getK {kyotil}

getK

Description

getK calculates the kernel matrix between X and itself and returns a n by n matrix. Alternatively, it calculates the kernel matrix between X and X2 and returns a n by n2 matrix.

Usage

getK (X,kernel,para=NULL,X2=NULL,C = NULL)

Arguments

X

covariate matrix with dimension n by d. Note this is not the paired difference of covariate matrix.

kernel

string specifying type of kernel: polynomial or p (1 + <x,y>)^para,
rbf or r exp(-para*||x-y||^2),
linear or l <x,y>,
ibs or i 0.5*mean(2.0 - |x-y|) or sum(w*(2.0 - |x-y|))/sum(w), with x[i],y[i] in {0,1,2} and weights 'w' given in 'para'.
hamming or h for sum(x == y) with x[i],y[i] binary,
no default.

para

parameter of the kernel fucntion. for ibs or hamming, para can be a vector of weights.

X2

optional second covariate matrix with dimension n2 by d

C

logical. If TRUE, kernels are computed by custom routines in C, which may be more memory efficient, and faster too for ibs and hamming kernels.

Details

IBS stands for 'Identical By State'. If 'x','y' are in in {0,1,2} then
IBS(x,y) = 0 if |x-y|=2, 1 if |x-y|=1, 2 if |x-y|=0, or IBS(x,y) = 2.0 - |x-y|.
K(u,v) = sum(IBS(u[i],v[i])) / 2K where K = length(u).
The 'hamming' kernel is the equivalent of the 'ibs' kernel for binary data. Note that 'hamming' kernel is based on hamming similarity(!), not on dissimilarity distance.

Within in the code, C is default to TRUE for ibs and hamming kernels and FALSE otherwise.

Value

A kernel matrix.

Author(s)

Youyi Fong [e-mail]
Krisztian Sebestyen [e-mail]
Shuxin Yin

Examples

X = cbind(x1=rnorm(n=5), x2=rnorm(n=5))
dim(X)
X2 = cbind(x1=rnorm(n=3), x2=rnorm(n=3))
dim(X2)

K = getK(X,"linear")
dim(K)

K = getK(X,"linear",X2=X2)
dim(K)
K1 = getK(X2,"l",X2=X)
dim(K1)
all(K==t(K1))


# RBF kernel
K = getK(X,"rbf",para=1,X2=X2)
K1 = getK(X2,"r",para=1,X2=X)
all(K==t(K1))


# IBS kernel for ternary data 
X <- as.matrix(expand.grid(0:2,0:2))
K = getK(X,kernel = 'ibs')

# add weight
w = runif(ncol(X))
K = getK(X,kernel = 'ibs',para = w) 


# IBS kernel for binary data via option 'h' for 'hamming similarity measure'
X <- as.matrix(expand.grid(0:1,0:1))
K=getK(X,kernel = 'h')