NETWORK ADALINE

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Introduction

Adaline (Linear Adaptive Element) is a type of artificial red neuron developed by Professor Bernard Windrow and Marcian E. Hoff in 1960.

Windrow focused on adaptive signal processing, adaptive control systems and adaptive neural networks, ie systems that have the ability to learn and improve their behavior in contact with the environment.

Characteristics

1. Adaline differs from the simple sensor because it is composed of a single neuron.
2. Its transfer function is linear or pureline.
3. Analog information processing, both input and output with linear or sigmoidal activation function.
4. Solve linearly separable problems.

Network architecture

They consist of a single neuron with an input layer and only one output.

Fig. 1. Network Adaline architecture [1].

• The values X1, x2 ... Xn are the inputs of the neuron.
• The values of W1, W2, .... Wn are the weights associated with the inputs.
• And the value of the activation threshold is defined by θ.

The activation function is given by:

Rules of Learning

The learning algorithm applied is that of the minimum error rule, mean square (LMS) or Windrow-Hoff rule.

The way to reduce this global error is to modify the values of the weights by processing each input, iteratively, by means of the rule of the descent of the gradient. Assuming we have an alpha learning constant:

That will be the expression that we will use for each entry to modify the weights. The training process adjusts the weights associated with each input to minimize the error between the outputs obtained and the desired outputs. Therefore, the neuron is expected to "learn" about the problem and can make decisions for other cases of inputs that were not presented during training.

Algorithm

1. Initialization of weights
2. A pattern of desired inputs and outputs is applied
3. It computes the linear output that is obtained from the network
4. The error committed for said pattern
5. The connections are updated using the equation previously obtained
6. Repeat steps 2-5 for all training patterns
7. If the quadratic error is an acceptable small value it ends the process but returns to step 2

References:

López, R. F., & Fernandez, J. M. F. (2008). Las redes neuronales artificiales. Netbiblo.

Osiro, L., Lima, R. H. P., Junior, F. R. L., & Carpinetti, L. C. R. (2013). PROPOSTA DE USO DE REDES NEURAIS ARTIFICIAIS EM UMA MATRIZ DE PORTFÓLIO DE COMPRAS. XXXIII Encontro Nacional de Engenharia de Producao, Salvador, Bahia, Brasil.

Salavert, I. R., & Graciani, M. A. F. (1995). Vida artificial (Vol. 10). Univ de Castilla La Mancha.