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									     SVM based Bankruptcy Prediction Model for Small & Micro
          Business using Credit Card Sales Information


                      Jongsik Yoon, Young S. Kwon, Tae Hyup Roh

      Department of Industrial and Systems Engineering, Dongguk University,
                 3-26 Pil-dong, Joong-gu, Seoul 100-715, Korea
                                King337@dgu.edu

      Department of Industrial and Systems Engineering, Dongguk University,
                 3-26 Pil-dong, Joong-gu, Seoul 100-715, Korea
                                 yskwon@dgu.edu

          Department of business administration, Seoul Woman University,
             126 Gongreung-dong, Newon-gu, Seoul 139-774, Korea
                                 rohth@swu.ac.kr


                                    ABSTRACT

     The small & micro business has the characteristics of both consumer credit risk
and business credit risk. In predicting the bankruptcy for small-micro businesses, the
problem is that in most cases, the financial data on business credit risks for small &
micro businesses are not available. To alleviate such problem, we propose a
bankruptcy prediction mechanism using the credit card sales information available,
because most small-micro businesses are member store of some credit card issuers,
which is the main purpose of this study.

      In order to perform this study, we derive some variables and analyze the
relationship between bankruptcy and non-bankruptcy signs. We employ the new
statistical learning technique, support vector machines (SVM) as a classifier. We use
grid search technique to find out better parameter for SVM. The experimental result
shows that credit card sales information could be a good substitute for the financial
data on business credit risk in predicting the bankruptcy for small-micro businesses.
In addition, we also find out that SVM performs best, when compared with other
classifiers such as neural networks, CART, C5.0, multivariate discriminant analysis
(MDA), and logistic regression analysis(LRA).

Keyword: small-micro business, credit evaluation, credit card, sales information,
bankruptcy prediction, support vector machines, grid search



                              I.   INTRODUCTION

Since 2000, due to spread of commencement of enterprise by small capital, the
Korean government has strengthened supporting of the commencement of enterprise
and consulting of the management as well as supporting of lending into the
small-micro business through confidential guarantee for initial expenses and working.
Also financial banking circles have developed the diverse derivative financial
commodities, targeting to the persons who run small-micro businesses because of
dullness of loan business caused by changing of real property policy by Korean
government and high raising up of interesting. Due such cause, government and
financing institutions have made an effort to develop more accurate and scientific
credit evaluation model for small-micro businesses.

 However, the credit evaluation model for small-micro businesses so has both
personal credit features and one of company, that modeling is too difficult (Park,
2001; Yang, 2003). At current, the patterns of credit evaluation for small-micro
business are using methodology of Analytic Hierarchy Process (AHP) which is using
personal credit model with personal credit features basically, and the evaluator
reflected the subjective knowledge of company’s credit features (Yang, 2003; Gim et
al., 2005). This is caused from no existence of objective criterion of the business
properties such as the predictive revenue, conditions of location and potentialities of
business.

Since 1990's, the enterprise of credit card have rapidly been grown up and after the
IMF economical recession in Korea, the government has led the policy that the use of
credit card would be vitalized, so the most categories of business except the
manufacturing business among the small-micro business have generated the revenue
through the credit card. Recently, as the system issuing the receipt of cash is also
spread, the objectivity of materials for presuming the revenue of the business is more
increased.

The purpose of this paper is to develop the bankruptcy prediction model for
small-micro business by utilizing the insolvent information of small-micro business
owner form banks and the credit card sales information occurred in their member
stores. Through this process, we develop a model with optimum accuracy which is
applied into various algorithms for investigating effectiveness by generating variety of
derivative variables. And we apply support vector machines (SVM), a new machine
learning technique, to bankruptcy prediction problem and provide a new model with
improved its prediction accuracy. Performance of SVM is compared with
LRA(Logistics Regression analysis), MDA(multiple Decision analysis), DT(Decision
Tree) and BPN(Back propagation Neural Network). Particularly, by training the SVM
(Support Vector Machine) with K-fold cross validation, and through the grid
searching method, the training group and validation group are applied into the model,
searching the skillful strategy which is able to show the best predictive power.



