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lssvm.R
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lssvm.R
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## reduced least squares support vector machines
## author : alexandros
setGeneric("lssvm", function(x, ...) standardGeneric("lssvm"))
setMethod("lssvm",signature(x="formula"),
function (x, data=NULL, ..., subset, na.action = na.omit, scaled = TRUE){
cl <- match.call()
m <- match.call(expand.dots = FALSE)
if (is.matrix(eval(m$data, parent.frame())))
m$data <- as.data.frame(data)
m$... <- NULL
m$formula <- m$x
m$x <- NULL
m$scaled <- NULL
m[[1L]] <- quote(stats::model.frame)
m <- eval(m, parent.frame())
Terms <- attr(m, "terms")
attr(Terms, "intercept") <- 0 ## no intercept
x <- model.matrix(Terms, m)
y <- model.extract(m, "response")
if (length(scaled) == 1)
scaled <- rep(scaled, ncol(x))
if (any(scaled)) {
remove <- unique(c(which(labels(Terms) %in% names(attr(x, "contrasts"))),
which(!scaled)
)
)
scaled <- !attr(x, "assign") %in% remove
}
ret <- lssvm(x, y, scaled = scaled, ...)
kcall(ret) <- cl
attr(Terms,"intercept") <- 0 ## no intercept
terms(ret) <- Terms
if (!is.null(attr(m, "na.action")))
n.action(ret) <- attr(m, "na.action")
return (ret)
})
setMethod("lssvm",signature(x="vector"),
function(x,...)
{ x <- t(t(x))
ret <- lssvm(x, ...)
return(ret)
})
setMethod("lssvm",signature(x="matrix"),
function (x,
y,
scaled = TRUE,
kernel = "rbfdot",
kpar = "automatic",
type = NULL,
tau = 0.01,
reduced = TRUE,
tol = 0.0001,
rank = floor(dim(x)[1]/3),
delta = 40,
## prob.model = FALSE,
cross = 0,
fit = TRUE,
...,
subset,
na.action = na.omit)
{
## subsetting and na-handling for matrices
ret <- new("lssvm")
if (!missing(subset)) x <- x[subset,]
df <- unique(na.action(data.frame(y, x)))
y <- df[,1]
x <- as.matrix(df[,-1])
n.action(ret) <- na.action
if(!is.null(type))
type(ret) <- match.arg(type,c("classification","regression"))
if (is.null(type)) type(ret) <- if (is.factor(y)) "classification" else "regression"
else type(ret) <- type
## scaling, subsetting, and NA handling
x.scale <- y.scale <- NULL
## scaling
if (length(scaled) == 1)
scaled <- rep(scaled, ncol(x))
if (any(scaled)) {
co <- !apply(x[,scaled, drop = FALSE], 2, var)
if (any(co)) {
scaled <- rep(FALSE, ncol(x))
warning(paste("Variable(s)",
paste("`",colnames(x[,scaled, drop = FALSE])[co],
"'", sep="", collapse=" and "),
"constant. Cannot scale data.")
)
} else {
xtmp <- scale(x[,scaled])
x[,scaled] <- xtmp
x.scale <- attributes(xtmp)[c("scaled:center","scaled:scale")]
}
}
ncols <- ncol(x)
m <- nrows <- nrow(x)
if(is.character(kernel)){
kernel <- match.arg(kernel,c("rbfdot","polydot","tanhdot","vanilladot","laplacedot","besseldot","anovadot","splinedot","matrix"))
if(kernel == "matrix")
if(dim(x)[1]==dim(x)[2])
return(lssvm(as.kernelMatrix(x), y = y,type = NULL,
tau = 0.01,
tol = 0.0001,
rank = floor(dim(x)[1]/3),
delta = 40,
cross = 0,
fit = TRUE,
...))
else
stop(" kernel matrix not square!")
