American Journal of Industrial and Business Management, 2013, 3, 429-434
http://dx.doi.org/10.4236/ajibm.2013.34049 Published Online August 2013 (http://www.scirp.org/journal/ajibm) 429
Study of Personal Credit Evaluation Method Based on
PSO-RBF Neural Network Model*
Shuai Li, Yuanmei Zhu, Chao Xu, Zongfang Zhou#
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, China.
Received April 1st, 2013; revised May 10th, 2013; accepted June 10th, 2013
Copyright © 2013 Shuai Li et al. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
Personal credit evaluation is the basic method for the commercial banks to avoid the consumer credit risk. On one hand,
the credit behavior of individuals is complex; on the other hand the personal credit assessment system in our country is
not sound, assessment methods are mostly objective, therefore, more and better scientific methods for credit risk as-
sessment need to be introduced. This paper proposed a method for personal credit evaluation based on PSO-RBF neural
network, which used PSO algorith m to optimize the parameters of RBF neural network, then applied the optimized RBF
neural network in the personal credit evaluation. This method combined the global searching ability of PSO algorithm
and the high effectiveness of local optimize o f RBF together, overcame the unstabitily of PSO algorithm and the draw-
back of RBF which easily leads to local minimum. The result shows that the personal credit assessment method based
on PSO-RBF neural network is highly accurate in classification and prediction, and is suitable in personal credit as-
sessment and prediction.
Keywords: Personal Credit Evaluation; PSO Algorithm; RBF Network; PSO-RBF Model
1. Introduction
With the rapid development of Chinese economy, the
personal credit is being taken more and more attention,
which strongly ch allenges the credit evaluation system in
our country. At present, the personal credit problem in
our country has seriously affected the development of
Chinese economy, therefore, to build scientific personal
credit evaluation system, and to introduce in scientific
personal credit evaluation is in urgent need. Regards to
the commercial bank, personal credit assessment is to
make comprehensive judgment and evaluate the possibil-
ity of the borrower to return the money on time, accord-
ing to the observation of the indexes which reflect the
personal credit ability, and so as to make a decision on
whether lend money [1].
In western countries, the theories and methods on
credit risk evaluation are maturing, and many interdisci-
plinary theories and methods are applied to credit risk
evaluation [2]. Personal credit risk evaluation methods
are separated into two types, statistic and non-statistic
method, and the statistic method includes decision theory
method, logic regression, linear and non-linear regression,
K-nearest-neighbor estimation etc, non-statistics method
includes mathematical programming, neural network,
genic algorithm, expert system and classification tree
method etc. [3]. Particle swarm optimization (PSO) [4] is
a recently developed numerical method for optimization,
which is simple, easy to apply and has a strong smart
background, and it has been used in many fields such as
function optimization, and pattern recognition. In 2007,
Fu Peizhong, Ying Yixin [5] pioneered in apply PSO
algorithm in determining the parameter of RBF neural
network (connection weight, centers and widths of the
hidden units), and checked its validity using simulation.
RBF neural network is a three-layered BP network,
which can approximate the continuous function with ar-
bitrary precision. It is characterized by single best ap-
proximation, no lo cal minimum, less calculation and fast
learning, and is widely applied to pattern classification,
system identification and functional approximation. At
present, PSO-RBF neural network model [5] is applied to
many industries, such as water quality assessment [6],
short time traffic flow prediction [7], and boiler super-
*Funding Project: Natural Science Foundation of China (71271043);
The Special Research Foundation of Ph.D. Program of China (2011
0185110021) and Sichuan Province Science and Technology Support
Project (2012SZ0001).
#Corresponding autho
r
.

