A novel complexity reduced Levenberge-Marquardt algorithm: Application to the training of interval type-2 fuzzy systems

Levenberge-Marquardt (LM) algorithm is a well-known optimization technique which has the advantages of the steepest descent and the Gauss-Newton methods. Unfortunately, LM algorithm-based parameter update rules, regardless of being used to tune the parameters of artificial neural networks or neuro-fuzzy systems, require the calculation of inversion of high dimensional matrices. Matrix inversions are generally computationally expensive, and it is not desired in a real-time application where the computation speed is critical. In this paper, using matrix inversion lemma, LM algorithm is modified to avoid matrix inversion calculations, and therefore lessen its computational burden. The proposed algorithm is compared with the conventional LM algorithm for the training of interval type-2 fuzzy logic systems in terms of its speed. Extensive simulation results demonstrate that that the proposed novel method can increase the speed of LM algorithm by 50% while remaining the same performance.