Extended Locality Preserving Projection (EXTLPP) is an unsupervised
dimension reduction algorithm with a bit of flavor in adopting
discriminative idea by nature. It raises a question on the data points
at *moderate* distance in that a Z-shaped function is introduced in
defining similarity derived from Euclidean distance.

```
do.extlpp(
X,
ndim = 2,
numk = max(ceiling(nrow(X)/10), 2),
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten")
)
```

## Arguments

- X
an \((n\times p)\) matrix or data frame whose rows are observations.

- ndim
an integer-valued target dimension.

- numk
the number of neighboring points for k-nn graph construction.

- 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

Shikkenawis G, Mitra SK (2012).
“Improving the Locality Preserving Projection for Dimensionality Reduction.”
In *2012 Third International Conference on Emerging Applications of Information Technology*, 161--164.

## Examples

```
## generate data
set.seed(100)
X <- aux.gensamples(n=75)
## run Extended LPP with different neighborhood graph
out1 <- do.extlpp(X, numk=5)
out2 <- do.extlpp(X, numk=10)
out3 <- do.extlpp(X, numk=25)
## Visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="EXTLPP::k=5")
plot(out2$Y, main="EXTLPP::k=10")
plot(out3$Y, main="EXTLPP::k=25")
par(opar)
```