Study of Personal Credit Evaluation Method Based on PSO-RBF Neural Network Model 430
heat steam temperature control systems identification [8]
etc.
This paper built personal credit assessment model by
using RBF neural network, and chose PSO algorithm to
train and optimize the network, then built personal credit
assessment model based on PSO-RBF neural network,
and made a further comparative analysis of it with sing le
RBF neural network, the second chapter of this paper
provided the modeling solution; the third chapter proc-
essed the sample data; the fourth chapter analyzed the
result of simulation.
2. Basic Theory and Modeling Solution
2.1. RBF Neural Network Model
RBF neural network [9] is firstly proposed by J. Moody
and C. Darken, in the late 1980s, it is a three-layered BP
network with a single-hidd en Layer. The first layer is the
input layer, constructed with signal source; the second
layer is the hidden layer, its action function is Gaussian
function, the hidden layer proceed space mapping and
transformation to the input information; the third layer is
output layer, its action function is linear function, the
output layer linear weighted the information from the
neuron of the hidden layer, then output the result of the
entire network. Its structure is as shown in Figure 1.
The figure abov e is the FBF neur al network, specially,
in this paper, 17 indicators are selected by the inputs
layer in the article. Gaussian basis functions are used in
Hidden layer. The hidden layer output results are
weighted to get the final output, which means that the
results of the assessment of the personal credit. As is
known, generally, the RBF Neural Network has n inputs,
m hidden node, 1 output; the action function of the radial
base layer (hidden layer) is Gaussian function, the output
of this layer neuron j is:
2
2
exp, 1,2,...,
2
i
i
i
xc
hi




 


m
h
(1)
Among them, x is an n sphere network input vector, ci
is a center vector with sphere of x, is the basic width. The
output of RBF neural network is: , among
1
m
ii
i
yw


them, w
i is the network weight vector between the ith
radius basic layer and output layer. When applying RBF
neural network, three parameters need to be determined:
the center vector of the Gaussian function ci, the basic
vector i

and the network weight wi.
2.2. Weighted PSO Algorithm
Particle Swarm Optimization (PSO) [10-12], proposed by
Kennedy and Eberhart in 1995, is a Cluster optimization
calculation method, which can be used as neural network
1
x
2
x
n
x
.... 2
h
m
h
y
1
w
m
w
2
w
1
h
Figure 1. The structure of RBF neural network based on
gaussian function.
training method. Its basic idea is to update the local op-
timal


12
,,,
best d
pppp and the global optimal


12
,,,
best d
g
gg g of the particles with the fitness
(the fitness function normally is determined by the opti-
mized function in practical issues) of each particle.
The particle updates their speed and location, by using
the following formula to dynamic trace the optimal of
individuals and the global optimal.


  
112 2
1
ij
ijj ijj ij
vt
wv tcrptx tcr g tx t



 


 
(2)


1
ijij ij
xtxt vt

1

 (3)
Among them, j = 1, 2, …, d; t is the number of itera-
tion; r1, r2, are the ra ndom number uniform distributed in
(0,1); c1, c2 are the accelerated factor, generally c1 = c2 =
2; w indicates the influence of the previous speed to the
present.
For better searching results, this paper adopts the im-
proved weighted PSO algorithm. The weigh w maintains
the balance of global and local searching capacity, high
w inclines to global search, otherwise inclines to local
searching [13]. This paper chose the following mean of
square error function as the fitness function of the PSO
algorithm.

2
,,
11
1nm d
ji ji
ij
MSEy y
n

 
(4)
Among them, n indicates the number of the input
variables, m indicate node number of the hidden layer,
,
d
j
i
y indicates the idea output value, ,
j
i
y indicates the
actual value.
2.3. RBF Neural Network Optimization Process
Based on PSO Algorithm
As is mentioned above, there are three important pa-
rameters in RBF neural network, namely the cen ter of the
Gaussian function cj, the basic vector i

and the net-
work weight wi. However, Currently, it is difficult to
obtain the best values of the parameters of the network
structure in theory, and the methods of training RBF

