CHEMICAL ENGINEERING TRANSACTIONS

VOL. 51, 2016

A publication of

The Italian Association

of Chemical Engineering
Online at www.aidic.it/cet

Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian
Copyright © 2016, AIDIC Servizi S.r.l.,

ISBN 978-88-95608-43-3; ISSN 2283-9216

The Research on the Electronic Commerce Sales Prediction
based on the Improved LSSVM Algorithm

Xiuhong Dong

Dongying Vocational Institute; Dongying, Shandong 257091 China
Dongxiuhong_1976@126.com

The emergence of the electronic commerce provides the consumers with more choices and provides the
enterprises with another way of life. In recent years, the development of the electronic commerce is very rapid
while it brings the huge competition. Like the offline enterprises, the electronic commerce needs to face with
the problems of the inventory. It can better solve the problems of the high inventory and the stock to predict
the electronic commerce sales. The enterprises can also take the relevant measures to increase the profits
according to the results of the prediction. In this paper, we propose an improved LSSVM algorithm to improve
the accuracy of e-commerce sales prediction and use the method to predict the sales. The experiment has
achieved the good results.

1. Introduction

The prediction of the electronic commerce was a very important question in the management of the electronic
commerce enterprises (Dakshata Argade, Hariram Chavan, (2015)). The accurate sales prediction can not
only reduce the inventory costs, but also can bring more profits for the enterprise. The development of the
electronic commerce in China was later. However, the development was very fast (Neil Towers, Kiki Xu
(2016)). From the beginning of 1997, the Internet users in China increased very quickly. It had provided the
broad basis for the development of the e-commerce activities in China (Hefu Liu et al. (2016)). In recent years,
with the emergence of the Internet of things, the cloud computing (Lackermair Georg (2011)) and other
technologies, the e-commerce has the new energy.
According to the different standards, the electronic commerce can be divided into the different types. From the
scope of the definition of the electronic commerce, it can be divided into the broad electronic commerce and
the narrow electronic commerce. From the perspective of the development of the e-commerce, it can be
divided into the traditional e-commerce and the modern e-commerce. Traditional e-commerce is to carry out
the business activities by using the electronic tools of the non-Internet forms. Aiming at the participating
subject, the online support platform, the contents of the transaction, the nature of the transaction and the
classification of the geographical scope of the transaction of the modern electronic commerce, we make the
summarize and manage. The specific categories are shown in the following table.

Table 1: Electronic commerce classification standard

Classification standard Classification
Participating subject B2C, B2B and C2C,
Online support platform Enterprise internal network, enterprise external network and Internet
Contents of the transaction Indirect e-commerce and direct E-commerce
Nature of the transaction International, ordinary e-commerce and finance e-commerce
Geographical scope of transaction Local, regional and international e-commerce

Lssvm algorithm is a kind of machine learning algorithm (Niyaz Mohammad Mahmoodi et al. (2014)).
Compared with the SVM algorithm, LSSVM algorithm is simple, the less operation time and the higher
accuracy of dealing with the large-scale sample set (Safari et al. Hossein (2014)). Therefore, LSSVM

DOI: 10.3303/CET1651154

Please cite this article as: Dong X.H., 2016, The research on the electronic commerce sales prediction based on the improved lssvm
algorithm, Chemical Engineering Transactions, 51, 919-924 DOI:10.3303/CET1651154

919

algorithm has been widely used (Zheng et al. Pan-Pan (2014)). At the same time, the LSSVM algorithm also
has appeared many derivatives in the process of the discovery.
In this paper, in order to be able to better predict the e-commerce sales, we propose an improved LSSVM and
use the algorithm to predict the e-commerce sales. Compared with the traditional LSSVM algorithm, the
results which are obtained in this paper are more accurate.

