Maximal Local Interclass Embedding

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.

See also

do.mfa

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)
}