These functions transform a \(n \times p\) matrix into a \(n \times n\) kernel matrix.
kernel.matrix(Z, whichkernel, rho = NULL, gamma = NULL, d = NULL)a \(n \times p\) matrix
kernel function
kernel hyperparameters (see details)
A \(n \times n\) matrix.
Given a \(n \times p\) matrix, this function returns a \(n \times n\) matrix where each cell represents the similarity between two samples defined by two \(p-\)dimensional vectors \(x\) and \(y\),
the Gaussian kernel is defined as \(k(x,y) = exp\left(-\frac{\parallel x-y \parallel^2}{\rho}\right)\) where \(\parallel x-y \parallel\) is the Euclidean distance between \(x\) and \(y\) and \(\rho > 0\) is the bandwidth of the kernel,
the linear kernel is defined as \(k(x,y) = x^Ty\),
the polynomial kernel is defined as \(k(x,y) = (\rho x^Ty + \gamma)^d\) with \(\rho > 0\), \(d\) is the polynomial order. Of note, a linear kernel is a polynomial kernel with \(\rho = d = 1\) and \(\gamma = 0\),
the sigmoid kernel is defined as \(k(x,y) = tanh(\rho x^Ty + \gamma)\) which is similar to the sigmoid function in logistic regression,
the inverse quadratic function defined as \(k(x,y) = \frac{1}{\sqrt{\parallel x-y \parallel^2 + \gamma}}\) with \(\gamma > 0\),
the equality kernel defined as \(k(x,y) = \left\lbrace \begin{array}{ll} 1 & if x = y \\ 0 & otherwise \end{array}\right.\).
kernel.gaussian, kernel.linear, kernel.polynomial, kernel.equality, kernel.sigmoid, kernel.inverse.quadratic.