2. LSSVM algorithm

We assume that the hypothetical training sample set is {( , ) 1, 2, 3, , }k kT x y k n  ,
n

k
x R and ky R .

k
x is the input data. ky is the output data. In the original space, the optimization problem can be described as,

* 2

1
min ( )

i i i

C   


  (1)

Subject to

( ) ( , )

( )

i i i

f x w x b

y f x e

f x y e



 


  


  

 

(2)

We use the sum of the error square to be instead of the slack variables, transform the inequality constraints to
equality constraints and obtain the regressed optimization problems.

, ,
1

1
min ( , )

2 2

N
T

k
b e

J w e e



 



   (3)

Subject to,

( )
T

k k k
y x b e    (4)

Where,

( ) :
n m

R R   (5)

( )  is the kernel space mapping function. mw R is the weight vector. ke R is the error vector. b is the
deviation vector. The loss function J is the sum of the error and the regular quantity.  is the adjustable
function. The purpose of the kernel space mapping function is to extract the features from the original space. It
maps the sample in the original space into a vector of the high dimensional space in order to solve the linear
non-separable problem in the original space.
Lagrange function,

1 1

1 1
( , , , ) ( )

2 2

N N
T T

i i i i i i

i i

L b x b y          
 

        
(6)

Where, Lagrange factor is belongs to k R  . The optimized formula is,

0, ( )

0, 0

0, ( ) 0

k k

k k k

L
x

L
e

L
x b e y

  




 

 





 





 



  



     






(7)

920

The matrix function is,

00
T bE

yE 

     
     

    

(8)

Where,

1
1

1
( )

E y
b

E E

E y
y E

E E




 















   



(9)

1 1 1 2 1

2 2 2

1 2

1
( , ) ( , ) ( , )

1
( , ) ( , )

1
( , ) ( , ) ( , )

N N N N

K x x K x x K x x

K x x K x x

K x x K x x K x x







 
 

 
 

 

 
 
 
 
  

(10)

The function of the LSSVM least squares support vector machine is estimated as,

( ) ( , )
N

k k

y x K x x b


  (11)

3. Improved LSSVM algorithm

If we want predict the monthly sales and get the better results, we need to find out the similar historical month
with the month which is to be predicted as the training sample. The data of the training sample are as the data
source to be modeled. There are many methods to determine the training samples, such as the clustering
method, the correlation analysis method etc. This paper is to predict the sales of the e-commerce. Therefore,
we adopt the grey incidence theory which has the smaller calculation to analyze. Grey relational analysis
theory is an important part of the grey system theory and is a kind of multivariate statistical analysis. It is
based on the sample data of the various factors. It uses the grey correlation degree to describe the strength,
size and order among the factors. Grey correlation degree is relatively to compare with the close to the data
curve geometry. The closer the geometry is, the closer the change trend is, the greater the correlation degree
is.
We constitute the daily maximum volume to a vector [ (1), (2), , ( )]Tx x x k . We assume that 0x and ix are the
vector that constitutes of the daily maximum volume for the month that to be predicted and the i month.
We can get,

0 0 0 0
[ (1), (2), , ( )]

T
x x x x k (12)

[ (1), (2), , ( )]
T

i i i i
x x x x k (13)
In addition, we can get the correlation coefficient,

min min ( ) max max ( )
( )

( ) max max ( )
i

i k i k i k i k
k

i k i k i k






  


   (14)
( )

i
k is the correlation coefficient in k point of 0x and ix .

Where,

0
( ) ( ) ( )

i
i k x k x k   (15)

 is the resolution factor and [0,1]  .

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In general, 0.5  .

Comprehensive the correlation coefficient of each point, we can get the whole Grey correlation degree of 0x

and ix .

( )
n

i i k

k  


 
(16)

We select the similar months according to the size of the Grey correlation degree. We make the
corresponding day of the month as the training sample of the largest sale and input into the LSSVM algorithm
to predict.
At the same time, we improve the LSSVM algorithm. The influence of the Lagrange factor multiplier is the
largest. Therefore, the bigger the value is, the bigger the effect is. We should pay more attention to the larger
value. We define the vector degree as follows.

min

max min

( ) (1 )( )
i

i i
s f

 
 

 


  

 (17)
The steps of the improved LSSVM algorithm are as follows.
1. According to the Grey correlation degree, we select the similar months as the input of the LSSVM.
2. Training the inputted data set information and obtain the Lagrange multiplier

1
{ }

i i



.

