alization ability. Fourth, a distinct trait of LS-FSVM can further lower computational complexity by transforming a quadratic programming prob- lem into a linear equation problem. Finally, an important advantage of LS- FSVM is that the support values αi in LS-FSVM are proportional to the membership degree and errors simultaneously at the data points thus mak- ing LS-FSVM more suitable for real-world problems. These important characteristics will also make LS-FSVM popular in many practical appli- cations.
5.3 Experiment Analysis
In this section, a real-world credit dataset is used to test the performance of LS-FSVM. For comparison purposes, linear regression (LinR), logistic re- gression (LogR), artificial neural network (ANN), Vapnik’s SVM, Lin &
Wang’s FSVM and LSSVM are also conducted the experiments.
The dataset in this chapter is from the financial service company of Eng- land, obtaining from accessory CDROM of Thomas et al. (2002). Every applicant includes 14 variables, listed by Table 5.1. The dataset includes detailed information of 1225 applicants, in which including 323 observed bad applicants.
Table 5.1. Variables of the experimental dataset
No. Variables
1 Year of birth
2 Number of children
3 Number of other dependents 4 Is there a home phone
5 Applicant’s income
6 Applicant’s employment status
7 Spouse’s income
8 Residential status
9 Value of home
10 Mortgage balance outstanding 11 Outgoings on mortgage or rent
12 Outgoings on loans
13 Outgoings on hire purchase 14 Outgoings on credit cards
In this experiment, LS-FSVM, FSVM, LSSVM and SVM models use RBF kernel to perform classification task. In the ANN model, a three-layer back-propagation neural network with 10 TANSIG neurons in the hidden
82 5 A Least Squares Fuzzy SVM Approach to Credit Risk Assessment layer and one PURELIN neuron in the output layer is used. The network training function is the TRAINLM. Besides, the learning rate and momen- tum rate is set to 0.1 and 0.15. The accepted average squared error is 0.05 and the training epochs are 1600. The above parameters are obtained by trial and error. The experiment runs by Matlab 6.1 with statistical toolbox, NNET toolbox and LS-SVM toolbox provided by Suyken and Vandewalle (1999). In addition, three evaluation criteria measure the efficiency of clas- sification.
bad observed of
number
bad as classified and
bad observed both of number accuracy
I
Type = (5.28)
good observed of
number
good as classified and
good observed both of number accuracy
II
Type = (5.29)
sample evaluation of
number the
tion classifica correct
of number accuracy
Total = (5.30)
To show its ability of LS-FSVM in discriminating potentially insolvent creditors from good creditors, we perform the testing with LS-FSVM at the beginning. This testing process includes five steps. First of all, we tri- ple every observed bad creditor to make the number of observed bad nearly equal the number of observed good. Second we preprocess the data- set so that the mean is 0 and the standard deviation is 1. Third the dataset is randomly separated two parts, training samples and evaluation samples, 1500 and 371 samples respectively. Fourth, fuzzy membership is generated by linear transformation function proposed by Wang et al. (2005) in terms of initial score by expert’s experience. Finally we train the FSVM classi- fier and evaluate the results. The above four steps are repeated 20 times to evaluate its robustness. The efficiency and robustness of credit risk evalua- tion by LS-FSVM are shown in Table 5.2.
From Table 5.2, we can find the LS-FSVM has a strong classification capability. In the 20 experiments, Type I accuracy, Type II accuracy and total accuracy are 81.34%, 93.27% and 88.16%, respectively, in the mean sense. Furthermore, the standard devation is rather small, revealing that the robustness of the LS-FSVM is good. These results imply that the LS- FSVM is a feasible credit risk evaluation technique.
For further illustration, LS-FSVM’s power of classification is also com- pared with other six commonly used classifiers: liner regression (LinR), logistics regression (LogR), artificial neural network (ANN), Vapnik’s SVM, FSVM and LSSVM. The results of comparison are reported in Ta- ble 5.3.
5.3 Experiment Analysis 83 Table 5.2. Credit risk evaluation results by LS-FSVM
Experiment No. Type I (%) Type II (%) Total (%)
1 81.56 93.81 88.54 2 86.98 95.14 92.53 3 82.02 91.84 88.49 4 79.81 98.36 93.53 5 87.77 94.03 92.24 6 81.56 96.85 92.38 7 79.19 93.05 87.41 8 85.69 92.11 88.86 9 79.27 89.33 87.63 10 82.45 96.58 90.45 11 77.96 93.08 85.06 12 80.61 89.57 85.89 13 81.16 93.41 88.34 14 78.96 89.88 87.56 15 85.56 97.35 94.53 16 70.36 98.13 84.11 17 80.14 92.01 88.68 18 75.22 89.54 86.25 19 86.72 89.61 88.04 20 83.85 94.70 92.64 Mean 81.34 93.41 89.21 Stdev 4.20 2.98 3.02 Table 5.3. Performance comparisons of different classifiers
Method Type I (%) Type II (%) Overall (%)
LinR 52.87 43.48 50.22 LogR 60.08 62.29 60.66 ANN 56.57 78.36 72.24 SVM 70.13 83.49 77.02 LSSVM 79.37 93.27 89.16 FSVM 80.08 92.86 88.38
LS-FSVM 81.34 93.41 89.21
As can be seen from Table 5.3, we can find the following several con- clusions:
(1) For type I accuracy, the LS-FSVM is the best of all the listed ap- proaches, followed by the FSVM, LSSVM, Vapnik’s SVM, logistics re- gression, artificial neural network model, and linear regression model, im- plying that the LS-FSVM is a very promising technique in credit risk assessment. Particularly, the performance of two fuzzy SVM techniques
84 5 A Least Squares Fuzzy SVM Approach to Credit Risk Assessment
(Lin & Wang’s FSVM and LS-FSVM) is better than that of other listed classifiers, implying that the fuzzy SVM classifier may be more suitable for credit risk assessment tasks than other deterministic classifiers, such as LogR.
(2) For Type II accuracy and total accuracy, the LS-FSVM and LSSVM outperforms the other five models, implying the strong capability of least squares version of SVM model in credit risk evaluation. Meantime, the proposed LS-FSVM model seems to be slightly better LSSVM, revealing that the LS-FSVM is a feasible solution to improve the accuracy of credit risk evaluation. Interestedly, the performance of the FSVM is slightly worse than that of the LSSVM, the main reasons leading to this phenome- non are worth exploring further.
(3) From the general view, the LS-FSVM dominates the other six classi- fiers, revealing that the proposed LS-FSVM is an effective tool for credit risk evaluation.