Components of an artificial neuron
Inputs, xi:
Typically, the input values are external stimulii from the environment
or come from the outputs of other artificial neurons. They can be discrete
values from a set, such as {0,1}, or real-valued numbers.
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Weights, wi:
The first thing an artificial neuron does is to compute the weighted
sum of its inputs (i.e., the inner product between the input pattern
and the connection strengths). The weights are real-valued numbers that
determine the contribution of each input.
The goal of neural network training algorithms is to determine the "best"
possible set of weight values for the problem under consideration. Finding
the optimal set is often a trade-off between computation time, minimizing
the network error, and maintaining the network's ability to generalize.
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Threshold, u:
The threshold is a real number that is subtracted from the weighted sum
of the input values. Sometimes the threshold is called a bias value.
In this case, the real number is added to the weighted sum. For simplicity,
the theshold can be regarded as another input / weight pair, where w0
= u and x0 = -1.
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Activation Function, f:
The activation function for the original McCulloch-Pitts neuron was the
unit step function. However, the artificial neuron model has since been
expanded to include other functions such as the sigmoid, piecewise linear,
and Gaussian.
The identity function is the simplest possible activation function;
the resulting unit is called a linear associator.
The activation functions available in this applet are shown in Table
1.
| Unit Step |
 |
 |
| Sigmoid |
 |
 |
| Piecewise Linear |
 |
 |
| Gaussian |
 |
 |
|
Identity
|
 |
f (x) = x |
Table 1: Activation Functions
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Neuron Output, y:
The artificial neuron computes its output according to the equation shown
below. This is the result of applying the activation
function to the weighted sum of the inputs,
less the threshold. This value can be discrete
or real depending on the activation function used.
Once the output has been calculated, it can be passed to another neuron
(or group of neurons) or sampled by the external environment.
The interpretation of the neuron output depends upon the problem under
consideration. For example, in pattern classification, an output of 1 might
imply the input belongs to a certain class, whereas an output of 0 might
mean that it doesn't.
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