Neural Networks journal Special

Getting started with neural networks - the single neuron
Poem as Neural Network Neural networks can model the relationship between input variables and output variables. A neural networks is built of artificial neurons which are connected. For the start it's the best to look at the architecture of a single neuron.
They are motivated by the architecture and functionality of neuron cells, of which brains are made of.  The neurons in the brain can receive multiple input signals, process them and fire a signal which again can be input to other neurons. The output is binary, so the signal can be fired (1) or not be fired (0) which depends on the input.
The artificial neuron has some inputs which we call \(x_1, x_2, ... x_p\). There can be an additional input \(x_0\), which is always set to \(1\) and is often referred to as bias. The inputs can be weighted with weights \(w_1, w_2, ..., w_p\) and \(w_0\) for the bias.  With the input and the weights we can calculate the activation of the neuron \[  a_i = \sum_{k = 1}^p w_k x_ik + w_0 \].
The output of the neuron is a function of it's activation. Here we are free to choose whatever function we want to use. If our output shall be binary or in the intervall \([0, 1]\) a good choice is the logistic function.
So the calculated output for the neuron and the observation i is  \[ o_i= \frac{1}{1 + exp(-a_i)}\]
Pretty

Source: Machine Master

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