3. Selecting the appropriate 0 1  and using the Lagrange multiplier to determine the support vector
degree.
4. Constructing new training data set, training the improved LSSVM and getting the model parameter

1
{ }

i i




and b .

5. According to
1

{ }
N

i i



, we ascend the training data and minus a small part of the minimum value of the data

points.
6. By the remainder of the Lagrange operator, we re-calculate and build the new training set. Then, we make
the LSSVM training and get the new Lagrange multiplier.
If the fitting performance drops, the training ends. Otherwise, it goes to step 4.
The flow chart is shown as below.

Select the training set
according to the grey

correlation degree

Input training set

Run the original
LSSVM

Original Lagrange
multiplier

Run the fuzzy LSSVM

Ordering Lagrange
multiplier

Shear

New Lagrange
multiplier

End

Figure 1: Flow chart of improved LSSVM algorithm

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4. Experiment

In this paper, we use the improved LSSVM algorithm to study and predict the sales of the electronic
commerce. According to the process of the proposed LSSVM algorithm, we need to select the month which
has the biggest correlation degree with the predicted month and take these months as the training samples
firstly. Then, we use the improved LSSVM algorithm to predict the target. Finally, we get the final predicted
value.
In order to predict the sales volume in August 2015, we pretreat the sales data from July 2012 to July 2015.
We selected 10 months which has the greater correlation degree as the source of the training sample. The
calculation results of the grey correlation degree are shown in the following table.

Table 2: Calculation results of grey relational degree

Month Grey relational degree
January 2015 0.7934
February 2015 0.8121
March 2015 0.7453
April 2015 0.7890
May 2015 0.7481
June 2015 0.9317
July 2015 0.8976
September 2014 0.8213
August 2013 0.7783
September 2013 0.7269

We select RBF as the kernel function of LSSVM. According to the experiment of the different kernel function
parameter selection, we select the experimental parameters. According to the kernel function and parameters,
we model and train to get the LSSVM model. Then, we input the training samples which select according to
the Grey correlation selection into LSSVM model to be trained. We can predict and get the sales prediction
results of August 2015. In addition, in order to verify the accuracy of the method, we compare the prediction
results with the traditional LSSVM method. Due to space limitations, we only give ten former data, the specific
data are shown in the following table

Table 3: Experimental data

Data Actual value Method in this paper LSSVM method
2015.8.1 35 37 39
2015.8.2 47 48 53
2015.8.3 43 44 52
2015.8.4 31 35 47
2015.8.5 25 28 38
2015.8.6 35 41 36
2015.8.7 41 42 43
2015.8.8 44 46 50
2015.8.9 52 54 58
2015.8.10 46 50 54

The predicted results and the actual results are shown in the following figure.

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Figure. 2: Comparison of experimental results

From the above figure, we can see that the experimental results of the method which is proposed by this
paper are more accurate. Compared with the actual value, the curve of the predicted result is more close to
the predicted value. From the prediction accuracy, the results obtained from the LSSVM algorithm have some
gaps compared with the improved LSSVM algorithm.

5. Conclusion

In recent years, the electronic commerce has been developing rapidly in our country. For the representative of
"Taobao" and "Jingdong", these e-commerce enterprises occupy a significant market share. E-commerce has
been integrated into people's daily life. At the same time, the competition of the electronic commerce
enterprises is also very intense. To predict the e-commerce sales can get the future sales. At the same time,
the electronic commerce enterprise can reduce or increase the inventory, reduce the inventory cost, and
increase the flow of funds according to the prediction results. In this paper, firstly, we introduce the
background of the research. After that, we introduce the LSSVM algorithm. In order to get the better prediction
results, we propose an improved LSSVM algorithm and use this algorithm to predict the sales volume of the
electronic commerce.

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