optimal value of the parameter α by manually
and empirically tuning it from 0.01 to 0.5 and check the
accuracy according to each value of α. We plot the precision and recall curves corresponding to different values

The precision is defined as the ratio between the number of correctly predicted items over the number of selected items, while the recall is the fraction of correctly
predicted items over all the number of true positive items
in the testing data. Suppose that there are N (true postive) items in the testing data. We select K of drugtarget pairs and k of them are in the testing set (i.e., the
correctly predicted), then the precision and recall are defined as,

P recision =

k
,
K

(7)

and

Recall =

k
,
N

(8)

respectively. In the simulation, we tune K from 1 to
10000 to draw the precision-recall curve. Note that PR
curve shows that the best method is the one that produces the curve closest to top-right corner.

5
TABLE IV: The AUC, AUPR and precision (Pre) by 5×10-fold cross validation for SLM and the three similarity-based
methods. The best performed results are emphasized in bold.
Dataset

MATADOR

CN
Katz
Jaccard
SLM

enzyme

AUPR Pre

AUC

AUPR Pre

AUC

AUPR Pre

AUC

AUPR Pre

0.930
0.903
0.933
0.943

0.369
0.342
0.377
0.657

0.892
0.872
0.893
0.898

0.475
0.472
0.540
0.603

0.911
0.889
0.916
0.935

0.506
0.500
0.469
0.659

0.821
0.800
0.829
0.846

0.228
0.224
0.235
0.387

0.380
0.344
0.396
0.650

0.8
α=0.01
α=0.05

Precision

α=0.10
α=0.15
α=0.20
α=0.25

0.5
0.4

α=0.30
α=0.35
α=0.40

0.3
0.2

α=0.45
α=0.50

0.1
0

0

0.1

0.2

0.493
0.492
0.566
0.655

0.472
0.468
0.450
0.639

0.258
0.256
0.302
0.407

effective method to estimate the optimal value of this parameter is still an open question. However, SLM is very
efficient. For example, SLM takes only about 6.6 minutes running with MATLAB on MATADOR dataset on
normal Intel(R) Core (TM) i5-2520M PC with 12 GB of
RAM.

0.9

0.6

GPCR

AUC

1

0.7

ion channel

0.3

0.4
Recall

0.5

0.6

0.7

0.8

FIG. 3: The precision and recall curves of SLM corresponding
to different values of α on MATADOR dataset.

of α on MATADOR dataset in Fig. 3. From the figure,
we can see that the proposed method performs well on
α = 0.1 and α = 0.15. In our simulations, we set α = 0.1
for MATADOR and α = 0.15 for enzyme, ion channel
and GPCR.

Similar to similarity-based methods, SLM has a drawback such that for a new drug that has no known interaction with any targets at all, SLM cannot predict the
potential interactions of that new drug. In order to predict the interactions of the new drugs, extra information
is required. Of course, SLM can be extended to take into
account the extra information and this problem is left to
the future work.

∗

[1]

[2]

CONCLUSION AND DISCUSSION
[3]

In this work, we have proposed a matrix-based method,
namely sparse learning method (SLM), to solve the
DTI prediction problem. It has been shown that SLM
overcomes the drawbacks of the machine learning and
similarity-based methods. On one hand, SLM does not
require additional information about the properties of
the drugs and targets or negative samples. On the other
hand, SLM performs much better than similarity-based
methods. In SLM, the low-rank matrix plays a very important role to make the data homogenous, meanwhile
the sparse matrix captures the noise or outliers in the
data. By decomposing the original data into a clean (a
linear combination of low-rank matrix and the adjacency
matrix) and noise (sparse matrix) parts, we can obtain
a clean data to predict the interactions between drugs
and target proteins. The disadvantage of SLM is that we
need to empirically tune α and check the accuracy corresponding to each value of α. Until now, designing the

[4]

[5]

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[7]

[8]

[9]
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Electronic
address:
haodong@uestc.edu.cn;
zhutou@ustc.edu
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