Kernel Perceptron

machine-learning algorithms kernel-methods

Definition

Kernel Perceptron

The kernel perceptron is a non-linear extension of the perceptron algorithm that utilises the kernel trick to identify decision boundaries in a high-dimensional Hilbert space. Formally, the classifier is represented in its dual form:

where is the number of times the -th training example was misclassified during training.

Algorithmic Update

For each training example , the model performs an update if the prediction is incorrect:
If :

This allows the perceptron to solve non-linearly separable problems, such as the XOR function, by implicitly mapping the data into a space where a linear hyperplane exists.