The Study on Risk Rating Model of Commercial Bank Credit Based on SVM
According to the basic theories of Logit regression analysis and support vector machine (SVM), this article involves improved binary classification combination algorithm to increase the accuracy. In addition, using financial data of listed companies to te
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Abstract According to the basic theories of Logit regression analysis and support vector machine (SVM), this article involves improved binary classification combination algorithm to increase the accuracy. In addition, using financial data of listed companies to test this improved model, it shows a better way of classification. When applying this model, there are some innovations: 1. Choose optimized composite indicator as a variable through principal component analysis and get more information; 2. Introduce Logit parameter model to the quadratic to increase prediction accuracy; 3. Put forward a combination of improved Logit model with SVM to increase prediction accuracy. This paper is supported by the Industrial Safety Engineering (239010522).
1 Basic Model Analysis 1.1 Logit Model Define probability of default as: T
eaþb xi pi ¼ T 1 þ eaþb xi
ð1Þ
Logit Model [1] is a linear function about the natural logarithm of the ratio of default: M. Li Center for Industrial Security Research, Beijing Jiaotong University, Beijing, China Z. Zhang (&) R. Bai School of Science, Beijing Jiaotong University, Beijing, China e-mail: [email protected]
Z. Wen and T. Li (eds.), Practical Applications of Intelligent Systems, Advances in Intelligent Systems and Computing 279, DOI: 10.1007/978-3-642-54927-4_76, Springer-Verlag Berlin Heidelberg 2014
805
806
M. Li et al.
ln
pi ¼ a þ bT xi 1 pi
ð2Þ
1.2 Support Vector Machine Support Vector Machine (SVM) was put forward by a Russian scholar called Vapnik, that a new way on machine learning is based on the statistics theories, which has already been widely applied on classification [2, 3]. Algorithm on SVM Classifier: 1. Suppose the known training set called T as follows: T ¼ fðx1 ; y1 Þ; . . .; ðxl ; yl Þg;
x i 2 Rn ;
yi 2 fþ1; 1g;
i ¼ 1; 2. . .; l
ð3Þ
2. Choose kernel function Kðx; x0 Þ and appropriate penalty parameter C to set up the optimization problem to find the best solution a ¼ ða1 ; . . .; al ÞT min a
s:t:
l X l l X 1X yi yj ai aj K xi ; xj aj 2 i¼1 j¼1 j¼1 l X
ð4Þ
y i ai ¼ 0
i¼1
0 ai C; i ¼ 1; . . .; l 3. Choose one component aj of a , which is between zero and C, and calculate the equation below. b ¼ y j
l X
yi ai Kðxi ; xj Þ
ð5Þ
i¼1
4. Attain a decision function recorded as: " # l X yi ai Kðxi ; xÞ þ b f ðxÞ ¼ sgn
ð6Þ
i¼1
1.3 Comparison and Analysis Between Logit Model and SVM According to the form above, these two algorithms can be complementary. Based on this point, the combined model between Logit and SVM is put forward (Table 1).
The Study on Risk Rating Model of Commercial Bank Credit Based on SVM
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Table 1 Comparison and analysis between logit model and SVM Advantage
Disadvantage
Logit model (1) No requirement of whether data If there is something wrong with data, shows a normal distribution; the result can be influenced greatly (2) decide degree of influence of because this model completely relies different factors; (3) evaluate on data quickly; (4) be good at large amount of samples SVM (1) Apply kern
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