Local Discriminant Embedding (LDE) is a supervised algorithm that learns
the embedding for the submanifold of each class. Its idea is to same-class
data points maintain their original neighborhood information while
segregating different-class data distinct from each other.

```
do.lde(
X,
label,
ndim = 2,
t = 1,
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.

- label
a length-\(n\) vector of data class labels.

- ndim
an integer-valued target dimension.

- t
kernel bandwidth in \((0,\infty)\).

- 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

Hwann-Tzong Chen, Huang-Wei Chang, Tyng-Luh Liu (2005).
“Local Discriminant Embedding and Its Variants.”
In *2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition*, volume 2, 846--853.

## Examples

```
## generate data of 2 types with clear difference
set.seed(100)
diff = 15
dt1 = aux.gensamples(n=50)-diff;
dt2 = aux.gensamples(n=50)+diff;
## merge the data and create a label correspondingly
X = rbind(dt1,dt2)
label = rep(1:2, each=50)
## try different neighborhood size
out1 <- do.lde(X, label, numk=5)
out2 <- do.lde(X, label, numk=10)
out3 <- do.lde(X, label, numk=25)
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="LDE::k=5")
plot(out2$Y, pch=19, col=label, main="LDE::k=10")
plot(out3$Y, pch=19, col=label, main="LDE::k=25")
par(opar)
```