https://doi.org/10.31449/inf.v45i1.3431 Informatica 45 (2021) 163 –168 163 
 
Prediction and Estimation of Book Borrowing in the Library: Machine 
Learning 
Jinbao Sun 
Graphic Center, Henan Mechanical and Electrical Vocation College, Zhengzhou, Henan 451191, China 
E-mail: baojian134597@yeah.net 
Keywords: data mining, library, book borrowing, radial basis function neural network, prediction 
Received: February 3, 2021 
In the library, the prediction and estimation of book borrowing plays an important role in library work. 
Based on the data mining method, this paper analyzed the prediction and estimation of book borrowing. 
Firstly, the radial basis function neural network (RBFNN) was analyzed. Then, the improved ant colony 
algorithm (IACO) was used to obtain the optimal parameters of RBFNN, and then the IACO-RBFNN 
model was established to realize the prediction and estimation of book borrowing. The results showed 
that the improved model had advantages in training time, iteration times, and error compared with BPNN 
and RBFNN. The results of book prediction and estimation showed that the results obtained by the IACO-
RBFNN model were closer to the actual book borrowing situation, with smaller error and higher precision 
(97.09%), and its precision was 11.18% and 4.74% higher than BPNN and RBFNN respectively. The 
training time and testing time of the IACO-RBFNN model were 5.12 s and 1.03 s, respectively, which were 
significantly shorter than the other two methods. The results show that the IACO-RBFNN model has a 
good performance in the prediction and estimation of book borrowing and can be further promoted and 
applied in practice. 
Povzetek: Opisana je metoda strojnega učenja za napovedovanje izposoje knjig v knjižnici. 
 
1 Introduction 
The library is an important facility in a school. It can meet 
the needs of teachers and students in teaching and 
scientific research by collecting and sorting books. With 
the expansion of the school scale, the amount of books 
borrowed in the library is also growing. In the 
management of the library, the borrowing amount can 
reflect the work quality of the library to a certain extent 
and has a reference value for the purchase of new book 
resources. Therefore, it is of great significance to predict, 
estimate, and analyze the borrowing amount [1]. Data 
mining refers to the process of finding hidden and useful 
information from massive data, which has been widely 
used in data prediction and estimation [2]. Shan et al. [3] 
studied the on-line prediction of tool wear, designed a 
method based on least squares support vector machine 
regression, and found through experiments that the 
method had better accuracy than a neural network. Qazi et 
al. [4] analyzed the role of artificial neural networks in 
predicting solar radiation. Through the analysis of 24 
literature, they found that the prediction error of the 
artificial neural network was smaller than 20% and it 
could process a variety of input meteorological 
parameters. Zhang et al. [5] combined the long short-term 
memory method with the recurrent neural network to 
predict the remaining life of lithium-ion batteries. 
Through experiments and comparison, they found that the 
method could predict the remaining life of the lithium-ion 
batteries effectively. Manek et al. [6] used the back 
propagation neural network (BPNN), generalized 
regression neural network (GRNN), and radial basis 
function neural network (RBFNN) to predict the rainfall 
in Thanjavur district of southern province Tamil Nadu, 
India, and found that the RBFNN could get the best 
prediction results. Ramos et al. [7] predicted delayed 
cerebral ischemia (DCI) in patients with aneurysmal 
subarachnoid hemorrhage, combined logistic regression 
model, machine learning model, and automatic encoder, 
trained and tested the model with 317 cases of data, and 
found that the method could effectively improve the 
prediction of DCI in patients. Souri et al. [8] studied the 
fault prediction of the Internet of things and proposed a 
model combining multi-layer perceptron and particle 
swarm optimization algorithm. The experiment showed 
that the method had short operation time and small 
memory consumption. Aiming at the problem of urban 
traffic flow prediction, Hu et al. [9] established GSTAR-
SVM model with wavelet transform and predicted the 
short-term traffic flow. Through experiments, they found 
that the model had high prediction accuracy. Iqbal et al. 
[10] evaluated the performance of seven machine learning 
methods in predicting dengue outbreak and found through 
an experiment that the LogitBoost integration model had 
the highest classification accuracy (92%), a sensitivity of 
90%, and a specificity of 94%. At present, the application 
of methods such as data mining and machine learning in 
library management is seldom, and artificial method is 
highly dependent, which is not conducive to the scientific 
management of a large number of books. Therefore, based 
on RBFNN, this study applied RBFNN to the prediction 
and estimation of book borrowing and optimized it with 

