Module kernels 

Kernel functions library (Linear, Polynomial, RBF, Laplacian, Sigmoid) Kernel Functions Library

Provides a comprehensive set of kernel functions for use in kernel methods such as Kernel PCA, Kernel Ridge Regression, and Support Vector Machines.

Available Kernels

• Linear: k(x, y) = x^T y
• Polynomial: k(x, y) = (gamma * x^T y + coef0)^degree
• RBF/Gaussian: k(x, y) = exp(-gamma * ||x - y||^2)
• Laplacian: k(x, y) = exp(-gamma * ||x - y||_1)
• Sigmoid/Tanh: k(x, y) = tanh(gamma * x^T y + coef0)

Gram Matrix and Centering

The module also provides utilities for computing Gram matrices (kernel matrices) and centering them in feature space.

Enums

KernelType

Kernel function type

Functions

center_kernel_matrix

Center a kernel matrix in feature space

center_kernel_matrix_test

Center a test kernel matrix using the training kernel matrix statistics

cross_gram_matrix

Compute the Gram matrix between two datasets

estimate_rbf_gamma

Estimate the RBF gamma parameter using the median heuristic

gram_matrix

Compute the Gram matrix (kernel matrix) for a dataset

is_positive_semidefinite

Check if a kernel matrix is positive semi-definite

kernel_alignment

Kernel alignment between two kernel matrices

kernel_diagonal

Compute the diagonal of a kernel matrix (self-similarities)

kernel_eval

Evaluate a kernel function between two vectors