A Regularized Monotonic Fuzzy Support Vector Machine Model for Data Mining With Prior Knowledge

Incorporating prior knowledge into data mining is an interesting but challenging problem, and this study proposes a novel fuzzy support vector machine (SVM) model to explore this issue. It considers the fact that in many applications, each input point may not be exactly labeled as one particular class, and thus, it applies a fuzzy membership to each input point. It also utilizes expert knowledge concerning the monotonic relations between the response and predictor variables, which is represented in the form of monotonicity constraints. We formulate the classification problem of a monotonically constrained fuzzy SVM, called a monotonic FSVM, derive its dual optimization problem, and theoretically analyze its monotonic property. The Tikhonov regularization method is further applied to ensure that the solution is unique and bounded. A new measure, i.e., the frequency monotonicity rate, is proposed to evaluate the ability of the model to retain the monotonicity. The results of the experiments on real-world and synthetic datasets show that this method, which considers different contributions of each data and the prior knowledge of the monotonicity, has a number of advantages with regard to predictive ability and retaining monotonicity over the original FSVM and SVM models when applied to classification problems.