if(is.character(kpar))
if((kernel == "tanhdot" || kernel == "vanilladot" || kernel == "polydot"|| kernel == "besseldot" || kernel== "anovadot"|| kernel=="splinedot") && kpar=="automatic" )
{
cat (" Setting default kernel parameters ","\n")
kpar <- list()
}
}
if (!is.function(kernel))
if (!is.list(kpar)&&is.character(kpar)&&(is(kernel, "rbfkernel") || is(kernel, "laplacedot") || kernel == "laplacedot"|| kernel=="rbfdot")){
kp <- match.arg(kpar,"automatic")
if(kp=="automatic")
kpar <- list(sigma=mean(sigest(x,scaled=FALSE)[c(1,3)]))
cat("Using automatic sigma estimation (sigest) for RBF or laplace kernel","\n")
}
if(!is(kernel,"kernel"))
{
if(is(kernel,"function")) kernel <- deparse(substitute(kernel))
kernel <- do.call(kernel, kpar)
}
if(!is(kernel,"kernel")) stop("kernel must inherit from class `kernel'")
if(type(ret)=="classification")
{
if (!is.vector(y) && !is.factor (y)) stop("y must be a vector or a factor.")
if(is(y,"vector"))
{
y <- as.matrix(y)
if (nrows != nrow(y)) stop("x and y don't match.")
}
if (is.factor(y)) {
lev(ret) <- levels (y)
y <- as.integer (y)
if (nrows != length(y)) stop("x and y don't match.")
}
else if (is.numeric(y))
{
y <- as.integer(y)
lev(ret) <- unique (y)
}
else
stop ("dependent variable has to be of factor or integer type for classification mode.")
## initialize
nclass(ret) <- length (unique(y))
p <- 0
svindex <- NULL
## create multidimensional y matrix
yind <- t(matrix(1:nclass(ret),nclass(ret),m))
ymat <- matrix(0, m, nclass(ret))
ymat[yind==y] <- 1
if(reduced == FALSE)
{
K <- kernelMatrix(kernel,x)
KP <- K - (1/m)*colSums(K)
beta <- solve((KP%*%K + m * tau * K), KP%*%ymat)
b <- colMeans(ymat) - colMeans(K%*%beta)
alphaindex(ret) <- 1:m
}
else
{
G <- csi(x, ymat, rank = rank ,kernel= kernel, delta = delta , tol = tol)
rep <- sort(pivots(G),index.return=TRUE)$ix
G <- G[rep,]
GtP <- t(G) - matrix(rowSums(t(G))/dim(G)[1],dim(G)[2],dim(G)[1])
Gtalpha <- (GtP)%*%G
diag(Gtalpha) <- diag(Gtalpha) + tau
Gtalpha <- solve(Gtalpha) %*% GtP %*% ymat[rep,,drop=FALSE]
beta <- solve(t(G[1:dim(G)[2],]), Gtalpha)
b <- colMeans(ymat) - colMeans(G%*%Gtalpha)
alphaindex(ret) <- rep[1:dim(G)[2]]
}
alpha(ret) <- beta
## nonzero alpha*y
coef(ret) <- alpha(ret)
## store SV indexes from current problem for later use in predict
## save the indexes from all the SV in a vector (use unique?)
svindex <- alphaindex(ret)
## store betas in a vector
b(ret) <- b
##store C in return object
param(ret)$tau <- tau
## calculate class prob.
## if (prob.model& reduced== TRUE)
# warning("Class Probapilities not supported for reduced model.)
## if(prob.model & reduced == FALSE)
## {
## pos <- as.vector(ymat)==1
## neg <- as.vector(ymat)==-1
## ones <- rep(1,dim(x)[1])
## onesneg <- ones[pos] <- 0
## ones <- rep(1,dim(x)[1])
## onespos <- ones[neg] <- 0
##Kpos <- kernelMult(kernel,x,x[pos,],rep(1,sum(pos)))
##Kneg <- kernelMult(kernel,x,x[neg,],rep(1,sum(neg)))
## Kpos <- K[,pos]%*%rep(1,sum(pos))
## Kneg <- K[,neg]%*%rep(1,sum(neg))
## classmeans <- c(sum( Kpos * coef(ret)[pos] * as.vector(ymat)[pos]),sum( Kneg * coef(ret)[pos] * as.vector(ymat)[pos]))
## kneg <- K%*%onesneg
## kpos <- K%*%onespos
## M <- (diag(dim(x)[1])- (1/dim(x)[1])*rep(1,dim(x)[1])%*%t(rep(1,dim(x)[1])))
## kcentered <- M%*%solve(diag(dim(x)[1]) - tau*M%*%K%*%M)%*%M
## prob.model(ret) <- list(Kpos=Kpos, Kneg=Kneg, kcentered=kcentered, classmeans=classmeans)
## }
}
if(type(ret)=="regression")
{
if (nrows != nrow(x)) stop("x and y don't match.")
