qkernmatrix: qKernel Matrix functions

In qkerntool: Q-Kernel-Based and Conditionally Negative Definite Kernel-Based Machine Learning Tools

Description

qkernmatrix calculates the qkernel matrix K_{ij} = k(x_i,x_j) or K_{ij} = k(x_i,y_j).

Usage

## S4 method for signature 'qkernel'
qkernmatrix(qkernel, x, y = NULL)

Arguments

qkernel	the kernel function to be used to calculate the qkernel matrix. This has to be a function of class qkernel, i.e. which can be generated either one of the build in kernel generating functions (e.g., rbfbase etc.) or a user defined function of class qkernel taking two vector arguments and returning a scalar.
x	a data matrix to be used to calculate the kernel matrix
y	second data matrix to calculate the kernel matrix

Details

Common functions used during kernel based computations.
The qkernel parameter can be set to any function, of class qkernel, which computes the kernel function value in feature space between two vector arguments. qkerntool provides more than 10 qkernel functions which can be initialized by using the following functions:

• nonlbase Non Linear qkernel function

• rbfbase Gaussian qkernel function

• laplbase Laplacian qkernel function

• ratibase Rational Quadratic qkernel function

• multbase Multiquadric qkernel function

• invbase Inverse Multiquadric qkernel function

• wavbase Wave qkernel function

• powbase d qkernel function

• logbase Log qkernel function

• caubase Cauchy qkernel function

• chibase Chi-Square qkernel function

• studbase Generalized T-Student qkernel function

(see example.)

Value

qkernmatrix returns a conditionally negative definite matrix with a zero diagonal element.

Author(s)

Yusen Zhang
[e-mail]

See Also

nonlcnd, rbfcnd,polycnd,laplcnd, anocnd, raticnd, multcnd, invcnd, wavcnd, powcnd, logcnd, caucnd, chicnd, studcnd

Examples

data(iris)
dt <- as.matrix(iris[ ,-5])

## initialize kernel function
rbf <- rbfbase(sigma = 1.4, q=0.8)
rbf

## calculate qkernel matrix
qkernmatrix(rbf, dt)

qkerntool documentation built on May 2, 2019, 6:11 a.m.