Introduction
The antecedents of Neural Networks began with many studies and researches about different areas, like psychology, physics, biology and neurophysiology, nevertheless the first approach to the current vision of neural networks began in the 1940s with Walter Pitts and Warren McCulloch, proposing a neural network to compute arithmetic problems.
The Artificial neural networks (ANN) have a biological inspiration, even though the structure and functions of the biologic neurons are not fully known, and what is known is very complex, there are general functions and advantages that can be analogous in an artificial network. The Neurons have between approximately 10ˆ11 interconnections conforming the brain, and the main aspects of its structure and function consist in the dendrites, the cell body and the axon. The cell body works as a processor, making a sum of depending on the thresholds for many signals, which comes from the different dendrites that carries information in an electrical form. The axon is a long fiber that allows the neuron to send a signal in electrical form to another neurons, conforming the process called synapsis. All these mechanisms imply electrical and chemical reactions, but is this big interaction between neurons that makes the network works to solve problems and improve the capabilities of the organisms, like the memory, learning, and all the control of the biological functions.
Perceptron
The first Structure of Neural Network was the perceptron ( see the images attached). It consist of an input vector P size R, a weight matrix W size S ×R, a bias vector b size S × 1, a net input n and the output vector a size S×1, this network uses a hardlim transfer function, that means that the value at the output can be just 1 or 0.
The learning rule of the perceptron is shown in the following equations: w_new = w_old + epT b_new = b_old + e e = t − a
Where e is the error of that epoch and t is the expected output for that pattern p
ADALINE
The structure of the ADALINE Neural network was developed to solve problems that were impossible to solve for the perceptron, the main difference is the transfer function and the corresponding change in the learning rule. The diagram of this neural network is shown in the pictures. The learning rule of the ADALINE neural Network is shown in the following equations:
w_new = w_old + 2αepT b_new = b_old + 2eα e = t − a Where α is the learning rate and must be higher than cero and lower than 1/λmax
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