Construction and Application Research of Isomap-RVM Credit Assessment Model

Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 197258, 7 pages http://dx.doi.org/10.1155/2015/197258 Research Article Construction and Application Research of Isomap-RVM Credit Assessment Model Guangrong Tong and Siwei Li School of Economics and Management, Wuhan University, Wuhan 430072, China Correspondence should be addressed to Guangrong Tong; Received 5 November 2014; Accepted 10 January 2015 Academic Editor: Honglei Xu Copyright © 2015 G. Tong and S. Li. 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. Credit assessment is the basis and premise of credit risk management systems. Accurate and scientific credit assessment is of great significance to the operational decisions of shareholders, corporate creditors, and management. Building a good and reliable credit assessment model is key to credit assessment. Traditional credit assessment models are constructed using the support vector machine (SVM) combined with certain traditional dimensionality reduction algorithms. When constructing such a model, the dimensionality reduction algorithms are first applied to reduce the dimensions of the samples, so as to prevent the correlation of the samples’ characteristic index from being too high. Then, machine learning of the samples will be conducted using the SVM, in order to carry out classification assessment. To further improve the accuracy of credit assessment methods, this paper has introduced more cutting-edge algorithms, applied isometric feature mapping (Isomap) for dimensionality reduction, and used the relevance vector machine (RVM) for credit classification. It has constructed an Isomap-RVM model and used it to conduct financial analysis of China’s listed companies. The empirical analysis shows that the credit assessment accuracy of the Isomap-RVM model is significantly higher than that of the Isomap-SVM model and slightly higher than that of the PCA-RVM model. It can correctly identify the credit risks of listed companies. 1. Introduction By constructing an accurate and reliable credit assessment model, we can conduct an in-depth analysis of the financial data of listed companies and identify the financial risks of such companies. This is of great significance to the operational decisions of shareholders, corporate creditors, and management. Along with the development of large data methods, the theory of applying machine learning methods to construct credit assessment models has become increasingly reliable. Machine learning methods are superior to traditional multivariate discriminant analysis methods and logistic discriminant analysis models, when processing any data subject to less stringent hypothetical restrictions and dealing with nonlinear relationships. At present, commonly used machine learning methods with good data classification results include the neural network (NN) [1] and the support vector machine (SVM). Odom and Sharda [2] built an early warning model for financial crises. They did so by applying the neural network and comparing this model with the Fisher multivariate discriminant analysis model. The research results showed that the artificial neural network has higher prediction accuracy and robustness. However, the neural network has methodological defects, such as slow convergence rate, overfitting, and falling into local minima [3, 4]. Later, Cortes and Vapnik [5] proposed the vector machine method, which is based on the theory of statistical machine learning. This method laid stress on structural risk minimization and is able to effectively overcome the defects of the neural network. Min and Lee [6] applied the SVM to build a financial early warning model for the purpose of corporate bankruptcy prediction. The results showed that the SVM has higher discriminant analysis accuracy than BP neural network, MDA, and logit models. However, SVM has the following main defects: the penalty parameter C must be determined in the model building process, and the selection of kernel function must comply with “Mercer’s theorem” [7]. For these reasons, this paper suggests using a relevance vector 2 machine (RVM) to overcome the defects of SVM. RVM is another efficient supervised learning method proposed by Tipping [8]. By applying this method to conduct machine learning under the Bayesian theory, the model obtained will be sparser than with SVM, and the result probability output can also be obtained. While properly maintaining all the advantages of SVM, this method has reduced the inaccurate assignment of key parameters, broadened the application scope of vector machines, provided a greater degree of freedom, and effectively overcome the defects of SVM [9]. This will help to improve the accuracy of vector machine classification. In credit risk assessment samples, there tends to be a close correlation between the selected financial risk characteristic indices. High dimensionality and high correlation of the sample characteristic indices may have a strong impact on the accuracy of risk assessment. Therefore, a data dimensionality reduction method is required for the pretreatment of the sample indices, so as to reflect the main features of the data as much as possible and reduce correlation between the characteristic indices. At present, the principal component analysis method (PCA) is one of the most widely used methods [10]. However, as a linear dimensionality reduction method, PCA may not achieve satisfactory dimensionality reduction results when applied to nonlinear data. Therefore, this paper attempts to apply a nonlinear dimensionality reduction method—isometric mapping (Isomap)—to conduct dimensionality reduction pretreatment on the sample data. Isomap is a nonlinear manifold learning algorithm proposed by Tenenbaum et al. [11]. By seeking low-dimensional embedding among high-dimensional manifolds, this algorithm has maintained low-dimensional embedding in the neighborhood structure between high-dimensional manifold data points, while producing excellent robustness and global optimality. Lin et al. [12] used the Isomap-SVM, PCA-SVM, and SVM separately to conduct risk assessment classification of more than one hundred listed Taiwan companies. It proved that Isomap-SVM has the highest prediction accuracy. This research showed that, in the process of nonlinear data classification, Isomap can improve accuracy through reasonable dimensionality reduction. Ribeiro et al. [13] constructed a Semi-Supervised Isomap model with Isomap and SVM. They used the Semi-Supervised Isomap model, SVM, RVM, and KNN separately to conduct bankruptcy prediction of more than one thousand industrial French companies. The results showed that the classification accuracy of Semi-Supervised Isomap model is comparable to SVM and RVM. But in the study they did not propos (...truncated)