The Signed Distance Function: A New Tool for Binary Classification

Abstract

From a geometric perspective most nonlinear binary classification algorithms, including state of the art versions of Support Vector Machine (SVM) and Radial Basis Function Network (RBFN) classifiers, and are based on the idea of reconstructing indicator functions. We propose instead to use reconstruction of the signed distance function (SDF) as a basis for binary classification. We discuss properties of the signed distance function that can be exploited in classification algorithms. We develop simple versions of such classifiers and test them on several linear and nonlinear problems. On linear tests accuracy of the new algorithm exceeds that of standard SVM methods, with an average of 50% fewer misclassifications. Performance of the new methods also matches or exceeds that of standard methods on several nonlinear problems including classification of benchmark diagnostic micro-array data sets.