## initialize
p <- 0
svindex <- NULL
ymat <- y
G <- csi(x, ymat, rank = rank ,kernel= kernel, delta = delta , tol = tol)
GtP <- t(G) - matrix(rowSums(t(G))/dim(G)[1],dim(G)[2],dim(G)[1])
Gtalpha <- (GtP)%*%G
diag(Gtalpha) <- diag(Gtalpha) + tau
Gtalpha <- solve(Gtalpha) %*% GtP %*% ymat
beta <- solve(t(G[1:dim(G)[2],]), Gtalpha)
b <- colMeans(ymat) - colMeans(G%*%Gtalpha)
alpha(ret) <- beta
## nonzero alpha*y
coef(ret) <- alpha(ret)
## store SV indexes from current problem for later use in predict
alphaindex(ret) <- pivots(G)[1:dim(G)[2]]
## save the indexes from all the SV in a vector (use unique?)
svindex <- alphaindex(ret)
## store betas in a vector
b(ret) <- b
##store C in return object
param(ret)$tau <- tau
}
kcall(ret) <- match.call()
kernelf(ret) <- kernel
## param(ret) <- list(C=C, nu = nu, epsilon = epsilon)
xmatrix(ret) <- x[alphaindex(ret),,drop = FALSE]
ymatrix(ret) <- y
nSV(ret) <- length(svindex)
if(nSV(ret)==0)
stop("No Support Vectors found. You may want to change your parameters")
fitted(ret) <- if (fit)
predict(ret, x) else NA
scaling(ret) <- list(scaled = scaled, x.scale = x.scale)
if (fit){
if(type(ret)=="classification")
error(ret) <- 1 - .classAgreement(table(y,as.integer(fitted(ret))))
if(type(ret)=="regression")
error(ret) <- drop(crossprod(fitted(ret) - y)/m)
}
cross(ret) <- -1
if(cross == 1)
cat("\n","cross should be >1 no cross-validation done!","\n","\n")
else if (cross > 1)
{
cerror <- 0
suppressWarnings(vgr<-split(sample(1:m,m),1:cross))
for(i in 1:cross)
{
cind <- unsplit(vgr[-i],factor(rep((1:cross)[-i],unlist(lapply(vgr[-i],length)))))
cret <- lssvm(x[cind,],y[cind],type = type(ret),kernel=kernel,kpar = NULL,reduced = reduced,
tau=tau, tol=tol, rank = floor(rank/cross), delta = floor(delta/cross), scaled=FALSE, cross = 0, fit = FALSE)
cres <- predict(cret, x[vgr[[i]],])
cerror <- (1 - .classAgreement(table(y[vgr[[i]]],as.integer(cres))))/cross + cerror
}
cross(ret) <- cerror
}
return(ret)
})
## kernelMatrix interface
setMethod("lssvm",signature(x="kernelMatrix"),
function (x,
y,
type = NULL,
tau = 0.01,
tol = 0.0001,
rank = floor(dim(x)[1]/3),
delta = 40,
cross = 0,
fit = TRUE,
...)
{
## subsetting and na-handling for matrices
ret <- new("lssvm")
if(!is.null(type))
type(ret) <- match.arg(type,c("classification","regression"))
if (is.null(type)) type(ret) <- if (is.factor(y)) "classification" else "regression"
else type(ret) <- type
ncols <- ncol(x)
m <- nrows <- nrow(x)
if(type(ret)=="classification")
{
if (!is.vector(y) && !is.factor (y)) stop("y must be a vector or a factor.")
if (is(y,"vector")) {
y <- as.matrix(y)
if (nrows != nrow(y)) stop("x and y don't match.")}
if (is.factor(y)) {
lev(ret) <- levels (y)
y <- as.integer (y)
if (nrows != length(y)) stop("x and y don't match.")
}
else if (is.numeric(y))
{
y <- as.integer(y)
lev(ret) <- unique (y)
}
else
stop ("dependent variable has to be of factor or integer type for classification mode.")
