Nonlinear Support Vector Machine Visualization for Risk Factor Analysis Using Nomograms and Localized Radial Basis Function Kernels

Nonlinear classifiers, e.g., support vector machines (SVMs) with radial basis function (RBF) kernels, have been used widely for automatic diagnosis of diseases because of their high accuracies. However, it is difficult to visualize the classifiers, and thus difficult to provide intuitive interpretation of results to physicians. We developed a new nonlinear kernel, the localized radial basis function (LRBF) kernel, and new visualization system visualization for risk factor analysis (VRIFA) that applies a nomogram and LRBF kernel to visualize the results of nonlinear SVMs and improve the interpretability of results while maintaining high prediction accuracy. Three representative medical datasets from the University of California, Irvine repository and Statlog dataset-breast cancer, diabetes, and heart disease datasets-were used to evaluate the system. The results showed that the classification performance of the LRBF is comparable with that of the RBF, and the LRBF is easy to visualize via a nomogram. Our study also showed that the LRBF kernel is less sensitive to noise features than the RBF kernel, whereas the LRBF kernel degrades the prediction accuracy more when important features are eliminated. We demonstrated the VRIFA system, which visualizes the results of linear and nonlinear SVMs with LRBF kernels, on the three datasets.