II.   THEORETICAL BAKGROUD



A.    Bankruptcy Prediction for Small-Micro Business

The study of bankruptcy prediction for small-micro business is yet in shortage, when
comparing with that for company or personal. This is because the small-micro
business contains both the enterprise characteristics and personnel nature at the same
time. And it is difficult to collect the financial material and information for designing.
Also because the difference of definition and policy for small business and
small-micro business in every country, it has been excluded from the subject to be
studied internationally.

In Korea, the number of small-micro business is about 2 million and five hundred
fifty thousand, and it has great specific gravity as much as occupied 88.8% of entire
small and medium enterprises. Specially, the number of employee (the person who is
engaged in) is about 4 million and nine hundred, and they have contributed greatly in
the national economy as much as occupied 42.9% of entire employees of country, as
well as into people economy (Small Business Development Center, 2002). For this,
the government and banks recently have made an effort to support the small-micro
business and to develop the derivative financial commodity. Altman et al.(1977) and
Kim(2006) mentioned that the size of enterprise is the critical component to decide
the value, and the smaller of enterprise is, higher probability of bankrupt exists, so
that they stressed the necessary of study with respect to the credit evaluation of the
small enterprise and small-micro business

Berger and Frame(2005) also said, applying the credit scoring of small Business may
reduce the variety risk in economical sides, and have small enterprise and small-micro
business lower down the interest rate and mortgage demanding by banks. To do it, he
mentioned that it is more necessary that forming the confident relationship between
the small-micro business and the financial agency. Frame et al.(2004) said, the
lending agencies have been shunned lending because of instability in finance. He said,
the model of confidence appraisal suitable, effective and efficiency to the small
enterprise is to release the unsymmetrical information between the creditor and debtor,
then, the lending with respect to small enterprise may be increased. Particularly, he is
insisting of useful of credit evaluation of small enterprise and small micro-business,
and showed that such system is more effective to the companies that have produced
little profit, so that they are faced the difficult to secure the fund, rather than the
companies that have generated much gain.

Since the model of Fair Isaac (FICO) of U.S.A had been introduced 1995, several big
size banks have begun to interest in credit evaluation of small enterprise and
small-micro business.

In Korean, recently Park(2001) had begun to study the model able to predict the
bankruptcy of small micro-business through MDA, and Jung(2002), Yang(2003) and
Kim(2006) have studied the model predicting insolvent or excellent by utilizing non
financial information of small -micro business and by using the Logit Analysis and
AHP (Analysis Hierarchy Process). This is because there absent the financial variable
using the model of credit evaluation of company, they perform the studying in putting
first on AHP technique utilizing the know-how of the person charging of lending
assessment of the small micro-business in putting on the first non financial variables.

B.    Support vector machines

As SVM is algorithm learning statistically by searching the optimal separated
hyperplane by means of using Support Vector (SV) to solve the classification problem,
it has showed higher performance than the Neural Network in application. And SVM
have the character able to avoid overfitting and local minimum problem through the
principal of SRM (Structural Risk Minimization), comparing that implementing the
principal of ERM (Empirical Risk Minimization) by the conventional algorithm
learning(Burges, 1998; Huang, 2004).

A simple description of the SVM algorithm is provided as follows. Given a training
set T  {xi , yi } , i  1,, l In the problem classifying two groups of yi  {1,1} with
inputting vector of xi  R d , when assumed that there exist the hyperplane, The
hyperplane may express as W t   ( x)  b  0 .

