Locally Weighted Interpolating Growing Neural Gas

Abstract

In this paper, we propose a new approach to function approximation based on a growing neural gas (GNG), a self-organizing map (SOM) which is able to adapt to the local dimension of a possible high-dimensional input distribution. Local models are built interpolating between values associated with the map's neurons. These models are combined using a weighted sum to yield the final approximation value. The values, the positions, and the "local ranges" of the neurons are adapted to improve the approximation quality. The method is able to adapt to changing target functions and to follow nonstationary input distributions. The new approach is compared to the radial basis function (RBF) extension of the growing neural gas and to locally weighted projection regression (LWPR), a state-of-the-art algorithm for incremental nonlinear function approximation.