Abstract
Locally linear model tree (LoLiMoT) and piecewise linear network (PLN) learning algorithms are two approaches in local linear neurofuzzy modeling. While both methods belong to the class of growing tree learning algorithms, they use different logics. PLN learning relies on training data, it needs rich training data set and no division test, so it is much faster than LoLiMoT, but it may create adjacent neurons that may lead to singularity in regression matrix. On the other hand, LoLiMoT almost always leads to acceptable output error, but it often needs more rules. In this paper, to exploit the complimentary performance of both algorithms piecewise linear model tree (PiLiMoT) learning algorithm is introduced. In essence, PiLiMoT is a combination of LoLiMoT and PLN learning. The initially proposed algorithm is improved by adding the ability to merge previously divided local linear models, and utilizing a simulated annealing stochastic decision process to select a local model for splitting. Comparing to LoLiMoT and PLN learning, our proposed improved learning algorithm shows the ability to construct models with less number of rules at comparable modeling errors. Algorithms are compared through a case study of nonlinear function approximation. Obtained results demonstrate the advantages of combined modified method.
Highlights
System modeling plays an important role in many areas such as control, expert systems, communication, and so forth
The local linear model tree algorithm proposed by Nelles and Isermann [5, 19, 20], is based on the idea to approximate a nonlinear function with piecewise linear models [5]
This new algorithm improved in two ways: (1) the ability to merge previously divided local linear models is added, and (2) a simulated annealing stochastic decision process is responsible to select a local model for splitting
Summary
System modeling plays an important role in many areas such as control, expert systems, communication, and so forth. Neurofuzzy approach, in contrast to pure neural or fuzzy methods, possesses both of their advantages: it brings the low-level learning and computational power of neural networks into fuzzy systems and provides the highlevel human-like thinking in reasoning of fuzzy systems into neural networks [3] This approach involves two major phases, structure identification and parameter estimation [4]. LoLiMoT and PLN learning algorithms are two approaches in structure optimization based on local linear modeling, which use different algorithms in their training phase. Because of some drawbacks in LoLiMoT and PLN, in this paper, a new learning algorithm is introduced for nonlinear approximation This method is a modified combination of these two main approaches in local linear modeling. It takes suitable error from LoLiMoT and suitable number of neurons from PLN that leads to efficient network which is applicable for function approximation.
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