ADALINE

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ADALINE (Adaptive Linear Neuron or later Adaptive Linear Element) is a single layer neural network. It was developed by Professor Bernard Widrow and his graduate student Ted Hoff at Stanford University in 1960. It is based on the McCulloch-Pitts neuron. It consists of a weight, a bias and a summation function.

Definition

Adaline is a single layer neural network with multiple nodes where each node accepts multiple inputs and generates one output. Given the following variables:

• x is the input vector
• w is the weight vector
• n is the number of nodes
• θ some constant
• y is the output

then we find that the output is . If we further assume that

• x_{n + 1} = 1
• w_{n + 1} = θ

then the output reduces to the dot product of x and w

Learning Algorithm

Let us assume:

• η is the learning rate (some constant)
• d is the desired output
• o is the actual output

then the weights are updated as follows . The ADALINE converges to the least squares error which is E = (d − o)². For a more comprehensive proof, see Adaline (Adaptive Linear)

Bibliography

Delta Learning Rule: ADALINE
Adaline (Adaptive Linear)
Perceptron and ADALINE