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kernels.R
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kernels.R
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## kernel functions
## Functions for computing a kernel value, matrix, matrix-vector
## product and quadratic form
##
## author : alexandros karatzoglou
## Define the kernel objects,
## functions with an additional slot for the kernel parameter list.
## kernel functions take two vector arguments and return a scalar (dot product)
rbfdot<- function(sigma=1)
{
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must a vector")
if (is(x,"vector") && is.null(y)){
return(1)
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
return(exp(sigma*(2*crossprod(x,y) - crossprod(x) - crossprod(y))))
# sigma/2 or sigma ??
}
}
return(new("rbfkernel",.Data=rval,kpar=list(sigma=sigma)))
}
setClass("rbfkernel",prototype=structure(.Data=function(){},kpar=list()),contains=c("kernel"))
laplacedot<- function(sigma=1)
{
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must a vector")
if (is(x,"vector") && is.null(y)){
return(1)
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
return(exp(-sigma*sqrt(-(round(2*crossprod(x,y) - crossprod(x) - crossprod(y),9)))))
}
}
return(new("laplacekernel",.Data=rval,kpar=list(sigma=sigma)))
}
setClass("laplacekernel",prototype=structure(.Data=function(){},kpar=list()),contains=c("kernel"))
besseldot<- function(sigma = 1, order = 1, degree = 1)
{
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must a vector")
if (is(x,"vector") && is.null(y)){
return(1)
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
lim <- 1/(gamma(order+1)*2^(order))
bkt <- sigma*sqrt(-(2*crossprod(x,y) - crossprod(x) - crossprod(y)))
if(bkt < 10e-5)
res <- lim
else
res <- besselJ(bkt,order)*(bkt^(-order))
return((res/lim)^degree)
}
}
return(new("besselkernel",.Data=rval,kpar=list(sigma=sigma ,order = order ,degree = degree)))
}
setClass("besselkernel",prototype=structure(.Data=function(){},kpar=list()),contains=c("kernel"))
anovadot<- function(sigma = 1, degree = 1)
{
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must a vector")
if (is(x,"vector") && is.null(y)){
return(1)
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
res <- sum(exp(- sigma * (x - y)^2))
return((res)^degree)
}
}
return(new("anovakernel",.Data=rval,kpar=list(sigma=sigma ,degree = degree)))
}
setClass("anovakernel",prototype=structure(.Data=function(){},kpar=list()),contains=c("kernel"))
splinedot<- function()
{
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must a vector")
if (is(x,"vector") && is.null(y)){
return(1)
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
minv <- pmin(x,y)
res <- 1 + x*y*(1+minv) - ((x+y)/2)*minv^2 + (minv^3)/3
fres <- prod(res)
return(fres)
}
}
return(new("splinekernel",.Data=rval,kpar=list()))
}
setClass("splinekernel",prototype=structure(.Data=function(){},kpar=list()),contains=c("kernel"))
fourierdot <- function(sigma = 1)
{
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must a vector")
if (is(x,"vector") && is.null(y)){
return(1)
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
res <- (1 - sigma^2)/2*(1 - 2*sigma*cos(x - y) + sigma^2)
fres <- prod(res)
return(fres)
}
}
return(new("fourierkernel",.Data=rval,kpar=list()))
}
setClass("fourierkernel",prototype=structure(.Data=function(){},kpar=list(sigma = 1)),contains=c("kernel"))
tanhdot <- function(scale = 1, offset = 1)
{
rval<- function(x, y = NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
if (is(x,"vector") && is.null(y)){
tanh(scale*crossprod(x)+offset)
