The refinement of models with the aid of the fuzzy k-nearest neighbors approach

In this paper, we propose a new design methodology that supports the development of hybrid incremental models. These models result through an iterative process in which a parametric model and a nonparametric model are combined so that their underlying and complementary functionalities become fully exploited. The parametric component of the hybrid model captures some global relationships between the input variables and the output variable. The nonparametric model focuses on capturing local input-output relationships and thus augments the behavior of the model being formed at the global level. In the underlying design, we consider linear and quadratic regression to be a parametric model, whereas a fuzzy <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest neighbors model serves as the nonparametric counterpart of the overall model. Numeric results come from experiments that were carried out on some low-dimensional synthetic data sets and several machine learning data sets from the University of California-Irvine Machine Learning Repository.