Where W is the weight vector having a unit length laid at right angle with the
hyperplane, b is bias. () : R d  R d k plays the role transferring the input vector into
a feature space (of higher space dimension)

Two boundary hyperplane opposed, and paralleled with the hyperplane is

             W t  ( xi )  b  1        f or     yi  1                           (1)
              t
             W  ( xi )  b  1          f or     yi  1

Which is equivalent to

               yi (W t   ( xi )  b)  1  0        i                               (2)

At this time, the normal distant of this hyperplane from the original point expresses as
b / W , and the normal distant between tow boundary hyperplane is 2 / W , and the
margin of normal distance expresses as " Margin".

The purpose of SVP is to seek for the hyperplane maximizing this margin.

To solve the most classification problem impossible to separate two group completely,
the method to seek for the weight vector after introduced error term ( i ) , which is
surplus variable (slack variable) by allowing misclassification as equation (3).

                   1             l                                                     (3)
              M i n W T W  C   i
                   2           i 1


subject to

               yi (W T  ( xi )  b)  1   i ,         i  1,, l
              
                                   i  0,                i  1,, l

Where C is weighing value of classification error with respect to the marginal gap, C
value plays as the role of random parameter.
C can play the role minimizing the error term if rise up the real value having plus
value, and while the lower of the value, the more maximizing role of the error term is
doing, the classification function of SVM may be tuned

The minimizing problem of equation (3) is a model of quadratic programming: QP
having the equation limiting linearity, the finite solution is to calculated by using the
Lagrange power  i .

At the time, the power      i is multiplied into each the training group, the data
existing non negative is defined as support vector. In conclusion, the value of
parameter is deduced by using only support vectors.

                                         l
                                                   1 l l                                  (4)
                  M a xLD    i                   i j yi y j ( xi )T ( x j )
                                        i 1       2 i 1 j 1

subject to

                                                                   i  1,, l ,
                       l

                    y  0 ,
                           i
                                                 0  i  C ,
                   i 1



Both equation (3) and equation (4) that express the minimization may convert into the
same dual problem, and K ( xi , x j )  ( xi )T ( x j ) shows the kernel function.

This means that the data within training group are moved into specified space of
higher dimension through the kernel function.

This plays the role making into set of input data able to separate into linear within the
specified space by moving the data into higher space.

Since  (x) cannot be calculated in real at SVM, the problem is solved by using the
Kernel function k (  ,  ) , which is mapping by means of Mercer's condition.

As the typical kernel function is a kernel of radial basis function (RBF), and by
utilizing

Gaussian distribution, the finite function is obtained by adjusting  expressed as

K ( xi , x j )  exp( xi  x j ) ,   0
                                 2                       and the dth order of polynomial function is

expressed as K ( xi , x j )  ( xiT x j  r ) d . Under              0 , the finite function is sought
by adjusting  and             d.              where d ,      R  and        N are constant.

Finally SVM as equation (5) is solved

                                   l                                                                   (5)
                  yi  sgn( i yi K ( x, xi )  b)
                                    i
Recently the study of variety fields utilizing

with diverse SVM has been done. Particularly, where the SVM is applied into
practical problem, the predictive power is excellent, comparing with other algorithm,
and avoiding the exceed sum by introducing error term. where approaching to a
function, it has the advantage that insensible to the ideal value(Min and Lee, 2005).

C.   Conventional prediction techniques for Bankruptcy Prediction

The study of Bankruptcy Prediction model had begun as calculating the weighing
value of main variable, and extracting the excellent and bad customer by using the
information of personnel confidence information of variety financial agencies
including bank and financial company by Durand (1941). Thereafter as Beaver (1966)
had begun the study through statistical analysis of single variable with the difference
between the bankrupt company and non-bankrupt company, the study with respect to
model to predict of company bankruptcy has been begun to grow. The study in early
of 1980s hereafter has been progressed vitally by means of the distinct analysis of
multi variables, regression analysis, and logit, which are the statistical model (Ohlson,
1980; Gentry et al., 1985).