## initialize
nclass(ret) <- length (unique(y))
p <- 0
svindex <- NULL
## create multidimensional y matrix
yind <- t(matrix(1:nclass(ret),nclass(ret),m))
ymat <- matrix(0, m, nclass(ret))
ymat[yind==y] <- 1
KP <- x - (1/m)*colSums(x)
beta <- solve((KP%*%x + m * tau * x), KP%*%ymat)
b <- colMeans(ymat) - colMeans(x%*%beta)
alphaindex(ret) <- 1:m
alpha(ret) <- beta
## nonzero alpha*y
coef(ret) <- alpha(ret)
## store SV indexes from current problem for later use in predict
## save the indexes from all the SV in a vector (use unique?)
svindex <- alphaindex(ret)
## store betas in a vector
b(ret) <- b
##store C in return object
param(ret)$tau <- tau
}
if(type(ret)=="regression")
{
if (nrows != nrow(x)) stop("x and y don't match.")
## initialize
p <- 0
svindex <- NULL
ymat <- y
G <- csi(x, ymat, rank = rank , delta = delta , tol = tol)
GtP <- t(G) - matrix(rowSums(t(G))/dim(G)[1],dim(G)[2],dim(G)[1])
Gtalpha <- (GtP)%*%G
diag(Gtalpha) <- diag(Gtalpha) + tau
Gtalpha <- solve(Gtalpha) %*% GtP %*% ymat[pivots(G),,drop=FALSE]
beta <- solve(t(G[1:dim(G)[2],]), Gtalpha)
b <- colMeans(ymat) - colMeans(G%*%Gtalpha)
alpha(ret) <- beta
## nonzero alpha*y
coef(ret) <- alpha(ret)
## store SV indexes from current problem for later use in predict
alphaindex(ret) <- pivots(G)[1:dim(G)[2]]
## save the indexes from all the SV in a vector (use unique?)
svindex <- alphaindex(ret)
## store betas in a vector
b(ret) <- b
##store C in return object
param(ret)$tau <- tau
}
kcall(ret) <- match.call()
## param(ret) <- list(C=C, nu = nu, epsilon = epsilon)
xmatrix(ret) <- x
ymatrix(ret) <- y
kernelf(ret) <- "Kernel matrix used for training."
nSV(ret) <- length(svindex)
if(nSV(ret)==0)
stop("No Support Vectors found. You may want to change your parameters")
fitted(ret) <- if (fit)
predict(ret, x) else NA
if (fit){
if(type(ret)=="classification")
error(ret) <- 1 - .classAgreement(table(y,as.integer(fitted(ret))))
if(type(ret)=="regression")
error(ret) <- drop(crossprod(fitted(ret) - y)/m)
}
cross(ret) <- -1
if(cross == 1)
cat("\n","cross should be >1 no cross-validation done!","\n","\n")
else if (cross > 1)
{
cerror <- 0
suppressWarnings(vgr<-split(sample(1:m,m),1:cross))
for(i in 1:cross)
{
cind <- unsplit(vgr[-i],factor(rep((1:cross)[-i],unlist(lapply(vgr[-i],length)))))
cret <- lssvm(x[cind,cind],y[cind],type = type(ret), tau=tau, rank = floor(rank/cross), delta = floor(delta/cross), cross = 0, fit = FALSE)
cres <- predict(cret, as.kernelMatrix(x[vgr[[i]], cind,drop = FALSE][,svindex,drop=FALSE]))
cerror <- (1 - .classAgreement(table(y[vgr[[i]]],as.integer(cres))))/cross + cerror
}
cross(ret) <- cerror
}
return(ret)
})
## list interface
setMethod("lssvm",signature(x="list"),
function (x,
y,
scaled = TRUE,
kernel = "stringdot",
kpar = list(length=4, lambda = 0.5),
type = NULL,
tau = 0.01,
reduced = TRUE,
tol = 0.0001,
rank = floor(dim(x)[1]/3),
delta = 40,
cross = 0,
fit = TRUE,
...,
subset)
{
## subsetting and na-handling for matrices
ret <- new("lssvm")
if (!missing(subset)) x <- x[subset]
if(!is.null(type))
type(ret) <- match.arg(type,c("classification","regression"))
if (is.null(type)) type(ret) <- if (is.factor(y)) "classification" else "regression"
else type(ret) <- type
m <- nrows <- length(x)
if(is.character(kernel)){
kernel <- match.arg(kernel,c("rbfdot","polydot","tanhdot","vanilladot","laplacedot","besseldot","anovadot","splinedot","stringdot"))
if(is.character(kpar))
if(kernel == "tanhdot" || kernel == "vanilladot" || kernel == "polydot"|| kernel == "besseldot" || kernel== "anovadot"|| kernel=="splinedot" || kernel == "rbfdot" || kernel == "laplacedot" )
{
stop("List interface supports only the stringdot kernel.")
