Recall that the perceptron separates the instances of the positive class from the instances of the negative class using a hyperplane as a decision boundary. The decision boundary is given by the following equation:
Predictions are made using the following function:
Note that previously we expressed the inner product as . To be consistent with the notational conventions used for support vector machines, we will adopt the former notation in this chapter.
While the proof is beyond the scope of this chapter, we can write the model differently. The following expression of the model is called the dual form. The expression we used previously is the primal form:
The most important difference between the primal and dual forms is that the primal form computes the inner product of the model parameters and the test instance's feature vector, while the dual form computes the inner product of the training instances and the test instance's feature vector. Shortly, we will exploit...