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
tanh(scale*crossprod(x,y)+offset)
}
}
return(new("tanhkernel",.Data=rval,kpar=list(scale=scale,offset=offset)))
}
setClass("tanhkernel",prototype=structure(.Data=function(){},kpar=list()),contains=c("kernel"))
setClass("polykernel",prototype=structure(.Data=function(){},kpar=list()),contains=c("kernel"))
polydot <- function(degree = 1, scale = 1, offset = 1)
{
rval<- function(x, y = NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
if (is(x,"vector") && is.null(y)){
(scale*crossprod(x)+offset)^degree
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
(scale*crossprod(x,y)+offset)^degree
}
}
return(new("polykernel",.Data=rval,kpar=list(degree=degree,scale=scale,offset=offset)))
}
setClass("vanillakernel",prototype=structure(.Data=function(){},kpar=list()),contains=c("kernel"))
vanilladot <- function( )
{
rval<- function(x, y = NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
if (is(x,"vector") && is.null(y)){
crossprod(x)
}
if (is(x,"vector") && is(y,"vector")){
if (!length(x)==length(y))
stop("number of dimension must be the same on both data points")
crossprod(x,y)
}
}
return(new("vanillakernel",.Data=rval,kpar=list()))
}
setClass("stringkernel",prototype=structure(.Data=function(){},kpar=list(length = 4, lambda = 1.1, type = "spectrum", normalized = TRUE)),contains=c("kernel"))
stringdot <- function(length = 4, lambda = 1.1, type = "spectrum", normalized = TRUE)
{
type <- match.arg(type,c("sequence","string","fullstring","exponential","constant","spectrum", "boundrange"))
## need to do this to set the length parameters
if(type == "spectrum" | type == "boundrange")
lambda <- length
switch(type,
"sequence" = {
rval<- function(x, y = NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
if (is(x,"vector") && is.null(y) && normalized == FALSE)
return(.Call(subsequencek,
as.character(x),
as.character(x),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(length),
as.double(lambda)))
if (is(x,"vector") && is(y,"vector") && normalized == FALSE)
return(.Call(subsequencek,
as.character(x),
as.character(y),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda)))
if (is(x,"vector") && is.null(y) && normalized == TRUE)
return(1)
if (is(x,"vector") && is(y,"vector") && normalized == TRUE)
return(.Call(subsequencek,
as.character(x),
as.character(y),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda)) /
sqrt(.Call(subsequencek,
as.character(x),
as.character(x),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(length),
as.double(lambda)) *
.Call(subsequencek,
as.character(y),
as.character(y),
as.integer(nchar(y)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda))))
}
},
"exponential" = {
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
x <- paste(x,"\n",sep="")
if(!is.null(y))
y <- paste(y,"\n",sep="")
if (normalized == FALSE){
if(is.null(y))
y <- x
return(.Call(stringtv,
as.character(x),
as.character(y),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(2),
as.double(lambda)))
}
if (is(x,"vector") && is.null(y) && normalized == TRUE)
return(1)
if (is(x,"vector") && is(y,"vector") && normalized == TRUE)
return(.Call(stringtv,
as.character(x),
as.character(y),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(2),
as.double(lambda)) /
sqrt(.Call(stringtv,
as.character(x),
as.character(x),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(2),
as.double(lambda)) *
.Call(stringtv,
as.character(y),
as.character(y),
as.integer(1),
as.integer(nchar(y)),
as.integer(nchar(y)),
as.integer(2),
as.double(lambda))))
}
},
"constant" = {
