1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
|
\name{kcca}
\alias{kcca}
\alias{kcca,matrix-method}
\title{Kernel Canonical Correlation Analysis}
\description{
Computes the canonical correlation analysis in feature space.
}
\usage{
\S4method{kcca}{matrix}(x, y, kernel="rbfdot", kpar=list(sigma=0.1),
gamma = 0.1, ncomps = 10, ...)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
\item{x}{a matrix containing data index by row}
\item{y}{a matrix containing data index by row}
\item{kernel}{the kernel function used in training and predicting.
This parameter can be set to any function, of class kernel,
which computes a inner product in feature space between two
vector arguments. kernlab provides the most popular kernel functions
which can be used by setting the kernel parameter to the following
strings:
\itemize{
\item \code{rbfdot} Radial Basis kernel function "Gaussian"
\item \code{polydot} Polynomial kernel function
\item \code{vanilladot} Linear kernel function
\item \code{tanhdot} Hyperbolic tangent kernel function
\item \code{laplacedot} Laplacian kernel function
\item \code{besseldot} Bessel kernel function
\item \code{anovadot} ANOVA RBF kernel function
\item \code{splinedot} Spline kernel
}
The kernel parameter can also be set to a user defined function of
class kernel by passing the function name as an argument.
}
\item{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 :
\itemize{
\item \code{sigma} inverse kernel width for the Radial Basis
kernel function "rbfdot" and the Laplacian kernel "laplacedot".
\item \code{degree, scale, offset} for the Polynomial kernel "polydot"
\item \code{scale, offset} for the Hyperbolic tangent kernel
function "tanhdot"
\item \code{sigma, order, degree} for the Bessel kernel "besseldot".
\item \code{sigma, degree} for the ANOVA kernel "anovadot".
}
Hyper-parameters for user defined kernels can be passed through the
kpar parameter as well.}
\item{gamma}{regularization parameter (default : 0.1)}
\item{ncomps}{number of canonical components (default : 10) }
\item{\dots}{additional parameters for the \code{kpca} function}
}
\details{
The kernel version of canonical correlation analysis.
Kernel Canonical Correlation Analysis (KCCA) is a non-linear extension
of CCA. Given two random variables, KCCA aims at extracting the
information which is shared by the two random variables. More
precisely given \eqn{x} and \eqn{y} the purpose of KCCA is to provide
nonlinear mappings \eqn{f(x)} and \eqn{g(y)} such that their
correlation is maximized.
}
\value{
An S4 object containing the following slots:
\item{kcor}{Correlation coefficients in feature space}
\item{xcoef}{estimated coefficients for the \code{x} variables in the
feature space}
\item{ycoef}{estimated coefficients for the \code{y} variables in the
feature space}
%% \item{xvar}{The canonical variates for \code{x}}
%% \item{yvar}{The canonical variates for \code{y}}
}
\references{ Malte Kuss, Thore Graepel \cr
\emph{The Geometry Of Kernel Canonical Correlation Analysis}\cr
\url{https://www.microsoft.com/en-us/research/publication/the-geometry-of-kernel-canonical-correlation-analysis/}}
\author{
Alexandros Karatzoglou \cr
\email{alexandros.karatzoglou@ci.tuwien.ac.at}
}
\seealso{\code{\link{cancor}}, \code{\link{kpca}}, \code{\link{kfa}}, \code{\link{kha}}}
\examples{
## dummy data
x <- matrix(rnorm(30),15)
y <- matrix(rnorm(30),15)
kcca(x,y,ncomps=2)
}
\keyword{multivariate}
|