Study of Personal Credit Evaluation Method Based on PSO-RBF Neural Network Model 431
neural network parameters have a major impact on the
performance of the network, so we must select the ap-
propriate parameters to improve the prediction perform-
ance of the RBF neural network. This paper chooses par-
ticle swarm optimization (PSO) to determine the pa-
rameters of RBF neural network, so that they are no
longer random. The optimized RBF neural network,
compared to the independent PSO algorithm and RBF
neural network algorithm, has a better evaluation effect
on the assessment of the personal credit with higher pre-
diction accuracy. Specific training steps [14] are as fol-
lows:
1) To set the related parameters of the PSO algorithm,
initialize the particles, including the v alue assignment for
hidden center vector, base width vector, weight of the
network; 2) Calculate the fitness value of each particle
according to Formula (4), and make the current position
of the particle as the individual maximum pbest, find out
the particle of the minimum fitness value, and make it the
initial gbest; 3) Compare fitness valu e of the current parti-
cle with pbest, if the fitness value of the current one is
sma ller, then upd ate pbest with the current fitness val ue; 4)
For each particle, compare pbest with gbest, if pbest is better,
then update gbest; 5) Update the speed and location of the
particle according to formulas (2) and (3); 6) Repeat
steps 4)-6), until the terminal condition is met, which is
either meet the maximum iterations or the error accuracy
requirement; 7) Set gbest as the parameter of the RBF neu-
ral network. Specific processes are shown in Figure 2.
3. Sample Data and Preprocess
3.1. Sample Data and the Selection of Variables
Because of the difficulty in collecting domestic credit
data, this paper uses the personal credit data of a Ger-
many bank, a total of 1000 data. Considering the specific
circumstance of Germany, removing too much index [15]
will influence the effect of the model, therefore this pa-
per removed two indexes, “the purpose of loan” and “na-
tionality”, which have little influence to the model. Spe-
cific indexes and quantification method are shown in
Table 1 [16].
First, this paper using stratified sampling, divided the
1000 sample clients into “good credit” and “bad credit”,
with 700 and 300 respectively, and for each sample con-
tains 17 attribute indexes. Then, 350 “good credit” and
Original data and the preprocessing
Building the RBF neural network model
Optimizing the parameters using PSO
Initial the speed, the location of the particles
Calculating the fitness value of the particles
Updating the speed and location of the particles
Updating P
b
est
with the current value
The current value is better
N
The current value is better
Updating g
b
est
with the current value
Make the optimal particles as the
p
arameter of the RBF
Complete the model training
Applying the PSO-RBF model in testing
the rest samples Meet the terminal condition
N
Y
N
Y
Out pu
t
Y
Figure 2. The flow chart of PSO-RBF neural model.

Study of Personal Credit Evaluation Method Based on PSO-RBF Neural Network Model 432
Table 1. Variable and its quantification.
Indexes Variable Definition
Age X1 Actual value
Marriage X2 1 = single; 2 = mar ried
Suppor t i n g f a mil y membe rs X3 Actual value
Occupation X4 1 = unemployed/manual workers, non-resident; 2 = non-proficient worker, resident;
3 = proficient worker/officer; 4 = manager/i ndepe nden t en tr epr e neur s
Year of working X5 1 = unemployed; 2 = less than 1 year; 3 = 1 - 4 years; 4 = 4 - 7 years;
5 = more than 7 year
Housing condition X6 1 = rent; 2 = owned; 3 =free housing
Year of live in current house X7 Actual value
Installment to deposable
disposable income rate X8 Actual value
assets X9 1 = real estate; 2 = if n o t 1 : a g reement of public construction savings/life insurance;
3 = if not 1 or 2: Automobile or other; 4 = vain
Current payment account status X10 1 = less than 0 mark; 2 = 0 - 200 dollar; 3 = more than 200 dollar or Salary contract has
been signed for at least a year; 4 = no payment account
The rest plan for the installment X11 1 = bank; 2 = stock ; 3 = no
Debt amount X12 Actual value
Saving account / bo nds X13 1 = less than 100 mark; 2 = 100 - 200 dollars; 3 = 500 - 1000 dollars;
4 = more than 1000 dollars; 5 = no saving account/bonds
Loan Period X14 Actual value
Credit record X15 0 = no bad credit record; 1 = has overdue payment record/other bad cr e di t record; 2 = overdue payment; 3 = has late payment record; 4 = no credit record/credit record is no
in this bank
Existing loan project number in this
bank X16 Actual value
other note debtor/guarantor X17 1 = no; 2 = joint applicants; 3 = secured
150 “bad credit” from the sample are selected as the
training sample; the rest 500 samples are used in testing
the model, to exam the classification effect of the model.
3.2. Normalizing the Data
To accelerate the convergence of the model and reduce
the effect to the network classification caused by the un-
balance of the data, first normalize the training sample
and the test sample. Divide the adopted 17 explanatory
variables into discr e te va riable and continuou s variable.
For the discrete variable, use the Minimum and maxi-
mum normalization method to process.
min
max min
xx
X
x
x

 (5)
Among them,


0,1X is the value of the variable
after normalizing, xmin, xmax are the maximum and mini-
mum value of the variables.
For the continuous variables, through observing the
distribution of the variables , we found that the amount of
the loan x12,and the time of the loan x14 both approxi-
mately obey the law of normal distribution, that is


