Polynomial Kernel Function

machine-learning statistics nlp

Definition

Polynomial Kernel Function

The polynomial kernel represents a feature mapping into a space of all possible monomial combinations of the input features up to a specified degree . Formally, for a degree and a constant :

Expressivity and Complexity

Feature Expansion: This kernel implicitly computes the inner product in a feature space of dimension . For example, a second-degree polynomial kernel on 2D data expands the features to include and .

Overfitting Risk: While providing higher capacity than the linear kernel, larger degrees significantly increase the risk of overfitting, particularly in domains like natural language processing. In practice, or are common choices to balance expressivity and generalisation.