A least squares fuzzy SVM approach to credit risk assessment

The support vector machine (SVM) is a class of powerful classification tools that have many successful applications. Their classification results usually belong to either one class or the other. But in many real-world applications, each data point no more exactly belongs to one of the two classes, it may 70% belong to one class and 30% to another. That is, there is a fuzzy membership associated with each data. In such an environment, fuzzy SVM (FSVM), which treats every sample as both positive and negative classes with the fuzzy membership, were introduced. In this way the FSVM will have more generalization ability, while preserving the merit of insensitive to outliers. Although the FSVM has good generalization capability, the computational complexity of the existing FSVM is rather large because the final solution is obtained from solving a quadratic programming (QP) problem. For reducing the complexity, this study proposes a least squares method to solve FSVM. In the proposed model, we consider equality constraints instead of inequalities for the classification problem with a formulation in a least squares sense. As a result the solutions follow directly from solving a set of linear equations instead of QP thus reducing the computational complexity greatly relative to the classical FSVM. For illustration purpose, a real-world credit risk assessment dataset is used to test the effectiveness of the LS-FSVM model.