A Generalization of the Local Estimator Technique

Nearest neighbor techniques are commonly used in cluster analysis and statistics either to classify objects into a predefined number of categories or to assess the value of a predictand based on a given set of characteristics or predictors. These techniques are specially useful if the relationship between the variables is highly nonlinear. In most studies, however, the distance measure is adopted a priori and applied to the whole set of observations. In this paper, on the contrary, a general procedure to find an adaptive metric that combines a local variance reducing technique and a linear embedding of the observation space into an appropriate Euclidean space is proposed. In order to illustrate the application of this technique, three applications are presented. The first one deals with the prediction of local discharge characteristics from catchment properties, the second addresses a land cover classification using the LANDSAT bands as predictors, and the third deals with a simple one day flood forecasting problem. The results of the study suggest that the goodness of the fit can be improved substantially.