do.kudp: Kernel-Weighted Unsupervised Discriminant Projection

Description

Kernel-Weighted Unsupervised Discriminant Projection (KUDP) is a generalization of UDP where proximity is given by weighted values via heat kernel, $$K_{i,j} = \exp(-\|x_i-x_j\|^2/bandwidth)$$ whence UDP uses binary connectivity. If bandwidth is $+\infty$, it becomes a standard UDP problem. Like UDP, it also performs PCA preprocessing for rank-deficient case.

Usage

do.kudp(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  bandwidth = 1
)

Arguments

an $(n\times p)$ matrix or data frame whose rows are observations and columns represent independent variables.

ndim

an integer-valued target dimension.

type

a vector of neighborhood graph construction. Following types are supported; c("knn",k), c("enn",radius), and c("proportion",ratio). Default is c("proportion",0.1), connecting about 1/10 of nearest data points among all data points. See also aux.graphnbd for more details.

preprocess

an additional option for preprocessing the data. Default is "center". See also aux.preprocess for more details.

bandwidth

bandwidth parameter for heat kernel as the equation above.

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.
projection: a $(p\times ndim)$ whose columns are basis for projection.
interimdim: the number of PCA target dimension used in preprocessing.

References

yang_globally_2007Rdimtools

Examples

Run this code

# NOT RUN {
## generate sample data
X = aux.gensamples(n=200)

## use different kernel bandwidth
out1 <- do.kudp(X, bandwidth=0.1)
out2 <- do.kudp(X, bandwidth=10)
out3 <- do.kudp(X, bandwidth=1000)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="bandwidth=0.1")
plot(out2$Y, main="bandwidth=10")
plot(out3$Y, main="bandwidth=1000")
par(opar)
# }
# NOT RUN {
# }