linear_ELDE: Exponential Local Discriminant Embedding

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

Exponential Local Discriminant Embedding

Description

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.

Usage

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,∞).
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.

Author(s)

Kisung You

References

\insertRef

dornaika_exponential_2013Rdimtools

See Also

do.lde

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)

kisungyou/Rdimtools documentation built on Jan. 2, 2023, 9:55 a.m.