164 Informatica 45 (2021) 163 –168 J. Sun 
 
the ant colony optimization (ACO) algorithm to improve 
the accuracy of prediction and estimation. This work aims 
to guide book purchase and management of libraries. 
2 Book borrowing prediction and 
estimation model 
2.1 RBF neural network 
The problem of book borrowing prediction and estimation 
is affected by many factors and has nonlinear 
characteristics. However, the models used in this problem, 
such as the regression analysis model [11] and grey model 
[12], are all linear estimation models, which has poor 
estimation accuracy. A neural network is a kind of data 
mining, which is a simulation of a biological neural 
network. A neural network is a kind of nonlinear 
estimation model with excellent nonlinear approximation 
ability [13]. BPNN [14] and RBFNN [15] have been 
widely used in prediction and estimation. Compared with 
BPNN, RBFNN has more advantages in operation speed 
and structure and has been successfully applied in fields 
such as human face recognition [16] and defect detection 
[17]. Therefore, this study used RBFNN to establish the 
prediction and estimation model of book borrowing. 
RBFNN is a three-layer forward network. It is 
assumed that the input layer of RBFNN has 
n
 nodes, 
) ,..., , ( = 2 1 n x x x X
, its output layer has 
m
 nodes, 
) ,..., , ( = 2 1 m y y y Y
, its hidden layer has 
h
 nodes, then the 
output of RBFNN can be written as: 
𝑦 𝑖 = 𝑓 𝑖 ( 𝑥 𝑖 ) = ∑ 𝑤 𝑖𝑘
𝜙 𝑘 ( ‖ 𝑥 − 𝑐 𝑘 ‖
2
)
𝑁 𝑘 = 1
, 𝑖 = 1 , 2 , ⋯ , 𝑚 ,  
where 
ik w
 refers to the weight between the hidden layer 
and output layer, 
k

 is the activation function, and 
k c
is 
to the center vector of the basis function. In RBFNN, the 
most commonly used activation function is Gaussian 
function. Compared with other functions, the Gaussian 
function is simpler and radial symmetric and has better 
smoothness. The formula of the Gaussian function is: 
𝜙 ( 𝑥 ) = 𝑒𝑥𝑝 ( −
𝑥 2
2 𝜎 2
),  
where 
2
σ is a  variance. In this case, the output of 
RBFNN can be written as: 
𝑦 𝑖 = 𝑓 𝑖 ( 𝑥 𝑖 ) = ∑ 𝑤 𝑖𝑘
𝑒𝑥𝑝 [ − (
‖ 𝑥 − 𝑐 𝑘 ‖
2
2
2 𝜎 2
) ]
𝑁 𝑘 = 1
, 𝑖 =
1 , 2 , ⋯ , 𝑚 .  
To sum up, it can be found that parameters 
ik w
, 
k c
, 
and σ have a great influence on the performance of 
RBFNN, which is also the key and difficult point to 
establish the RBFNN model. In order to find the optimal 
parameters, this study selected the ACO algorithm. 
2.2 Ant colony algorithm 
ACO algorithm is a heuristic algorithm based on 
simulated ant colony behaviors [18]. In the process of 
ants ’ foraging, pheromones will be released. In the process 
of searching for paths, ants will find the path with high 
pheromone concentration and release pheromone at the 
same time, which will make the pheromone concentration 
on the path higher and higher, and all ants will gather on 
one path finally. For ant 
k
, the probability of ant 
k
 from 
city 
i
 to city 
j
 at time 
t
 can be written as: 
𝜌 𝑖 𝑗 𝑘 ( 𝑡 ) = {
𝛿 𝑖𝑗
𝛼 ( 𝑡 ) 𝜂 𝑖𝑗
𝛽 ∑ 𝛿 𝑖𝑗
𝛼 ( 𝑡 ) 𝜂 𝑖𝑗
𝛽 𝑗 ∈ 𝑁 𝑗 𝑘 , 𝑗 ∈ 𝑎𝑙 𝑙𝑜 𝑤 𝑒 𝑑 𝑘 0 , 𝑜𝑡 ℎ 𝑒𝑟 𝑤 𝑖 𝑠 𝑒 .  
The update process of pheromone can be written as: 
𝛿 𝑖𝑗
( 𝑡 + 𝑛 ) = 𝑝 𝛿 𝑖𝑗
( 𝑡 ) + ∑ 𝛥 𝛿 𝑖𝑗
𝑘 𝑚 𝑘 = 1
, 
𝛥 𝛿 𝑖𝑗
𝑘 = {
𝐿 𝑘 − 1
, 𝑗 ∈ 𝑎𝑙 𝑙𝑜 𝑤 𝑒𝑑 0 , 𝑜𝑡 ℎ 𝑒𝑟 𝑤 𝑖 𝑠 𝑒 . 
In the above formula, the parameters involved and 
their meanings are shown in Table 1. 
In the ACO algorithm, the value of volatilization 
factor p is between 0 and 1. When the value of 
p
 is too 
large, it may affect the global search ability of the 
algorithm. Therefore, this study used an adaptive method 
to improve the ACO algorithm. The initial value of p is 
set as 0.9, and then it changes followed the following 
formula: 
𝑝 𝑡 = {
0 . 9 𝑝 ( 𝑡 − 1 ) , 0 . 9 𝑝 ( 𝑡 − 1 ) ≥ 𝑝 𝑙 𝑜 𝑤 𝑝 𝑙 𝑜𝑤 , 𝑝 𝑙 𝑜 𝑤 ,  
where 
low p
is the minimum value of 
p
. 
2.3 Improved ACO-RBFNN model 
The parameters of RBF were optimized using the 
improved ACO (IACO) algorithm. It is assumed that there 
are 
m
 parameters including 
ik w
, 
k c
, and 
σ
, and they 
are randomly sorted, which is set as 
i R
, 
m] [1, ∈ i
. 
i R
Parameter Meaning 
ij
δ Pheromone concentration 
ij
η Heuristic factor 
α
 The importance of 
pheromone 
β The importance of 
heuristic factor 
k
j
N
 
