Laevenberg-Marquardt Training Method

I.INTRODUCTION
The advent of high speed global communication ranks as one of the important developments of human civilization from the second half of twentieth century to till date. This was only feasible with the introduction of digital communication systems. Today there is a need for high speed and efficient data transmission over the communication channels. It is a challenging task for the engineers and scientists to provide a reliable communication service by utilizing the available resources effectively in-spite many factors that distort the signal. The main objective of the digital communication system is to transmit symbols with minimum errors. The high speed digital communication requires large bandwidth, which is not possible due to

Its transfer function is inverse to the transfer function of the associated channel [4], is able to reduce the error causes between the desired and estimated signal. This is achieved through a process of training. There are various training methods used to train a neural network. In this paper we have considered two training methods i.eLevenberg- Marquardt training method and scaled conjugate training method.
A. LEVENBERG-MARQUARDT TRAINING METHOD:
The Levenberg–Marquardt algorithm provides a numerical solution to the problem of minimizing a nonlinear function. It is fast and has stable convergence. In the artificial neural-networks field, this algorithm is suitable for training small- and medium-sized problems.
The Levenberg–Marquardt algorithm blends the steepest descent method and the Gauss–Newton algorithm. Fortunately, it inherits the speed advantage of the Gauss–Newton algorithm and the stability of the steepest descent method. It’s more robust than the Gauss–Newton algorithm
Although the Levenberg–Marquardt algorithm tends to be a bit slower than Gauss–Newton algorithm(in convergent situation), it converges much faster than the steepest descent

When combination coefficient μ is very large, Equation 12.25 approximates to Equation 12.4 and the steepest descent method is used.
B.SCALED CONJUGATE TRAINING METHOD:
SCG uses second order information from the neural network but requires only O(N) memory usage, where N is the number of weights in the network.
The Conjugate Gradient Methods are also based on the general optimization strategy, but chooses the search direction and the step size more carefully by using information from the second order approximation (6a)
Where w: Weight vector
E(w):Global error function