kernlMatrix between x and y values (only for the
kernelMatrix interface)
kernel
the kernel function used in training and predicting.
This parameter can be set to any function, of class kernel, which computes a dot product between two
vector arguments. kernlab provides the most popular kernel functions
which can be used by setting the kernel parameter to the following
strings:
rbfdot Radial Basis kernel function "Gaussian"
polydot Polynomial kernel function
vanilladot Linear kernel function
tanhdot Hyperbolic tangent kernel function
laplacedot Laplacian kernel function
besseldot Bessel kernel function
anovadot ANOVA RBF kernel function
splinedot Spline kernel
stringdot String kernel
The kernel parameter can also be set to a user defined function of
class kernel by passing the function name as an argument.
kpar
the list of hyper-parameters (kernel parameters).
This is a list which contains the parameters to be used with the
kernel function. Valid parameters for existing kernels are :
sigma inverse kernel width for the Radial Basis
kernel function "rbfdot" and the Laplacian kernel "laplacedot".
degree, scale, offset for the Polynomial kernel "polydot"
scale, offset for the Hyperbolic tangent kernel
function "tanhdot"
sigma, order, degree for the Bessel kernel "besseldot".
sigma, degree for the ANOVA kernel "anovadot".
lenght, lambda, normalized for the "stringdot" kernel
where length is the length of the strings considered, lambda the
decay factor and normalized a logical parameter determining if the
kernel evaluations should be normalized.
Hyper-parameters for user defined kernels can be passed
through the kpar parameter as well. In the case of a Radial
Basis kernel function (Gaussian) kpar can also be set to the
string "automatic" which uses the heuristics in 'sigest' to
calculate a good 'sigma' value for the Gaussian RBF or
Laplace kernel, from the data. (default = "automatic").
alpha
the confidence level of the test (default: 0.05)
asymptotic
calculate the bounds asymptotically (suitable for
smaller datasets) (default: FALSE)
replace
use replace when sampling for computing the asymptotic
bounds (default : TRUE)
ntimes
number of times repeating the sampling procedure (default
: 150)
frac
fraction of points to sample (frac : 1)
...
additional parameters.
Details
kmmd calculates the kernel maximum mean discrepancy for
samples from two distributions and conducts a test as to whether the samples are
from different distributions with level alpha.
Value
An S4 object of class kmmd containing the
results of whether the H0 hypothesis is rejected or not. H0 being
that the samples x and y come from the same distribution.
The object contains the following slots :
H0
is H0 rejected (logical)
AsympH0
is H0 rejected according to the asymptotic bound (logical)