Maximal Local Interclass Embedding (MLIE) is a linear supervised method that
the local interclass graph and the intrinsic graph are constructed to find a set of
projections that maximize the local interclass scatter and the local
intraclass compactness at the same time. It can be deemed an extended version of MFA.

```
do.mlie(
X,
label,
ndim = 2,
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
k1 = max(ceiling(nrow(X)/10), 2),
k2 = max(ceiling(nrow(X)/10), 2)
)
```

## 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.

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

for more details.

- k1
the number of same-class neighboring points (homogeneous neighbors).

- k2
the number of different-class neighboring points (heterogeneous neighbors).

## 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

Lai Z, Zhao C, Chen Y, Jin Z (2011).
“Maximal Local Interclass Embedding with Application to Face Recognition.”
*Machine Vision and Applications*, **22**(4), 619--627.

## Examples

```
if (FALSE) {
## generate data of 3 types with clear difference
set.seed(100)
diff = 100
dt1 = aux.gensamples(n=20)-diff
dt2 = aux.gensamples(n=20)
dt3 = aux.gensamples(n=20)+diff
## merge the data and create a label correspondingly
X = rbind(dt1,dt2,dt3)
label = rep(1:3, each=20)
## try different numbers for neighborhood size
out1 = do.mlie(X, label, k1=5, k2=5)
out2 = do.mlie(X, label, k1=10,k2=10)
out3 = do.mlie(X, label, k1=25,k2=25)
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="MLIE::nbd size=5")
plot(out2$Y, main="MLIE::nbd size=10")
plot(out3$Y, main="MLIE::nbd size=25")
par(opar)
}
```