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November  2020, 16(6): 2743-2756. doi: 10.3934/jimo.2019078

## Corporate and personal credit scoring via fuzzy non-kernel SVM with fuzzy within-class scatter

 1 School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian 116025, China 2 School of Business Administration and Collaborative Innovation Center of Financial Security, Southwestern University of Finance and Economics, Chengdu 611130, China

* Corresponding author

Received  August 2018 Revised  March 2019 Published  July 2019

Fund Project: The first author is supported by NNSFC grant # 71701035 and # 71831003

Nowadays, the effective credit scoring becomes a very crucial factor for gaining competitive advantages in credit market for both customers and corporations. In this paper, we propose a credit scoring method which combines the non-kernel fuzzy 2-norm quadratic surface SVM model, T-test feature weighting strategy and fuzzy within-class scatter together. It is worth pointing out that this new method not only saves computational time by avoiding choosing a kernel and corresponding parameters in the classical SVM models, but also addresses the "curse of dimensionality" issue and improves the robustness. Besides, we develop an efficient way to calculate the fuzzy membership of each training point by solving a linear programming problem. Finally, we conduct several numerical tests on two benchmark data sets of personal credit and one real-world data set of corporation credit. The numerical results strongly demonstrate that the proposed method outperforms eight state-of-the-art and commonly-used credit scoring methods in terms of accuracy and robustness.

Citation: Jian Luo, Xueqi Yang, Ye Tian, Wenwen Yu. Corporate and personal credit scoring via fuzzy non-kernel SVM with fuzzy within-class scatter. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2743-2756. doi: 10.3934/jimo.2019078
##### References:

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##### References:
Credit Data Sets
 data set # of features Class $C_1$ Class $C_2$ name # of points name # of points German 20 Creditworthy 700 Non-creditworthy 300 Australian 14 Non-default 383 Default 307 Chinese 7 Good credit 58 Bad credit 48
 data set # of features Class $C_1$ Class $C_2$ name # of points name # of points German 20 Creditworthy 700 Non-creditworthy 300 Australian 14 Non-default 383 Default 307 Chinese 7 Good credit 58 Bad credit 48
German Credit Data Test
 model misclassification rate (%) CPU time (s) mean std LOG_REG 23.04 0.35 0.14 FFBP_NN 24.30 0.57 3.83 SVM_GausKer 24.31 0.71 3.30 W2NSVM_GausKer 23.85 0.56 5.72 W2NSVM_QuadKer 23.92 0.81 5.36 FSVMWCS_GausKer 23.42 1.84 6.87 Clu_SVM 24.49 0.71 0.25 Dagher's QSVM 24.26 0.62 4.63 SQSSVM 23.86 0.59 2.82 FNKSVM-FWS 21.36 0.51 4.23
 model misclassification rate (%) CPU time (s) mean std LOG_REG 23.04 0.35 0.14 FFBP_NN 24.30 0.57 3.83 SVM_GausKer 24.31 0.71 3.30 W2NSVM_GausKer 23.85 0.56 5.72 W2NSVM_QuadKer 23.92 0.81 5.36 FSVMWCS_GausKer 23.42 1.84 6.87 Clu_SVM 24.49 0.71 0.25 Dagher's QSVM 24.26 0.62 4.63 SQSSVM 23.86 0.59 2.82 FNKSVM-FWS 21.36 0.51 4.23
Australian Credit Data Test
 model misclassification rate (%) CPU time (s) mean std LOG_REG 13.56 0.27 0.12 FFBP_NN 14.42 1.16 2.72 SVM_GausKer 15.00 1.06 1.30 W2NSVM_GausKer 14.87 0.53 2.73 W2NSVM_QuadKer 14.59 0.46 3.01 FSVMWCS_GausKer 14.63 3.68 3.75 Clu_SVM 14.34 0.53 0.16 Dagher's QSVM 26.42 1.23 1.63 SQSSVM 14.57 0.57 0.80 FNKSVM-FWS 11.96 0.43 1.56
 model misclassification rate (%) CPU time (s) mean std LOG_REG 13.56 0.27 0.12 FFBP_NN 14.42 1.16 2.72 SVM_GausKer 15.00 1.06 1.30 W2NSVM_GausKer 14.87 0.53 2.73 W2NSVM_QuadKer 14.59 0.46 3.01 FSVMWCS_GausKer 14.63 3.68 3.75 Clu_SVM 14.34 0.53 0.16 Dagher's QSVM 26.42 1.23 1.63 SQSSVM 14.57 0.57 0.80 FNKSVM-FWS 11.96 0.43 1.56
Chinese Credit Data Test
 model misclassification rate (%) CPU time (s) mean std LOG_REG 7.56 0.57 0.235 FFBP_NN 24.01 2.25 4.412 SVM_GausKer 13.75 0.90 0.034 W2NSVM_GausKer 12.13 1.89 0.053 W2NSVM_QuadKer 12.07 2.01 0.062 FSVMWCS_GausKer 21.18 2.88 0.063 Clu_SVM 10.96 0.55 0.048 Dagher's QSVM 11.24 2.33 0.087 SQSSVM 10.87 1.96 0.056 FNKSVM-FWS 8.50 0.51 0.083
 model misclassification rate (%) CPU time (s) mean std LOG_REG 7.56 0.57 0.235 FFBP_NN 24.01 2.25 4.412 SVM_GausKer 13.75 0.90 0.034 W2NSVM_GausKer 12.13 1.89 0.053 W2NSVM_QuadKer 12.07 2.01 0.062 FSVMWCS_GausKer 21.18 2.88 0.063 Clu_SVM 10.96 0.55 0.048 Dagher's QSVM 11.24 2.33 0.087 SQSSVM 10.87 1.96 0.056 FNKSVM-FWS 8.50 0.51 0.083
Robustness of Models on Australian Credit Data
 model mean of misclassification rates (%) without outliers with outliers LOG_REG 13.56 17.87 FFBP_NN 14.42 15.94 SVM_GausKer 15.00 15.80 W2NSVM_GausKer 14.87 15.65 W2NSVM_QuadKer 14.59 15.36 FSVMWCS_GausKer 14.63 18.43 Clu_SVM 14.34 17.84 Dagher's QSVM 26.42 53.21 SQSSVM 14.57 15.58 FNKSVM-FWS 11.96 12.61
 model mean of misclassification rates (%) without outliers with outliers LOG_REG 13.56 17.87 FFBP_NN 14.42 15.94 SVM_GausKer 15.00 15.80 W2NSVM_GausKer 14.87 15.65 W2NSVM_QuadKer 14.59 15.36 FSVMWCS_GausKer 14.63 18.43 Clu_SVM 14.34 17.84 Dagher's QSVM 26.42 53.21 SQSSVM 14.57 15.58 FNKSVM-FWS 11.96 12.61
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