And from early of 1990s year, through comparing the neural network that is machine
learning technique with variety techniques, many studies over the relative superiority
in the predictive power of the artificial neural network had been carried out (Odom
and Sharda, 1990; Tam and Kinag, 1992). Also, recently, the methods like deduction
on the base of for instance, gene algorithm, decision tree, SVM have been studied
vitally (Miller et. al 1996; Huang et al.,2004)

In the present study, by developing the model through the distinct analysis of
multivariate discriminant analysis (MDA) and logit regression analysis(LRA),
decision tree (CART, C50), and neural network, we would compare in predictive
power with the model of SVM proposed in present study.



III. RESEARCH DATA AND EXPERIMENTS

A.    data

In this study, the credit card sales information of the merchant joined small-micro
business was used to predict. In Korea, since the credit card company manages its
own card, they do not have the information related the sales of entire credit of the
joined merchants happening variety transaction of card. However, Credit card VAN
company manages all transaction information happening on the terminal unit of
joined merchant, and plays the role branching off the particulars of transaction to each
credit card company.

All transaction particulars happened within the joined merchants due such things is
controlled by VAN company. Also VAN is systematized able to open the sales
information of credit card in any time, where demanding of sales information
happened on the merchant joined the owner himself by obtained agreement written
with the owner of joined merchant for providing the information.

This study was experimented by utilizing the sales amount of credit card in every
month among the data happened for 28 months from the years of 2000, 2001 and
2002. And its cases at 412,773 joined merchants using of the service of K-VAN and
with the information related to revenue by credit card over business type of joined
merchant. And we used the insolvent information of small-micro business and owner
at Korea Federation of Banks.

B.   Experiment Design

Present experiment is carried out according to the procedure as figure 1.




                              Figure. 1. Experimental process

In the total 412,773 data subjected to the study, we delete outlier and missing value of
measurement among these are excluded. And we define the bankruptcy of
small-micro business using the month of happening to insolvency and the month of
stopping the card transactions at merchant. And we produce variety derivative
variables by analyzing the variety information including business type, the term of
continual transaction, and average transaction, standard deviation, and transaction
pattern. These variety derivative variables produced by this way are used into the
input variable to the model, and are analyzed, we compare with the bankruptcy
prediction model developed through the variety techniques.

The insolvent merchant joined in real data is only 3%. In this case, if we extract the
sample in the real ratio of excellent and insolvent merchant, the learning with respect
to the excellent merchant may be over-fit.

In such reason, to design the model predicting the insolvent merchant joined, by
extracting each 5000 samples randomly from the excellent merchant and insolvent
merchant, these are reconstituted with 7000 of learning set and 3000 of validation set.
To select the significant variable to apply into the model, we verify variety derived
variables obtained through sales information of credit card through t-test, and reduce
the variables to increase prediction accuracy for the model by stepwise logistic
regression analysis. Finally, we find out that SVM has the best accuracy and stability
at the bankruptcy prediction model for small-micro business through comparing the
other technique’s.
IV. EMPIRICAL ANALYSIS AND RESULT

A.      Definition of bankruptcy and derived variables

The business cycle of small micro-business is generally shorter than general
company’s. And the information with respect to whether the stagnation of revenue or
close by nonpayment, or movement of company or intentional close in other purpose
exist nearly non because the information related movement or close is unreliable.

                     Num. of
                     merchants                                            Month of Insolvency

                        2500

                        2000

                        1500

                        1000

                         500

                           0
                               -28 -24 -20 -16 -12    -8   -4    0    4    8    12    16   20    24   28

                                                                     Interval between stopping the credit card
                                                                         transactions and Insolvency (month)


         Figure. 2. Distribution of the number of merchants according each difference in the month
              registered of credit insolvent and the month of stopped credit card transactions.

To define the bankruptcy of small micro-business by utilizing the information of
transaction suspension of merchant and information of confidence insolvent of Korea
Federation of Banks, the bankruptcy is defined when the transaction of credit card is
suspended within 6months before the day registered the confidence insolvent and
within 3month after the day registered as figure 2.