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
x <- paste(x,"\n",sep="")
if(!is.null(y))
y <- paste(y,"\n",sep="")
if (normalized == FALSE){
if(is.null(y))
y <- x
return(.Call(stringtv,
as.character(x),
as.character(y),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(1),
as.double(lambda)))
}
if (is(x,"vector") && is.null(y) && normalized == TRUE)
return(1)
if (is(x,"vector") && is(y,"vector") && normalized == TRUE)
return(.Call(stringtv,
as.character(x),
as.character(y),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(1),
as.double(lambda)) /
sqrt(.Call(stringtv,
as.character(x),
as.character(x),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(1),
as.double(lambda)) *
.Call(stringtv,
as.character(y),
as.character(y),
as.integer(1),
as.integer(nchar(y)),
as.integer(nchar(y)),
as.integer(1),
as.double(lambda))))
}
},
"spectrum" = {
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
x <- paste(x,"\n",sep="")
if(!is.null(y))
y <- paste(y,"\n",sep="")
n <- nchar(x)
m <- nchar(y)
if(n < length | m < length){
warning("String length smaller than length parameter value")
return(0)}
if (normalized == FALSE){
if(is.null(y))
y <- x
return(.Call(stringtv,
as.character(x),
as.character(y),
as.integer(1),
as.integer(n),
as.integer(m),
as.integer(3),
as.double(length)))
}
if (is(x,"vector") && is.null(y) && normalized == TRUE)
return(1)
if (is(x,"vector") && is(y,"vector") && normalized == TRUE)
return(.Call(stringtv,
as.character(x),
as.character(y),
as.integer(1),
as.integer(n),
as.integer(m),
as.integer(3),
as.double(length)) /
sqrt(.Call(stringtv,
as.character(x),
as.character(x),
as.integer(1),
as.integer(n),
as.integer(n),
as.integer(3),
as.double(lambda)) *
.Call(stringtv,
as.character(y),
as.character(y),
as.integer(1),
as.integer(m),
as.integer(m),
as.integer(3),
as.double(length))))
}
},
"boundrange" = {
rval <- function(x,y=NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
x <- paste(x,"\n",sep="")
if(!is.null(y))
y <- paste(y,"\n",sep="")
if (normalized == FALSE){
if(is.null(y))
y <- x
return(.Call(stringtv,
as.character(x),
as.character(y),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(4),
as.double(lambda)))
}
if (is(x,"vector") && is.null(y) && normalized == TRUE)
return(1)
if (is(x,"vector") && is(y,"vector") && normalized == TRUE)
return(.Call(stringtv,
as.character(x),
as.character(y),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(4),
as.double(lambda)) /
sqrt(.Call(stringtv,
as.character(x),
as.character(x),
as.integer(1),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(4),
as.double(lambda)) *
.Call(stringtv,
as.character(y),
as.character(y),
as.integer(1),
as.integer(nchar(y)),
as.integer(nchar(y)),
as.integer(4),
as.double(lambda))))
}
},
"string" =
{
rval<- function(x, y = NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
if (is(x,"vector") && is.null(y) && normalized == FALSE)
return(.Call(substringk,
as.character(x),
as.character(x),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(length),
as.double(lambda)))
if (is(x,"vector") && is(y,"vector") && normalized == FALSE)
return(.Call(substringk,
as.character(x),
as.character(y),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda)))
if (is(x,"vector") && is.null(y) && normalized == TRUE)
return(1)
if (is(x,"vector") && is(y,"vector") && normalized == TRUE)
return(.Call(substringk,
as.character(x),
as.character(y),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda)) /
sqrt(.Call(substringk,
as.character(x),
as.character(x),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(length),
as.double(lambda)) *
