Piecewise Linear Model Tree: A modified combination of two learning algorithms for neuro-fuzzy models

Abstract

Locally Linear Model Tree (LOLIMOT) and Piecewise Linear Network (PLN) learning algorithms are two approaches in local linear modeling use different algorithm in each part of training phase. PLN learning is more depended on training data than LOIMOT and needs rich training data set. In PLN learning no division test is needed and it causes this algorithm to be much faster than LOLIMOT, but it may create adjacent neurons that would lead to singularity in regression matrix. In LOLIMOT, because of regular splitting of input space, this problem does not occur and always it leads to acceptable output error, but needs large number of neuron. Therefore, PILIMOT learning algorithm is introduced as modified combination of these two main Locally Linear approaches. This new method takes suitable error and neuron number from both of algorithms and leads to efficient network which is applicable to identify all functions. Simulation results show the advantage and behavior of new method.