                                        TABLE 1. Definition of variables
       Class                                         Variables                                                   description
                                   The months suspended during 6months                                Continual Business Power
                       The term between the month of max sales and min sales.                         Continual Business Power
       Term
                    The term of continual trade until the point of the time of basis Continual Business Power
                                     Months happened card transactions                                     Business History
                                         average of sales in a month                                        Size of Sales
amount of sales                  amount of difference between max and min                                  Frailty of Sales
                                      Min. amount of sales in 6months                                      Frailty of Sales
     transaction                             at least transaction                                          Frailty of Sales
     percentile                  percentile of transaction average of 3months                               Size of Sales
                                    change direction of trade in 3months                                    Size of Sales
 sales pattern
                                     change degree of trade in 3months                                      Size of Sales
Business type           Bankruptcy rate of business type of middle assortment                              Frailty of Sales
To predict whether the merchant is the bankruptcy or not through the credit card sales
information of merchant, about 40 of the derivative variables are made.

To compare the predictive power of the model of SVM, BPN, DT, MDA, and LRA
using the variable derived by this way, 22 variables selected among about 40 variables
at the 0.05 significance level by t-test. And 12 variables consisted finally at the 0.01
significance level by stepwise logistic regression analysis for modeling are constituted
as TABLE 1.

The 12 variables chosen can be explained as business history, continual business
power, revenue size, and frailty of revenue, four types largely, and the critical variable
for bankruptcy predicting of small micro-business can be defined.

B.   Experiment

To design the model through SVM in this study, the kernel of RBF and kernel of d th
of polynomial were used. we used the 7-fold cross validation to learn the train set ,
and “LIBSVM” was used the experiment of SVM. To search the optimal SVM
utilized the kernel of RBF first, allowable error C and  parameter of kernel were
used into the method of grid search. The method of grid search is the way looking for
the combination of optimal C and  by progressing the learn with respect to each
combination, making several of C and  combination Though this method has the
vulnerability requiring approximation expense because the learning over all
combinations must be done, the advantage able to seek finite parameter is existed in
the comparison with heuristic approach(Min and Lee, 2005). In present study, the
finite C and  are calculated by learning the training groups, combining C and 
into the exponent of 10 and verifying it.

<Table 2> shows that the best predictive accuracy was appeared as 79.70%
(non-bankruptcy: 79.75%, bankruptcy: 79.64%), as the optimum C and  obtained
through the grid searching over the training set were 105 and 10-6.

     TABLE 2. Predictive accuracy (%) according to each RBF parameter through training set.
                    
                        100    10-1    10-2    10-3     10-4     10-5    10-6     10-7
            C
           100          58.8   76.6   78.4     78.7     77.5    70.5     69.9     70.0
           101          59.1   68.6   78.0     79.0     78.9    77.4     70.4     70.0
                2
           10           59.1   67.3   75.8     78.6     79.1    78.6     77.4     70.4
                3
           10           59.1   67.3   68.9     79.0     78.7    79.4     78.7     77.4
           104          59.1   67.3   67.2     78.0     79.0    79.4     79.6     78.6
           105          59.1   67.3   66.0     76.4     79.1    78.6     79.7     79.5
                6
           10           59.1   67.3   65.6     74.4     78.7    79.2     78.6     79.6
           107          59.1   67.3   66.2     74.4     76.3    78.9     78.4     79.6
However, the result verified through the validation set was 70.83% (non-bankruptcy:
71.4%, bankruptcy: 86.96%), and showed lower predictive accuracy in comparison
with other parameters. When the grid search over the training set is combined with the
grid search over validation set, C and  were analyzed 103and 10-3 as having the
best predictive accuracy of 79.0% in the training set (non-bankruptcy: 79.55%,
bankruptcy: 78.44%), and 74.20% in the validation set (non-bankruptcy: 74.86%,
bankruptcy: 88.66%).

          TABLE 3. Predictive accuracy (%) according to each RBF parameter through validation set.
                            
