Spatially adaptive binary classifier using B-splines and total variation penalty

This paper reports on our study of a binary classifier based on B-splines and the total variation penalty. The decision boundary of the proposed classifier is obtained using a variant of the hinge loss function. We restrict our focus to a two-dimensional predictor space to analyse the theoretical behaviour of the spline decision curve estimator. Theoretical investigation shows that the proposed estimator achieves the same optimal rate of convergence as in nonparametric regression estimation under some regularity conditions. The proposed method is implemented with a coordinate descent algorithm. Numerical studies using real and simulated data are conducted to complement the theoretical results. The results show that the proposed estimator adapts well to the data and yields more accurate predictions than other existing support vector machine methods. We also discuss directions for future research.