Backpropagation learning algorithm

B. Walczak, Neural networks with robust backpropagation learning algorithm. Anal. Chim. Acta, 322 (1996) 21-30. 

Riedmiller, M. Braun, H. (1993). A (Greet adaptive method for faster backpropagation learning the Rprop algorithm. In Proceedings of the IEEE International Conference on Neural Networks (ICNN 93). (ed. Ruspini H.), pp. 586-91. 

Multilayer perceptrons are used nowadays in connection with the backpropagation algorithm. In analytics, more than 90% of applications are based on this learning algorithm. A first approach for this forward directed learning algorithm was made by Werbos (1974). This was further developed by McClelland and Rumelhart [11] (Figure 8.12). 

Several different types of ANN are available and the most popular is the backpropagation approach. In this procedure, input patterns presented to the input layer, for example, signals from an array of chemical sensors, generate a flow of activation to the output layer. Errors in the output are then fed back to the input layer to modify the weights of the interconnections. It should be emphasized that backpropagation does not describe a network but represents a learning algorithm. In this way, the network can be trained with known parameters, such as sensor array responses to sets of known chemicals. 

This is useful for pattern recognition. The parameter / influences the nonlinearity of the hidden layer transfer function. The training of the NN is then based on the feedforward and backpropagation algorithm, in which the weighing factors Wn are adjusted during the NN learning in order to minimize the difference between the desired output D and the actual output Y. 

The backpropagation (BP) network is the most commonly used FNN. Its structure is the same as that shown in Fig. 2.6 except that it can contain more than one hidden layer. A BP algorithm is used for BP network learning, which is described in detail below. 

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