Basis function networks for interpolation of local linear models

Abstract

In this paper, a new algorithm (LOLIMOT) for nonlinear dynamic system identification with local linear models is proposed. The input space is partitioned by a tree-construction algorithm. The local models are interpolated by overlapping local basis functions. The resulting structure is equivalent to a Sugeno-Takagi fuzzy system and a local model network and can therefore be interpreted correspondingly. The LOLIMOT algorithm is very simple, easy to implement, and fast. Moreover, this approach has the following appealing properties: it does not underlie the "curse of dimensionality", it reveals irrelevant inputs, it detects inputs that influence the output mainly in a linear way, and it applies robust local linear estimation schemes. The drawbacks are that only orthogonal cuts are performed and that the local estimation approach may lead to interpolation errors.