Introduction: The Basic Neuron
The Basic/Single Neuron is a model based on the biological neuron which is found in the brain. The biological neuron works in the following way:
It recieves inputs along the "dendrites" and add's them up. The neuron shall then produce an output if the sum is greater than the "threshold value". The dendrites are connected to the output's of other neurons via special junctions known as "synapses". The synapses alter the effectiveness with which the signal is transmitted.
Obviously this is a very rough summary of what the biological neuron does, and since we are not doing a tutorial on the brain we need not delve any deeper into those topics. As mentioned earlier this rough summary provides us with our Single Neuron model. Hence our Basic Neuron can be summed up in the following way.
The Neuron's output is either on or off.
The output depends only on the inputs. A certain number must be on at any one time in order to make the neuron fire.
Each input has a multiplicative weight on it into the neuron. A bigger weight represents a strong signal being transmitted, and a lower weight represents a weak signal being transmitted.
So our basic model performs a weighted sum on its inputs and compares this to its internal threshold level. If the the threshold is exceeded the neuron shall turn on. This system is known as a feedforward one. We can represent this in a pictorial fashion below.
Now that we have our model of the neuron, we must go about formulaitng it mathematically so we can put it into practice. Looking back at our model the neuron calculates the weighted sum of its inputs which have n inputs, and n associated weights on those input lines; ie. it takes the first input and multiplies it by the weight on that input line, and so on for each input. Hence we can write:
total input = (weight on line 1 x input on 1) + (weight on line 2 x input on 2) + ... + (weight on line n x input on n)
ftg= w1x1 + w2x2 + ... + wnxn
Now this sum must have the threshold value (lets say ø)within the neuron subtracted from it. If the resulting value is greater than zero then we output a 1, otherwise output a 0. The thresholding function is shown below, it is a "step" function as you can see.
Finally we shall call our output y, we get:
y = fh[ t - ø ] where,
fh(x) is known as the activation function:
fh(x) = 1 , x > 0
fh(x) = 0 , x < 0
We now have our basic model of the neuron and in the next section there is a applet demonstrating it. At the moment you may be wondering, what is the point of this model, it does nothing? Not so! Yes it is a simple, but it allows us to investigate the arrangement of neuron connections further and what they can do.
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Next:- Example 1: The Basic Neuron