2
~,xNu

, and convert them into [0,1].
'
x
u
X







(6)
Among them,

2
2
1
2
t
x
x
edt 


 is the standard
normal distribution, through converting, we can get the
corresponding probability.
4. Simulation and the Result Analysis
In the process of designing RBF neural network, the key
is the determining of the number of the hidden neurons,
because there are many parameters in this paper, when
we set the number of the hidden neurons as 3, the result
meet the setting condition, and the input parameters has
17 variables, then the structure or RBF network is 17-3-1.
To obtain better training result, this paper chose the im-
provement PSO algorithm with the inertia weight, the
inertia weight w = 0.1, the learning factor c1 c2 are both 2,
and, the maximum iterations tmax is 1500, which is the
termination condition of the algorithm. To keep the con-

Study of Personal Credit Evaluation Method Based on PSO-RBF Neural Network Model 433
sistency of the data, we chose the 500 sample data in the
testing sample as the fundament of the assessment, when
evaluating the credit of the creditor, use 0.5 as the critical
value, the one whose predicted value is higher than 0.5 is
viewed as “good credit” client, otherwise is “bad credit”
client, the result of the comparison is shown in Table 2.
In practice, there ar e two types of errors: type one and
type two, th e former is to misjudge the good credit clien t
as bad credit client and rejects their loan application; the
latter is to misjudge the bad credit client as good credit
client and accept their loan application. Therefore type
two errors cause more damage to the bank, and the false
rate of it should be reduced.
From the table above, it can be seen that PSO-RBF
neural network when compared with the pure RBF neural
network model, both the type one error, and type two
error rate are reduced , therefore the total false rate is
reduced, what’s more, the type two error rate is reduced
from 8.67% to 4%, namely, the probability of misjudging
“bad credit” client as “good credit” client is reduced ,
which has more practical value for the commercial bank
to avoid the personal credit risk.
To test the perdition accuracy of the model, after 1500
iterations, we get the following evaluation error char t
As the below Figure 3 shown, evaluation error rate of
PSO-RBF model is apparently lower than RBF model,
which means PSO-RBF model is effective and of better
accuracy. If adopting the RBF model directly, because
the initial value of the network is random, the evaluation
effect is poor. In conclusion, first adopt PSO algorithm to
adjust and optimize the parameter of the RBF model, and
reduce the inner error of the model, and then apply the
Table 2. Comparison between RBF neural networ k and PSO-RBF neural network model prediction accuracy.
Model Actual value
Predicted value
1.00 0.00 Sample number Accuracy (%) False rate (%)
1.00 317 33 350 90.57 9.43
0.00 13 137 150 91.33 8.67 RBF
Total 330 170 500 90.80 9.20
1.00 326 24 350 93.14 6.86
0.00 6 144 150 96.00 4.00 PSO-RBF
Total 332 168 500 94.00 6.00
Figure 3. Evaluation error curve of PSO-RBF model and RBF model.

Study of Personal Credit Evaluation Method Based on PSO-RBF Neural Network Model 434
optimized model in the personal credit evaluation, the
evaluation result is more accurate than the single RBF
model.
5. Conclusions
This paper adopting PSO algorithm in the training of
RBF neural network, proposed PSO-RBF neural network
method, used PSO algorithm to proceed global dynamic
searching, and used RBF neural network to proceed local
optimizing, finally got the PSO-RBF neural network.
This paper first adopted PSO-RBF neural network in
personal credit risk evaluation, and through simulation
and the empirical study of the 1000 personal credit sam-
ple data from a Germany commercial bank, indicated that
this method when compared with the pure RBF model,
showed higher classification and evaluation accuracy, re-
duced the type two error, and effectively reduced the
personal credit risk that the commercial bank facing.
Therefore PSO-RBF neural network is applicable in per-
sonal credit risk evaluation. There is potential im-
provement in this paper, mainly in three aspects:
1) According to reducing the type two error, how to
choose the fitness function of the particles in the PSO
algorithm;
2) The number of the hidden neurons in the RBF
model can be found through other optimizing algorithm,
so as to improve the performance of the model;
3) Because there are too many input variables, the
convergence of the model is comparatively slow, the
time performance is poor.
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