Local Discriminant Embedding

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.

Author

Kisung You

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)