                                    100      10-1          10-2     10-3          10-4     10-5          10-6     10-7
                  C
                  100               58.3    72.5          73.4     72.2          69.7     65.4          64.8     64.8
                  101               59.1    67.8          73.8     72.7          71.3     69.6          65.3     64.8
                       2
                  10                59.1    67.2          71.9     73.0          71.9     70.8          69.7     65.3
                  103               59.1    67.3          69.3     74.2          72.7     71.0          70.7     69.6
                  104               59.1    67.3          66.1     73.6          72.7     71.9          70.4     70.8
                  105               59.1    67.3          65.3     72.8          73.6     72.9          70.8     70.3
                       6
                  10                59.1    67.3          64.8     67.4          73.2     72.9          71.0     70.2
                  107               59.1    67.3          64.7     67.4          73.2     72.2          71.6     69.7

TABLE 4. Predictive accuracy (%) according to each parameter of polynomial Kernel through training
                                      and validation group.
                          10-2                   10-3                   10-4                   10-5                   10-6
 C            d   Train           val      Train         val      Train          val     Train         val      Train         val
              1   79.9            70.3     79.9          70.3     79.6          70.3     79.1          70.6     76.2          68.9
              2   79.9            72.7     78.5          72.2     76.8          70.5     60.7          58.7     60.7          58.7
 102          3   76.8            72.2     76.8          71.6     61.8          59.0     54.2          53.6     54.2          53.6
              4   74.6            71.7     73.7          68.4     51.6          51.7     51.6          51.7     51.6          51.7
              5   73.1            70.8     71.7          66.7     51.0          51.2     51.0          51.2     51.0          51.2
              1   79.9            70.4     80.0          70.3     79.9          70.3     79.6          70.3     79.1          70.6
              2   79.2            72.4     79.0          72.1     78.2          71.5     69.9          64.4     60.7          58.7
      3
 10           3   77.4            71.1     79.2          73.6     76.5          69.5     54.2          53.6     54.2          53.6
              4   76.7            70.7     76.3          70.4     58.2          55.9     51.6          51.8     51.6          51.8
              5   74.4            70.4     73.1          68.0     51.0          51.2     51.0          51.2     51.0          51.2
              1   79.9            70.3     80.0          70.3     79.9          70.3     79.9          70.3     79.6          70.3

              2   79.2            72.8     79.0          72.0     78.5          72.2     76.8          70.5     60.7          58.7

 104          3   76.9            70.8     78.3          73.0     75.9          69.2     54.2          53.6     54.2          53.6

              4   76.8            70.6     76.3          71.8     64.8          60.9     51.6          51.8     51.6          51.8

              5   74.6            70.3     74.0          69.9     53.8          53.5     51.0          51.2     51.0          51.2
To calculate the optimum SVM by utilizing degree d th polynomial kernel, the result
experimented in combination with several of allowable error C and kernel parameter
 , and order number d is shown as table 4.

Through RBF kernel, the experiment was carried out by expanding from the center of
the optimum value C of 103, to the range 102 and 104 and 10-3 of the optimum value
to the range 10-2 and 10-6, and from 1 to 5 of degree d.

The best accuracy of SVM with polynomial Kernel through the training set may be
constituted when C,  and degree are 103, 10-3 and 1. However, when it is
compared with the predictive accuracy of the validation set, the predictive accuracy of
training set was 79.2% (non-bankruptcy: 79.95%, bankruptcy: 78.44%) when C, 
and degree are 103, 10-3 and 3, and the predictive accuracy of validation set,
73.6% (non-bankruptcy: 74.4 %, bankruptcy: 72.8%), which has the best predictive
accuracy.

The experimental result of SVM showed that RBF kernel has predictive accuracy of
about higher 1% than that of polynomial Kernel. Also in the speed of learning, RBF
kernel was faster than polynomial Kernel.

C.   Comparing prediction accuracy of Model

In this study, to compare the predictive accuracy of SVM with the that of other
predictive techniques, “Clementine 8.5” as the experimental tool of BPN and DT was
used and “SPSS 12.0” as the experimental tool of analysis of MDA and LRA.

