Exponential Local Discriminant Embedding

Local Discriminant Embedding (LDE) suffers from a small-sample-size problem where scatter matrix may suffer from rank deficiency. Exponential LDE (ELDE) provides not only a remedy for the problem using matrix exponential, but also a flexible framework to transform original data into a new space via distance diffusion mapping similar to kernel-based nonlinear mapping.

do.elde(
  X,
  label,
  ndim = 2,
  t = 1,
  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.

t

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

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

Dornaika F, Bosaghzadeh A (2013). “Exponential Local Discriminant Embedding and Its Application to Face Recognition.” IEEE Transactions on Cybernetics, 43(3), 921--934.

See also

do.lde

Author

Kisung You

Examples

## generate data of 3 types with difference
set.seed(100)
dt1  = aux.gensamples(n=20)-50
dt2  = aux.gensamples(n=20)
dt3  = aux.gensamples(n=20)+50

## merge the data and create a label correspondingly
X      = rbind(dt1,dt2,dt3)
label  = rep(1:3, each=20)

## try different kernel bandwidth
out1 = do.elde(X, label, t=1)
out2 = do.elde(X, label, t=10)
out3 = do.elde(X, label, t=100)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="ELDE::bandwidth=1")
plot(out2$Y, pch=19, col=label, main="ELDE::bandwidth=10")
plot(out3$Y, pch=19, col=label, main="ELDE::bandwidth=100")

par(opar)