}
}
if(is(kernel,"kernel"))
if(!is(kernel,"kernel"))
{
if(is(kernel,"function")) kernel <- deparse(substitute(kernel))
kernel <- do.call(kernel, kpar)
}
if(!is(kernel,"kernel")) stop("kernel must inherit from class `kernel'")
if(type(ret)=="classification")
{
if (!is.vector(y) && !is.factor (y)) stop("y must be a vector or a factor.")
if (nrows != nrow(x)) stop("x and y don't match.")
if (is.factor(y)) {
lev(ret) <- levels (y)
y <- as.integer (y)
}
else if (is.numeric(y))
{
y <- as.integer(y)
lev(ret) <- unique (y)
}
else
stop ("dependent variable has to be of factor or integer type for classification mode.")
## initialize
nclass(ret) <- length (unique(y))
p <- 0
svindex <- NULL
## create multidimensional y matrix
yind <- t(matrix(1:nclass(ret),nclass(ret),m))
ymat <- matrix(0, m, nclass(ret))
ymat[yind==y] <- 1
if(reduced == FALSE)
{
K <- kernelMatrix(kernel,x)
KP <- K - (1/m)*colSums(K)
beta <- solve((KP%*%K + m * tau * K), KP%*%ymat)
b <- colMeans(ymat) - colMeans(K%*%beta)
alphaindex(ret) <- 1:m
}
else
{
G <- csi(x, ymat, rank = rank ,kernel= kernel, delta = delta , tol = tol)
GtP <- t(G) - matrix(rowSums(t(G))/dim(G)[1],dim(G)[2],dim(G)[1])
Gtalpha <- (GtP)%*%G
diag(Gtalpha) <- diag(Gtalpha) + tau
Gtalpha <- solve(Gtalpha) %*% GtP %*% ymat[pivots(G),,drop=FALSE]
beta <- solve(t(G[1:dim(G)[2],]), Gtalpha)
b <- colMeans(ymat) - colMeans(G%*%Gtalpha)
alphaindex(ret) <- pivots(G)[1:dim(G)[2]]
}
alpha(ret) <- beta
## nonzero alpha*y
coef(ret) <- alpha(ret)
## store SV indexes from current problem for later use in predict
## save the indexes from all the SV in a vector (use unique?)
svindex <- alphaindex(ret)
## store betas in a vector
b(ret) <- b
##store C in return object
param(ret)$tau <- tau
}
if(type(ret)=="regression")
{
if (nrows != nrow(x)) stop("x and y don't match.")
## initialize
p <- 0
svindex <- NULL
ymat <- y
G <- csi(x, ymat, rank = rank ,kernel= kernel, delta = delta , tol = tol)
GtP <- t(G) - matrix(rowSums(t(G))/dim(G)[1],dim(G)[2],dim(G)[1])
Gtalpha <- (GtP)%*%G
diag(Gtalpha) <- diag(Gtalpha) + tau
Gtalpha <- solve(Gtalpha) %*% GtP %*% ymat[pivots(G),,drop=FALSE]
beta <- solve(t(G[1:dim(G)[2],]), Gtalpha)
b <- colMeans(ymat) - colMeans(G%*%Gtalpha)
alpha(ret) <- beta
## nonzero alpha*y
coef(ret) <- alpha(ret)
## store SV indexes from current problem for later use in predict
alphaindex(ret) <- pivots(G)[1:dim(G)[2]]
