Abstract-Software defect prediction strives to improve software quality and testing efficiency by constructing predictive classification models from code attributes to enable a timely identification of fault-prone modules. Several classification models have been evaluated for this task. However, due to inconsistent findings regarding the superiority of one classifier over another and the usefulness of metric-based classification in general, more research is needed to improve convergence across studies and further advance confidence in experimental results. We consider three potential sources for bias: comparing classifiers over one or a small number of proprietary data sets, relying on accuracy indicators that are conceptually inappropriate for software defect prediction and cross-study comparisons, and, finally, limited use of statistical testing procedures to secure empirical findings. To remedy these problems, a framework for comparative software defect prediction experiments is proposed and applied in a large-scale empirical comparison of 22 classifiers over 10 public domain data sets from the NASA Metrics Data repository. Overall, an appealing degree of predictive accuracy is observed, which supports the view that metric-based classification is useful. However, our results indicate that the importance of the particular classification algorithm may be less than previously assumed since no significant performance differences could be detected among the top 17 classifiers.

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In this paper, we study the performance of various state-of-the-art classification algorithms applied to eight real-life credit scoring data sets. Some of the data sets originate from major Benelux and UK financial institutions. Different types of classifiers are evaluated and compared. Besides the well-known classification algorithms (eg logistic regression, discriminant analysis, k-nearest neighbour, neural networks and decision trees), this study also investigates the suitability and performance of some recently proposed, advanced kernel-based classification algorithms such as support vector machines and least-squares support vector machines (LS-SVMs). The performance is assessed using the classification accuracy and the area under the receiver operating characteristic curve. Statistically significant performance differences are identified using the appropriate test statistics. It is found that both the LS-SVM and neural network classifiers yield a very good performance, but also simple classifiers such as logistic regression and linear discriminant analysis perform very well for credit scoring.

Abstract. In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LS-SVMs), a least squares cost function is proposed so as to obtain a linear set of equations in the dual space. While the SVM classifier has a large margin interpretation, the LS-SVM formulation is related in this paper to a ridge regression approach for classification with binary targets and to Fisher's linear discriminant analysis in the feature space. Multiclass categorization problems are represented by a set of binary classifiers using different output coding schemes. While regularization is used to control the effective number of parameters of the LS-SVM classifier, the sparseness property of SVMs is lost due to the choice of the 2-norm. Sparseness can be imposed in a second stage by gradually pruning the support value spectrum and optimizing the hyperparameters during the sparse approximation procedure. In this paper, twenty public domain benchmark datasets are used to evaluate the test set performance of LS-SVM classifiers with linear, polynomial and radial basis function (RBF) kernels. Both the SVM and LS-SVM classifier with RBF kernel in combination with standard cross-validation procedures for hyperparameter selection achieve comparable test set performances. These SVM and LS-SVM performances are consistently very good when compared to a variety of methods described in the literature including decision tree based algorithms, statistical algorithms and instance based learning methods. We show on ten UCI datasets that the LS-SVM sparse approximation procedure can be successfully applied.

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C redit-risk evaluation is a very challenging and important management science problem in the domain of financial analysis. Many classification methods have been suggested in the literature to tackle this problem. Neural networks, especially, have received a lot of attention because of their universal approximation property. However, a major drawback associated with the use of neural networks for decision making is their lack of explanation capability. While they can achieve a high predictive accuracy rate, the reasoning behind how they reach their decisions is not readily available. In this paper, we present the results from analysing three real-life credit-risk data sets using neural network rule extraction techniques. Clarifying the neural network decisions by explanatory rules that capture the learned knowledge embedded in the networks can help the credit-risk manager in explaining why a particular applicant is classified as either bad or good. Furthermore, we also discuss how these rules can be visualized as a decision table in a compact and intuitive graphical format that facilitates easy consultation. It is concluded that neural network rule extraction and decision tables are powerful management tools that allow us to build advanced and userfriendly decision-support systems for credit-risk evaluation.

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