As we saw in the previous articles, normal classifiers like perceptron and single adaline are unable to classify non-linear problem like XOR. To over come this we have different methods. They are:
2)Polynomial Discriminant Function.
Madaline is a neural network with multiple adalines i.e. multiple adaptive neurons. To take a simple example as XOR gate, there two adalines interconnected with each other and the outputs of those two adalines are connected to AND gate to get final output. The theory behind this is when we use two adalines with the help of an AND gate then we get two linear decision boundaries. So, by using this two linear decision boundaries, we can condition it to classify the outputs between the boundaries as one class and output outside the boundaries as other class and hence we are successfully able to classify a non-linear problem.
Polynomial Discriminant Function:
Polynomial Discriminant Function is used to create decision boundaries for non-linear problems. The same inputs are mapped to non-linearities and are sent as other inputs to form a polynomial discriminant function and hence it can create non-linear decision boundary. If we take XOR as an example, then after proceeding through polynomial discriminant function, it forms a elliptical separating boundary to classify which are linearly not seperable.