A city without passing by 
k
allowed Feasible solution set 
p Pheromone volatilization 
factor 
k L 
The length of a path that 
ant k
 
passes 
Table 1: Parameter table. 

Prediction and Estimation of Book Borrowing in the Library... Informatica 45 (2021) 163 –168 165 
 
is taken as the food source, and the optimal parameters are 
searched according to the IACO algorithm. When all the 
ants concentrated on the same route, the parameters 
obtained at that moment were optimal for RBF. The flow 
chart of the IACO-RBFNN model designed for book 
borrowing prediction and estimation is shown in Figure 1. 
As shown in Figure 1, the optimal parameters of 
RBFNN are obtained using the IACO algorithm after the 
collected data are processed, those parameters are used for 
establishing the RBFNN model, and the model is trained 
by inputting training samples until the model iterates out 
the most accurate result. The obtained result is the 
prediction and estimation result of book borrowing. 
3 Experimental analysis 
3.1 Experimental data 
Taking the Graphic Center of Henan Mechanical and 
Electrical Vocation College as an example, the book 
borrowing data from January 2018 to June 2020 (24 
months) were collected through the library information 
system. During the training of the IACO-RBFNN model, 
the data from January 2018 to December 2019 was used 
as training samples, the number of books borrowed in one 
month as one sample. The data of the fourth month were 
predicted based on the data of the first three months, for 
example, estimating the data of April 2018 based on the 
data of January 2018 ~ March 2018, i.e., the number of 
books borrowed in January, February, and March 2018 
were taken as the input of the RBFNN model, and the 
number of books borrowed April 2018 was taken as the 
output of the RBFNN model. The training sample is 
shown in Figure 2. 
It was seen from Figure 2 that there is a law in the 
borrowing of books. In January, June, and December of 
each year, the number of books borrowed is relatively 
large, while the number in February and August is small. 
The above phenomenon may be related to the particularity 
of the school. In the months of the final examination, the 
borrowing demand for books is great, while the borrowing 
demand significantly decreases during the winter and 
summer vacation. 
In order to speed up the operation of the formula, it is 
necessary to standardize the collected data using the 
following formula: 
𝑥 ′ =
𝑥 − 𝑥 𝑚 𝑖 𝑛 𝑥 𝑚 𝑖 𝑛 𝑚 𝑎 𝑥 ,  
where
' x
refers to the normalized data, 
x
 is the 
original data, and
max x
and 
min x
 are the maximum and 
minimum values of the original data. 
3.2 Experimental results 
Firstly, a nonlinear function, 
( ) x f y =
, 
  1 , 1 −  x
, was 
used to verify the performance of the IACO-RBFNN 
model, and it was compared with the traditional BPNN 
and traditional RBFNN models. The target accuracy was 
0.01, and the maximum number of iterations was 500. The 
performance of the three methods is shown in Table 2. 
It was seen from Table 2 that the IACO-RBFNN 
model had obvious advantages in performance. Firstly, in 
terms of training time, the BPNN model took 36.78 s in 
training, the RBFNN model took 10.16 s, and the IACO-
RBFNN model only took 2.34 s, which was significantly 
shorter than the other two models; secondly, in terms of 
the number of iterations, the BPNN model needed 245 
times of iterations to get the optimal value, the RBFNN 
model needed 148 times, and the IACO-RBFNN model 
only needed 34 times; finally, from the perspective of 
error, BPNN model > RBFNN model > IACO-RBFNN 
model. In a comprehensive view, the model designed in 
this paper had the best performance. 
In the book borrowing prediction and estimation from 
January 2020 to June 2020, the results of the three models 
are shown in Figure 3. 
It was seen from Figure 3 that there was a gap between 
the estimated results of the BPNN and RBFNN models 
and the actual borrowing situation. The error of the 
 