BPN is greatly impacted by choosing learning rate, momentum, number of neuron in
input layer, number of hidden layer, number of neuron, and training method (Odom
and Sharda, 1990; Tam and Kinag, 1992; Miller and Cadden, 1995). In BPN, each
data set is split into three subsets: a training set of 50%(5000), a test set of 20%(2000),
and a validation set of 30%(3000) with the same size of SVM. we used 86 neurons of
input layer, and one of hidden layer, and one neuron of output layer, and Sigmod
function, and the rate of learning and momentum was fixed into 0.3, and the
experiment was repeated to obtain the best model, tuning the number of learn from
100 to 300, and the number of hidden layer from 8 to 32 increased 4. The best
predictive accuracy was appeared when number of learn is 200, and neuron number of
hidden layer is 24.

The prediction rate shows 76.20 % where group trained is, and 71.90% (excellent
75.0% insolvent 68.8%) where the validation set is.

The model used CART for DT was tested by increment by one from 4 the deep of
branch, and the training set showed 74.70% at 8 of depth, and the validation set
showed 70.33%. Where the model using C5.0 for DT is, the prediction accuracy of
training set was shown as 78.2%, and the validation set was lower than CART’s as
70.83% at 14 of depth. In the analysis of MDA and LRA, 12 variables mentioned in
previous paragraph are chosen equally through the selection method by stepwise with
20 input variables, and the prediction accuracy of training and validation was
appeared in the near same.
     TABLE 5. Comparison of prediction accuracies (%) according to                  classification techniques.
                                 Accuracy (%)                                                    Accuracy (%)

          model                                                    model
                         Train                  Val.                                     Train                  Val.
        SVM              79.0                   74.2           DT(C5.0)                  78.2                   70.8
        BPN              76.2                   71.9               MDA                   69.0                   70.1
     DT(CART)            74.7                   70.3               LRA                   68.9                   70.1


When comparing in the prediction accuracy of the techniques experimented in
previous, the accuracy of SVM was appeared as 4% of higher than that of other
techniques, and as shown in table 5.

         TABLE 6. McNemar values (p-values) for the pairwise comparion of performance
           model                   NN                    DT                   MDA                         LRA

                                 8.875a                18.416a               35.021a                    35.021a
            SVM
                                (0.003b) *             (0.000) *             (0.000) *                  (0.000) *

                                                              (* : p<0.01,   a
                                                                                 :McNemar statistic,b:p-value )


To statistically compare the accuracy of SVM and that of the rest predictive
techniques, The McNemar test, which is used into the verification of the difference of
the paired two groups was carried out.

From the result of McNemar test, we could find out a fact that the SVM as table 6
showed the statistical difference from the prediction result of DT, BPN, MDA, LRA
at 1% statistical significance level.



V.   CONCLUSION

In this study, the bankruptcy prediction model for small micro-business was
developed by using the credit card sales information. Also it was proved the fact that
the SVM has high predictive accuracy in comparison with various conventional
classification techniques.

The derived variables having high interpretation in the model were chosen
representing the continuation of business, the period of business, the size of sales, and
the frailty of sales as company’s credit features of small-micro business. Although the
model is developed by only those variables, the accuracy is very reasonable. The
months when the revenue had happened representing business power, and the term of
continual trade until the basis time representing the power of continual business,
months suspended of trade during 6months and the term between the month happened
the greatest revenue and the month of minimum revenue were chosen.

SVM was well-known as having excellent performance in comparison with the
conventional classification techniques in the preceding study related to credit
evaluation of general company. Also its excellent ability was also displayed in the
region of small-micro business.

The limitation of this study could be not rising up the hitting rate of model by
combining the information of each merchants joined, the information concerning
financial state and management ability due to limitation of data collection. And as the
experiment made in the side of prediction accuracy, the comparison with more variety
methodology to decide the best parameter was lack.



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