kyotil (version 2015.11-13)

getK: 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 + )^para, rbf or r exp(-para*||x-y||^2), linear or l , 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'. hammin

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.

Value

• A kernel matrix.

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.

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')