One of drawbacks of Neighborhood Preserving Embedding (NPE) is the small-sample-size problem
under high-dimensionality of original data, where singular matrices to be decomposed suffer from
rank deficiency. Instead of applying PCA as a preprocessing step, Complete NPE (CNPE) transforms the
singular generalized eigensystem computation of NPE into two eigenvalue decomposition problems.

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

## 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.

## 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.

## References

Wang Y, Wu Y (2010).
“Complete Neighborhood Preserving Embedding for Face Recognition.”
*Pattern Recognition*, **43**(3), 1008--1015.

## Examples

```
# \donttest{
## generate data of 3 types with clear difference
dt1 = aux.gensamples(n=20)-50
dt2 = aux.gensamples(n=20)
dt3 = aux.gensamples(n=20)+50
lab = rep(1:3, each=20)
## merge the data
X = rbind(dt1,dt2,dt3)
## try different numbers for neighborhood size
out1 = do.cnpe(X, type=c("proportion",0.10))
out2 = do.cnpe(X, type=c("proportion",0.25))
out3 = do.cnpe(X, type=c("proportion",0.50))
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=lab, pch=19, main="CNPE::10% connected")
plot(out2$Y, col=lab, pch=19, main="CNPE::25% connected")
plot(out3$Y, col=lab, pch=19, main="CNPE::50% connected")
par(opar)
# }
```