Figure 1: The IACO-RBFNN model. 
 
Figure 2: Data of the training sample. 
  BPNN RBFN
N 
IACO-
RBFNN 
Training 
time/s 
36.78 10.16 2.34 
Number of 
iterations 
245 148 34 
Error 1.26 0.53 0.26 
Table 2: Comparison of model performance. 

166 Informatica 45 (2021) 163 –168 J. Sun 
 
RBFNN model was larger than the BPNN model, which 
indicated that the RBFNN model had a better 
performance. Compared with the RBFNN model, the 
estimated result of the IACO-RBFNN model was closer to 
the actual borrowing result, which showed that the 
RBFNN model had a significantly improved performance 
after improvement by the IACO algorithm, and it had 
better accuracy in the prediction and estimation of book 
borrowing. In order to further verify the effectiveness of 
the model designed in this study, the error and precision 
of the three models were calculated, and the results are 
shown in Table 3. 
It was seen from Table 3 that the error of the BPNN 
model was the largest, while that of the IACO-RBFNN 
model was the smallest. In the prediction and estimation, 
the average error of the BPNN, RBFNN, and IACO-
RBFNN models was 9404 books, 4967 books, and 1955 
books, respectively, and the average error of the IACO-
RBFNN model was 79.21% less than that of the BPNN 
model and 60.64% less than that of the RBFNN model. 
The average precision of the BPNN and RBFNN models 
was 85.91% and 92.35%, respectively, while the average 
precision of the IACO-RBFNN model was 97.09%, which 
was 11.18 higher than the BPNN model and 4.74% higher 
than the RBFNN model. Thus, it was concluded that the 
IACO-RBFNN model was the most effective in the 
prediction and estimation of book borrowing. 
Finally, the operation time of the model was 
compared, as shown in Figure 4. 
It was seen from Figure 4 that the operation time of 
the BPNN model was the longest, followed by the 
RBFNN and IACO-RBFNN models. The training time 
and testing time of the BPNN model were 21.34 s and 3.68 
s, respectively; the operation time of the RBFNN model 
significantly reduced. The training time of the IACO-
RBFNN model was 5.12 s, which improved 52.06% 
compared to the RBFNN model, and the testing time of 
the model was 1.03 s, which improved 58.13% compared 
to the RBFNN model. It was found that the algorithm 
improved by the IACO algorithm had improved precision 
and significantly shortened operation time and showed a 
better performance in the prediction and estimation of 
book borrowing. 
4 Discussion 
The development of information technology has brought 
new changes to many fields. Many industries have 
established information systems to realize information 
management, so does the library [19]. In the process of 
library informatization, a large amount of information has 
been accumulated, but most digital libraries cannot 
effectively develop and utilize these data and make the 
information accumulate, which brings great difficulties to 
the resource management and data processing of the 
library. In order to develop the library better, a method is 
urgently needed to realize the analysis and utilization of 
these data, and the emergence of data mining solves this 
problem [20]. 
This study mainly analyzed RBFNN. For the 
parameter selection of RBFNN, many algorithms have 
been applied, such as the gravity search algorithm [21], 
genetic algorithm [22], grey wolf optimization algorithm 
[23], etc. This paper selected the ACO algorithm, 
improved the ACO algorithm to optimize the parameters 
of RBFNN, carried out experiments with the actual book 
lending data, and compared the IACO-RBFNN model 
with the BPNN and RBFNN models. The results 
suggested that the IACO-RBFNN model needed fewer 
times of iterations, shorter training time, and smaller error 
compared to the BPNN and RBFNN models, indicating 
 
