Reference point logistic classification

This article describes a new method for pattern recognition. Reference point logistic classification uses normalized exponential functions of squared distance from reference points in the feature space to determine approximately piecewise linear classification boundaries. Reference points and other parameters are determined by minimizing a smoothed training risk; i.e., the expected loss based on a smoothed nonparametric estimate of the distribution. A general loss function can be specified. The risk is minimized by a stochastic gradient algorithm, a technique common in neural networks. The number of reference points and the smoothing parameter are selected, using test data or cross-validation, to provide an appropriate level of complexity and avoid overfitting. The method performs well in comparison with 22 other classification methods on ten data sets from the European (ESPRIT) project StatLog.