## save the indexes from all the SV in a vector (use unique?)
svindex <- alphaindex(ret)
## store betas in a vector
b(ret) <- b
##store C in return object
param(ret)$tau <- tau
}
kcall(ret) <- match.call()
kernelf(ret) <- kernel
## param(ret) <- list(C=C, nu = nu, epsilon = epsilon)
xmatrix(ret) <- x[alphaindex(ret)]
ymatrix(ret) <- y
SVindex(ret) <- svindex
nSV(ret) <- length(svindex)
if(nSV(ret)==0)
stop("No Support Vectors found. You may want to change your parameters")
fitted(ret) <- if (fit)
predict(ret, x) else NA
if (fit){
if(type(ret)=="classification")
error(ret) <- 1 - .classAgreement(table(y,as.integer(fitted(ret))))
if(type(ret)=="regression")
error(ret) <- drop(crossprod(fitted(ret) - y)/m)
}
cross(ret) <- -1
if(cross == 1)
cat("\n","cross should be >1 no cross-validation done!","\n","\n")
else if (cross > 1)
{
cerror <- 0
suppressWarnings(vgr<-split(sample(1:m,m),1:cross))
for(i in 1:cross)
{
cind <- unsplit(vgr[-i],factor(rep((1:cross)[-i],unlist(lapply(vgr[-i],length)))))
cret <- lssvm(x[cind,],y[cind],type = type(ret),kernel=kernel,kpar = NULL,reduced = reduced,
tau=tau, tol=tol, rank = floor(rank/cross), delta = floor(delta/cross), scaled=FALSE, cross = 0, fit = FALSE )
cres <- predict(cret, x[vgr[[i]],])
cerror <- (1 - .classAgreement(table(y[vgr[[i]]],as.integer(cres))))/cross + cerror
}
cross(ret) <- cerror
}
return(ret)
})
#**************************************************************#
setMethod("predict", signature(object = "lssvm"),
function (object, newdata, type = "response", coupler = "minpair")
{
sc <- 0
type <- match.arg(type,c("response","probabilities","decision"))
if (missing(newdata) && type!="response")
return(fitted(object))
else if(missing(newdata))
{
newdata <- xmatrix(object)
sc <- 1
}
ncols <- ncol(xmatrix(object))
nrows <- nrow(xmatrix(object))
oldco <- ncols
if (!is.null(terms(object)))
{
if(!is.matrix(newdata))
newdata <- model.matrix(delete.response(terms(object)), as.data.frame(newdata), na.action = n.action(object))
}
else
newdata <- if (is.vector(newdata)) t(t(newdata)) else as.matrix(newdata)
newcols <- 0
newnrows <- nrow(newdata)
newncols <- ncol(newdata)
newco <- newncols
if (oldco != newco) stop ("test vector does not match model !")
p<-0
if (!is.null(scaling(object)$x.scale) && sc != 1)
newdata[,scaling(object)$scaled] <-
scale(newdata[,scaling(object)$scaled, drop = FALSE],
center = scaling(object)$x.scale$"scaled:center",
scale = scaling(object)$x.scale$"scaled:scale"
)
if(is(newdata,"kernelMatrix"))
res <- newdata %*% coef(object) - b(object)
else
res <- t(t(kernelMult(kernelf(object), newdata,xmatrix(object), alpha(object))) + b(object))
if(type == "response" && type(object)=="classification"){
predres <- max.col(res)
return(factor (lev(object)[predres], levels = lev(object)))
}
if (type == "decision" || type(object)=="regression")
return(res)
if (type =="probabilities" && type(object)=="classification")
{
res - prob.model(object)$classmeans
return(res)
}
})
#****************************************************************************************#
setMethod("show","lssvm",
function(object){
cat("Least Squares Support Vector Machine object of class \"lssvm\"","\n")
cat("\n")
cat(paste("problem type :",type(object), "\n"))
cat(paste(" parameter : tau =",param(object)$tau, "\n"))
cat("\n")
show(kernelf(object))
cat(paste("\nNumber of data points used for training :", nSV(object),"\n"))
if(!is.null(fitted(object)))
cat(paste("Training error :", round(error(object),6),"\n"))
if(cross(object)!= -1)
cat("Cross validation error :",round(cross(object),6),"\n")
})
##.partopro <- function(z,s,m){
##return(2*pi*(1/sqrt((1/z)+s^2))*exp(-(m^2)/(2*((1/z)+s^2))))
##}