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#Kernel Hebbian Algorithm function
setGeneric("kha",function(x, ...) standardGeneric("kha"))
setMethod("kha", signature(x = "formula"),
function(x, data = NULL, na.action = na.omit, ...)
{
mt <- terms(x, data = data)
if(attr(mt, "response") > 0) stop("response not allowed in formula")
attr(mt, "intercept") <- 0
cl <- match.call()
mf <- match.call(expand.dots = FALSE)
mf$formula <- mf$x
mf$... <- NULL
mf[[1L]] <- quote(stats::model.frame)
mf <- eval(mf, parent.frame())
na.act <- attr(mf, "na.action")
Terms <- attr(mf, "terms")
x <- model.matrix(mt, mf)
res <- kha(x, ...)
## fix up call to refer to the generic, but leave arg name as `formula'
cl[[1]] <- as.name("kha")
kcall(res) <- cl
attr(Terms,"intercept") <- 0
terms(res) <- Terms
if(!is.null(na.act))
n.action(res) <- na.act
return(res)
})
setMethod("kha",signature(x="matrix"),
function(x, kernel = "rbfdot", kpar = list(sigma = 0.1),
features = 5, eta = 0.005, th = 1e-4, maxiter = 10000, verbose = FALSE, na.action = na.omit, ...)
{
x <- na.action(x)
x <- as.matrix(x)
m <- nrow(x)
ret <- new("kha")
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'")
## Initialize A dual variables
A <- matrix(runif(features*m),m,features)*2 - 1
AOld <- A
## compute square norm of data
a <- rowSums(x^2)
## initialize the empirical sum kernel map
eskm <- rep(0,m)
for (i in 1:m)
eskm[i] <- sum(kernelFast(kernel,x,x[i,,drop=FALSE], a))
eks <- sum(eskm)
counter <- 0
step <- th + 1
Aold <- A
while(step > th && counter < maxiter)
{
y <- rep(0, features)
ot <- rep(0,m)
## Hebbian Iteration
for (i in 1:m)
{
## compute y output
etkm <- as.vector(kernelFast(kernel,x,x[i,,drop=FALSE], a))
sum1 <- as.vector(etkm %*% A)
sum2 <- as.vector(eskm%*%A)/m
asum <- colSums(A)
sum3 <- as.vector(eskm[i]*asum)/m
sum4 <- as.vector(eks * asum)/m^2
y <- sum1 - sum2 - sum3 + sum4
## update A
yy <- y%*%t(y)
yy[upper.tri(yy)] <- 0
tA <- t(A)
A <- t(tA - eta * yy%*%tA)
A[i,] <- A[i,] + eta * y
}
if (counter %% 100 == 0 )
{
step = mean(abs(Aold - A))
Aold <- A
if(verbose)
cat("Iteration :", counter, "Converged :", step,"\n")
}
counter <- counter + 1
}
## Normalize in Feature space
cA <- t(A) - colSums(A)
Fnorm <- rep(0,features)
for (j in 1:m)
Fnorm <- Fnorm + colSums(t(cA[,j] * cA) * as.vector(kernelFast(kernel,x,x[j,,drop=FALSE],a)))
if(any(Fnorm==0))
{
warning("Normalization vector contains zeros, replacing them with ones")
Fnorm[which(Fnorm==0)] <- 1
}
A <- t(t(A)/sqrt(Fnorm))
pcv(ret) <- A
eig(ret) <- Fnorm
names(eig(ret)) <- paste("Comp.", 1:features, sep = "")
eskm(ret) <- eskm
kcall(ret) <- match.call()
kernelf(ret) <- kernel
xmatrix(ret) <- x
return(ret)
})
## Project a new matrix into the feature space
setMethod("predict",signature(object="kha"),
function(object , x)
{
if (!is.null(terms(object)))
{
if(!is.matrix(x))
x <- model.matrix(delete.response(terms(object)), as.data.frame(x), na.action = n.action(object))
}
else
x <- if (is.vector(x)) t(t(x)) else as.matrix(x)
if (is.vector(x)||is.data.frame(x))
x<-as.matrix(x)
if (!is.matrix(x)) stop("x must be a matrix a vector or a data frame")
n <- nrow(x)
m <- nrow(xmatrix(object))
A <- pcv(object)
y <- matrix(0,n,dim(A)[2])
eks <- sum(eskm(object))
a <- rowSums(xmatrix(object)^2)
## Project data
sum2 <- as.vector(eskm(object)%*%A)/m
asum <- colSums(A)
sum4 <- as.vector(eks * asum)/m^2
for (i in 1:n)
{
## compute y output
etkm <- as.vector(kernelFast(kernelf(object),xmatrix(object),x[i,,drop=FALSE], a))
sum1 <- as.vector(etkm %*% A)
sum3 <- sum(etkm)*asum/m
y[i,] <- sum1 - sum2 - sum3 + sum4
}
return(y)
})
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