Figure 3: Book borrowing prediction results of three 
models. 
  BPNN model RBFNN 
model 
IACO-
RBFNN 
model 
Error Precisi
on 
Error Precisi
on 
Error Precisi
on 
January 
2020 
12175  
86.42
% 
7836  
91.26
% 
2457  
97.26
% 
Februar
y 2020 
962  
87.26
% 
577  
92.35
% 
139  
98.16
% 
March 
2020 
5553  
86.54
% 
3437  
91.67
% 
1452  
96.48
% 
April 
2020 
9702  
85.26
% 
4305  
93.46
% 
2646  
95.98
% 
May 
2020 
12516  
85.64
% 
6467  
92.58
% 
1874  
97.85
% 
June 
2020 
15518  
84.36
% 
7183  
92.76
% 
3165  
96.81
% 
Average 
value 
9404 
85.91
% 
4967 
92.35
% 
1955 
97.09
% 
Table 3: Comparison results of error and precision. 
 
Figure 4: Comparison of operation time. 

Prediction and Estimation of Book Borrowing in the Library... Informatica 45 (2021) 163 –168 167 
 
that the IACO-RBFNN model had more obvious 
advantages in performance. In the prediction and 
estimation of book borrowing, the prediction result of the 
RBFNN model was closer to the actual situation than that 
of the BPNN model, suggesting that the performance of 
the RBFNN model was better than that of RBFNN. Then, 
the comparison between the IACO-RBFNN model and the 
RBFNN model found that the prediction result of the 
IACO-RBFNN model was closer to the actual situation. It 
was seen from Table 3 that the IACO-RBFNN model had 
smaller prediction error and higher precision, and the 
average precision of the method was 97.09%, which was 
11.18% higher than that of the BPNN model and 4.74% 
higher than that of the RBFNN model. In the comparison 
of the operation time, the IACO-RBFNN model was 
significantly shorter, i.e., it could obtain results with high 
precision in a short time, which showed that the IACO-
RBFNN model had better usability in the prediction and 
estimation of book borrowing. 
Although some useful achievements have been made 
in this article, there are some deficiencies that need to be 
solved in future work: 
(1) comparing the performance of more data mining 
methods; 
(2) further optimizing the precision of the RBFNN 
model; 
(3) studying more applications of data mining methods in 
libraries. 
5 Conclusion 
This study designed the IACO-RBFNN model for the 
prediction and estimation of book borrowing in the library. 
Taking the data in the Graphic Center of Henan 
Mechanical and Electrical Vocation College as an 
example, the experiment was carried out. The comparison 
with the BPNN and RBFNN models found that: 
(1) the IACO-RBFNN model needed shorter training 
time and fewer times of iterations and had smaller error; 
(2) the predicted result of the IACO-RBFNN model 
was closer to the actual book borrowing situation; 
(3) the average error and average precision of the 
IACO-RBFNN model was 1955 books and 97.09%, which 
was better than the other two models; 
(4) the training time and testing time of the IACO-
RBFNN model were only 5.12 s and 1.03 s, respectively. 
It was found from the results that the IACO-RBFNN 
model had a good performance in the prediction and 
estimation of book borrowing and could be applied in the 
actual library work to give guidance for the library work. 
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