Linear Kernel Function

machine-learning statistics

Definition

Linear Kernel Function

The linear kernel is the simplest kernel function, corresponding to the standard dot product in the original instance space. Formally, for two vectors :

This represents a identity feature map , meaning the “higher-dimensional” Hilbert space is identical to the input space.

Computational Efficiency

Runtime Complexity: Evaluating the linear kernel requires operations, making it the most computationally efficient choice for large-scale datasets.

Applicability: It is the preferred choice when the data is already linearly separable or when the number of features is very large relative to the number of samples (e.g., in text classification with one-hot encoded words), as high-dimensional spaces are often linearly separable without further expansion.