Nonparametric regression analysis achieved with topographic maps developed in combination with projection pursuit learning: an application to density estimation and adaptive filtering of grey-scale images

Abstract

A novel approach to nonparametric regression analysis using topographic maps is proposed. The maps are trained with the extended maximum entropy learning rule (eMER) in combination with projection pursuit regression (PPR) learning. Rather than a single map, several maps are developed along optimally chosen projection directions in the input space. In this way, the regression performance improves in the case of sparsely sampled input spaces. We explore two applications of the eMER/PPR combination: (1) probability density estimation from pilot estimates and (2) adaptive filtering of grey-scale images. The first case is used as a testbed for comparing different, both classic and neural network-based, regression techniques. The results show that our eMER/PPR combination yields a superior regression performance for small data sets. In the second case, the regression model is trained on a noisy subimage. The model obtained after training reduces the noise content of the full image by more than 20 dB.