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.

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

- 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 J, Zhang D, Yang J, Niu B (2007).
“Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Applications to Face and Palm Biometrics.”
*IEEE Transactions on Pattern Analysis and Machine Intelligence*, **29**(4), 650--664.

## Examples

```
## use iris dataset
data(iris)
set.seed(100)
subid = sample(1:150,50)
X = as.matrix(iris[subid,1:4])
lab = as.factor(iris[subid,5])
## 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$Y, col=lab, pch=19, main="bandwidth=0.1")
plot(out2$Y, col=lab, pch=19, main="bandwidth=10")
plot(out3$Y, col=lab, pch=19, main="bandwidth=1000")
par(opar)
```