.Call(substringk,
as.character(y),
as.character(y),
as.integer(nchar(y)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda))))
}
},
"fullstring" =
{
rval<- function(x, y = NULL)
{
if(!is(x,"vector")) stop("x must be a vector")
if(!is(y,"vector")&&!is.null(y)) stop("y must be a vector")
if (is(x,"vector") && is.null(y) && normalized == FALSE)
return(.Call(fullsubstringk,
as.character(x),
as.character(x),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(length),
as.double(lambda)))
if (is(x,"vector") && is(y,"vector") && normalized == FALSE)
return(.Call(fullsubstringk,
as.character(x),
as.character(y),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda)))
if (is(x,"vector") && is.null(y) && normalized == TRUE)
return(1)
if (is(x,"vector") && is(y,"vector") && normalized == TRUE)
return(.Call(fullsubstringk,
as.character(x),
as.character(y),
as.integer(nchar(x)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda)) /
sqrt(.Call(fullsubstringk,
as.character(x),
as.character(x),
as.integer(nchar(x)),
as.integer(nchar(x)),
as.integer(length),
as.double(lambda)) *
.Call(fullsubstringk,
as.character(y),
as.character(y),
as.integer(nchar(y)),
as.integer(nchar(y)),
as.integer(length),
as.double(lambda))))
}
})
return(new("stringkernel",.Data=rval,kpar=list(length=length, lambda =lambda, type = type, normalized = normalized)))
}
## show method for kernel functions
setMethod("show",signature(object="kernel"),
function(object)
{
switch(class(object),
"rbfkernel" = cat(paste("Gaussian Radial Basis kernel function.", "\n","Hyperparameter :" ,"sigma = ", kpar(object)$sigma,"\n")),
"laplacekernel" = cat(paste("Laplace kernel function.", "\n","Hyperparameter :" ,"sigma = ", kpar(object)$sigma,"\n")),
"besselkernel" = cat(paste("Bessel kernel function.", "\n","Hyperparameter :" ,"sigma = ", kpar(object)$sigma,"order = ",kpar(object)$order, "degree = ", kpar(object)$degree,"\n")),
"anovakernel" = cat(paste("Anova RBF kernel function.", "\n","Hyperparameter :" ,"sigma = ", kpar(object)$sigma, "degree = ", kpar(object)$degree,"\n")),
"tanhkernel" = cat(paste("Hyperbolic Tangent kernel function.", "\n","Hyperparameters :","scale = ", kpar(object)$scale," offset = ", kpar(object)$offset,"\n")),
"polykernel" = cat(paste("Polynomial kernel function.", "\n","Hyperparameters :","degree = ",kpar(object)$degree," scale = ", kpar(object)$scale," offset = ", kpar(object)$offset,"\n")),
"vanillakernel" = cat(paste("Linear (vanilla) kernel function.", "\n")),
"splinekernel" = cat(paste("Spline kernel function.", "\n")),
"stringkernel" = {
if(kpar(object)$type =="spectrum" | kpar(object)$type =="boundrange")
cat(paste("String kernel function.", " Type = ", kpar(object)$type, "\n","Hyperparameters :","sub-sequence/string length = ",kpar(object)$length, "\n"))
else
if(kpar(object)$type =="exponential" | kpar(object)$type =="constant")
cat(paste("String kernel function.", " Type = ", kpar(object)$type, "\n","Hyperparameters :"," lambda = ", kpar(object)$lambda, "\n"))
else
cat(paste("String kernel function.", " Type = ", kpar(object)$type, "\n","Hyperparameters :","sub-sequence/string length = ",kpar(object)$length," lambda = ", kpar(object)$lambda, "\n"))
if(kpar(object)$normalized == TRUE) cat(" Normalized","\n")
if(kpar(object)$normalized == FALSE) cat(" Not Normalized","\n")}
)
})
## create accesor function as in "S4 Classses in 15 pages more or less", well..
if (!isGeneric("kpar")){
if (is.function(kpar))
fun <- kpar
else fun <- function(object) standardGeneric("kpar")
setGeneric("kpar",fun)
}
setMethod("kpar","kernel", function(object) object@kpar)
