Lazy learning for nonparametric locally weighted regression

Abstract

In this study, a newly designed local model called locally weighted regression model is proposed for the regression problem. This model predicts the output for a newly submitted data point. In general, the local regression model focuses on an area of the input space specified by a certain kernel function (Gaussian function, in particular). The local area is defined as a region enclosed by a neighborhood of the given query point. The weights assigned to the local area are determined by the related entries of the partition matrix originating from the fuzzy C-means method. The local regression model related to the local area is constructed using a weighted estimation technique. The model exploits the concept of the nearest neighbor, and constructs the weighted least square estimation once a new query is provided given. We validate the modeling ability of the overall model based on several numeric experiments.