Linear separation

When a set of output values can be split by a straight line, the output values are said to be linearly separable. Geometrically, this condition describes the situation in which there is a hyperplane that separates, in the vector space of inputs, those that require positive output from those that require a negative output, as shown in the following figure:

Here, one side of the separator are those predicted to belong to one class whilst those on the other side are predicted to belong to a different class. The decision rule of the Boolean neuron corresponds to the breakdown of the input features space, operated by a hyperplane.

If, in addition to the output neuron, even the input of the neural network is Boolean, then using the neural network to perform a classification is equivalent to determining a Boolean function of the input vector. This function takes the value 1 where it exceeds the threshold value, 0 otherwise. For example, with two input and output Boolean neurons...