## Functions that return usefull kernel calculations (kernel matrix etc.)
## kernelMatrix function takes two or three arguments
kernelMatrix <- function(kernel, x, y=NULL)
{
if(is(x,"vector"))
x <- as.matrix(x)
if(is(y,"vector"))
y <- as.matrix(y)
if(!is(x,"matrix")) stop("x must be a matrix")
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix")
n <- nrow(x)
res1 <- matrix(rep(0,n*n), ncol = n)
if(is.null(y)){
for(i in 1:n) {
for(j in i:n) {
res1[i,j] <- kernel(x[i,],x[j,])
}
}
res1 <- res1 + t(res1)
diag(res1) <- diag(res1)/2
}
if (is(y,"matrix")){
m<-dim(y)[1]
res1 <- matrix(0,dim(x)[1],dim(y)[1])
for(i in 1:n) {
for(j in 1:m) {
res1[i,j] <- kernel(x[i,],y[j,])
}
}
}
return(as.kernelMatrix(res1))
}
setGeneric("kernelMatrix",function(kernel, x, y = NULL) standardGeneric("kernelMatrix"))
kernelMatrix.rbfkernel <- function(kernel, x, y = NULL)
{
if(is(x,"vector"))
x <- as.matrix(x)
if(is(y,"vector"))
y <- as.matrix(y)
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix or a vector")
sigma = kpar(kernel)$sigma
n <- dim(x)[1]
dota <- rowSums(x*x)/2
if (is(x,"matrix") && is.null(y)){
res <- crossprod(t(x))
for (i in 1:n)
res[i,]<- exp(2*sigma*(res[i,] - dota - rep(dota[i],n)))
return(as.kernelMatrix(res))
}
if (is(x,"matrix") && is(y,"matrix")){
if (!(dim(x)[2]==dim(y)[2]))
stop("matrixes must have the same number of columns")
m <- dim(y)[1]
dotb <- rowSums(y*y)/2
res <- x%*%t(y)
for( i in 1:m)
res[,i]<- exp(2*sigma*(res[,i] - dota - rep(dotb[i],n)))
return(as.kernelMatrix(res))
}
}
setMethod("kernelMatrix",signature(kernel="rbfkernel"),kernelMatrix.rbfkernel)
kernelMatrix.laplacekernel <- function(kernel, x, y = NULL)
{
if(is(x,"vector"))
x <- as.matrix(x)
if(is(y,"vector"))
y <- as.matrix(y)
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix or a vector")
sigma = kpar(kernel)$sigma
n <- dim(x)[1]
dota <- rowSums(x*x)/2
if (is(x,"matrix") && is.null(y)){
res <- crossprod(t(x))
for (i in 1:n)
res[i,]<- exp(-sigma*sqrt(round(-2*(res[i,] - dota - rep(dota[i],n)),9)))
return(as.kernelMatrix(res))
}
if (is(x,"matrix") && is(y,"matrix")){
if (!(dim(x)[2]==dim(y)[2]))
stop("matrixes must have the same number of columns")
m <- dim(y)[1]
dotb <- rowSums(y*y)/2
res <- x%*%t(y)
for( i in 1:m)
res[,i]<- exp(-sigma*sqrt(round(-2*(res[,i] - dota - rep(dotb[i],n)),9)))
return(as.kernelMatrix(res))
}
}
setMethod("kernelMatrix",signature(kernel="laplacekernel"),kernelMatrix.laplacekernel)
kernelMatrix.besselkernel <- function(kernel, x, y = NULL)
{
if(is(x,"vector"))
x <- as.matrix(x)
if(is(y,"vector"))
y <- as.matrix(y)
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix or a vector")
sigma = kpar(kernel)$sigma
nu = kpar(kernel)$order
ni = kpar(kernel)$degree
n <- dim(x)[1]
lim <- 1/(gamma(nu+1)*2^(nu))
dota <- rowSums(x*x)/2
if (is(x,"matrix") && is.null(y)){
res <- crossprod(t(x))
for (i in 1:n){
xx <- sigma*sqrt(round(-2*(res[i,] - dota - rep(dota[i],n)),9))
