polynomklassificeringen

Polynomklassifikation, or polynomial classification, is a supervised learning task where the decision function is a polynomial of the input features. It extends linear classifiers by enabling non-linear decision boundaries, allowing better separation of data that are not linearly separable.

One common approach is to augment the input vector with polynomial features up to a chosen degree d, then apply a linear classifier such as logistic regression or a regularized linear support vector machine. Another approach uses kernel methods, notably the polynomial kernel, which computes inner products in a high-dimensional polynomial feature space without explicit feature expansion. In support vector machines with a polynomial kernel, the separation boundary in the original input space can have degrees up to d.

Model complexity grows with the degree and the number of features, leading to a rapid increase in the size of the feature space. This can cause overfitting, higher computational cost, and challenges in interpretability. Regularization, feature selection, and cross-validation help mitigate these risks and support more robust generalization.

Polynomial classifiers are used in domains where data exhibit non-linear relationships, such as image or signal classification, pattern recognition, and text categorization when engineered features capture interactions between attributes. They relate to, but are distinct from, kernelized methods and from polynomial regression used in regression tasks. Overall, polynomial classification provides a flexible approach for capturing interactions among features while maintaining the interpretability of linear models to a degree.