nonlinear_KPCA: Kernel Principal Component Analysis

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

Kernel Principal Component Analysis

Description

Kernel principal component analysis (KPCA/Kernel PCA) is a nonlinear extension of classical PCA using techniques called kernel trick, a common method of introducing nonlinearity by transforming, usually, covariance structure or other gram-type estimate to make it flexible in Reproducing Kernel Hilbert Space.

Usage

do.kpca(
  X,
  ndim = 2,
  preprocess = c("null", "center", "scale", "cscale", "whiten", "decorrelate"),
  kernel = c("gaussian", 1)
)

Arguments

X	an (n\times p) matrix or data frame whose rows are observations and columns represent independent variables.
ndim	an integer-valued target dimension.
preprocess	an additional option for preprocessing the data. Default is "null". See also aux.preprocess for more details.
kernel	a vector containing name of a kernel and corresponding parameters. See also aux.kernelcov for complete description of Kernel Trick.

Value

a named list containing

Y

an (n\times ndim) matrix whose rows are embedded observations.

trfinfo

a list containing information for out-of-sample prediction.

vars

variances of projected data / eigenvalues from kernelized covariance matrix.

Author(s)

Kisung You

References

\insertRef

scholkopf_kernel_1997Rdimtools

See Also

aux.kernelcov

Examples

## load iris data
data(iris)
set.seed(100)
subid = sample(1:150,50)
X     = as.matrix(iris[subid,1:4])
label = as.factor(iris[subid,5])

## try out different settings
output1 <- do.kpca(X)                         # default setting
output2 <- do.kpca(X,kernel=c("gaussian",5))  # gaussian kernel with large bandwidth
output3 <- do.kpca(X,kernel=c("laplacian",1)) # laplacian kernel

## visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, col=label, pch=19, main="Gaussian kernel")
plot(output2$Y, col=label, pch=19, main="Gaussian kernel with sigma=5")
plot(output3$Y, col=label, pch=19, main="Laplacian kernel")
par(opar)

kisungyou/Rdimtools documentation built on Jan. 2, 2023, 9:55 a.m.