res[i,] <- besselJ(xx,nu)*(xx^(-nu))
res[i,which(xx<10e-5)] <- lim
}
return(as.kernelMatrix((res/lim)^ni))
}
if (is(x,"matrix") && is(y,"matrix")){
if (!(dim(x)[2]==dim(y)[2]))
stop("matrixes must have the same number of columns")
m <- dim(y)[1]
dotb <- rowSums(y*y)/2
res <- x%*%t(y)
for( i in 1:m){
xx <- sigma*sqrt(round(-2*(res[,i] - dota - rep(dotb[i],n)),9))
res[,i] <- besselJ(xx,nu)*(xx^(-nu))
res[which(xx<10e-5),i] <- lim
}
return(as.kernelMatrix((res/lim)^ni))
}
}
setMethod("kernelMatrix",signature(kernel="besselkernel"),kernelMatrix.besselkernel)
kernelMatrix.anovakernel <- function(kernel, x, y = NULL)
{
if(is(x,"vector"))
x <- as.matrix(x)
if(is(y,"vector"))
y <- as.matrix(y)
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix or a vector")
sigma = kpar(kernel)$sigma
degree = kpar(kernel)$degree
n <- dim(x)[1]
if (is(x,"matrix") && is.null(y)){
a <- matrix(0, dim(x)[2], n)
res <- matrix(0, n ,n)
for (i in 1:n)
{
a[rep(TRUE,dim(x)[2]), rep(TRUE,n)] <- x[i,]
res[i,]<- colSums(exp( - sigma*(a - t(x))^2))^degree
}
return(as.kernelMatrix(res))
}
if (is(x,"matrix") && is(y,"matrix")){
if (!(dim(x)[2]==dim(y)[2]))
stop("matrixes must have the same number of columns")
m <- dim(y)[1]
b <- matrix(0, dim(x)[2],m)
res <- matrix(0, dim(x)[1],m)
for( i in 1:n)
{
b[rep(TRUE,dim(x)[2]), rep(TRUE,m)] <- x[i,]
res[i,]<- colSums(exp( - sigma*(b - t(y))^2))^degree
}
return(as.kernelMatrix(res))
}
}
setMethod("kernelMatrix",signature(kernel="anovakernel"),kernelMatrix.anovakernel)
kernelMatrix.polykernel <- function(kernel, x, y = NULL)
{
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix")
scale = kpar(kernel)$scale
offset = kpar(kernel)$offset
degree = kpar(kernel)$degree
if (is(x,"matrix") && is.null(y))
{
res <- (scale*crossprod(t(x))+offset)^degree
return(as.kernelMatrix(res))
}
if (is(x,"matrix") && is(y,"matrix")){
if (!(dim(x)[2]==dim(y)[2]))
stop("matrixes must have the same number of columns")
res <- (scale*crossprod(t(x),t(y)) + offset)^degree
return(as.kernelMatrix(res))
}
}
setMethod("kernelMatrix",signature(kernel="polykernel"),kernelMatrix.polykernel)
kernelMatrix.vanilla <- function(kernel, x, y = NULL)
{
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix")
if (is(x,"matrix") && is.null(y)){
res <- crossprod(t(x))
return(as.kernelMatrix(res))
}
if (is(x,"matrix") && is(y,"matrix")){
if (!(dim(x)[2]==dim(y)[2]))
stop("matrixes must have the same number of columns")
res <- crossprod(t(x),t(y))
return(as.kernelMatrix(res))
}
}
setMethod("kernelMatrix",signature(kernel="vanillakernel"),kernelMatrix.vanilla)
kernelMatrix.tanhkernel <- function(kernel, x, y = NULL)
{
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix")
if (is(x,"matrix") && is.null(y)){
scale = kpar(kernel)$scale
offset = kpar(kernel)$offset
res <- tanh(scale*crossprod(t(x)) + offset)
return(as.kernelMatrix(res))
}
if (is(x,"matrix") && is(y,"matrix")){
if (!(dim(x)[2]==dim(y)[2]))
stop("matrixes must have the same number of columns")
res <- tanh(scale*crossprod(t(x),t(y)) + offset)
return(as.kernelMatrix(res))
}
}
setMethod("kernelMatrix",signature(kernel="tanhkernel"),kernelMatrix.tanhkernel)
kernelMatrix.splinekernel <- function(kernel, x, y = NULL)
{
if(is(x,"vector"))
x <- as.matrix(x)
if(is(y,"vector"))
y <- as.matrix(y)
if(!is(y,"matrix")&&!is.null(y)) stop("y must be a matrix or a vector")
sigma = kpar(kernel)$sigma
degree = kpar(kernel)$degree
n <- dim(x)[1]
if (is(x,"matrix") && is.null(y)){
a <- matrix(0, dim(x)[2], n)
res <- matrix(0, n ,n)
x <- t(x)
for (i in 1:n)
{
dr <- x + x[,i]
dp <- x * x[,i]
dm <- pmin(x,x[,i])
res[i,] <- apply((1 + dp + dp*dm - (dr/2)*dm^2 + (dm^3)/3),2, prod)
}
return(as.kernelMatrix(res))
}
if (is(x,"matrix") && is(y,"matrix")){
if (!(dim(x)[2]==dim(y)[2]))
stop("matrixes must have the same number of columns")
m <- dim(y)[1]
b <- matrix(0, dim(x)[2],m)
res <- matrix(0, dim(x)[1],m)
x <- t(x)
y <- t(y)
for( i in 1:n)
{
dr <- y + x[,i]
dp <- y * x[,i]
dm <- pmin(y,x[,i])
res[i,] <- apply((1 + dp + dp*dm - (dr/2)*dm^2 + (dm^3)/3),2, prod)
}
return(as.kernelMatrix(res))
}
}
setMethod("kernelMatrix",signature(kernel="splinekernel"),kernelMatrix.splinekernel)
kernelMatrix.stringkernel <- function(kernel, x, y=NULL)
{
n <- length(x)
res1 <- matrix(rep(0,n*n), ncol = n)
normalized = kpar(kernel)$normalized
if(is(x,"list"))
x <- sapply(x,paste,collapse="")
if(is(y,"list"))
y <- sapply(y,paste,collapse="")
if (kpar(kernel)$type == "sequence" |kpar(kernel)$type == "string"|kpar(kernel)$type == "fullstring")
{
resdiag <- rep(0,n)
if(normalized == TRUE)
kernel <- stringdot(length = kpar(kernel)$length, type = kpar(kernel)$type, lambda = kpar(kernel)$lambda, normalized = FALSE)
## y is null
if(is.null(y)){
if(normalized == TRUE){
## calculate diagonal elements first, and use them to normalize
for (i in 1:n)
resdiag[i] <- kernel(x[[i]],x[[i]])
for(i in 1:n) {
for(j in (i:n)[-1]) {
res1[i,j] <- kernel(x[[i]],x[[j]])/sqrt(resdiag[i]*resdiag[j])
}
}
res1 <- res1 + t(res1)
diag(res1) <- rep(1,n)
}
else{
for (i in 1:n)
resdiag[i] <- kernel(x[[i]],x[[i]])
for(i in 1:n) {
for(j in (i:n)[-1]) {
res1[i,j] <- kernel(x[[i]],x[[j]])
}
}
res1 <- res1 + t(res1)
diag(res1) <- resdiag
}
}
if (!is.null(y)){
m <- length(y)
res1 <- matrix(0,n,m)
resdiag1 <- rep(0,m)
if(normalized == TRUE){
for(i in 1:n)
resdiag[i] <- kernel(x[[i]],x[[i]])
for(i in 1:m)
resdiag1[i] <- kernel(y[[i]],y[[i]])
for(i in 1:n) {
for(j in 1:m) {
res1[i,j] <- kernel(x[[i]],y[[j]])/sqrt(resdiag[i]*resdiag1[j])
}
}
}
else{
for(i in 1:n) {
for(j in 1:m) {
res1[i,j] <- kernel(x[[i]],y[[j]])
}
}
}
}
return(as.kernelMatrix(res1))
}
else {
switch(kpar(kernel)$type,
"exponential" =
sktype <- 2,
"constant" =
sktype <- 1,
"spectrum" =
sktype <- 3,
"boundrange" =
sktype <- 4)