Kernel Local Discriminant Embedding

Kernel Local Discriminant Embedding (KLDE) is a variant of Local Discriminant Embedding in that it aims to preserve inter- and intra-class neighborhood information in a nonlinear manner using kernel trick. Note that the combination of kernel matrix and its eigendecomposition often suffers from lacking numerical rank. For such case, our algorithm returns a warning message and algorithm stops working any further due to its innate limitations of constructing weight matrix.

do.klde(
  X,
  label,
  ndim = 2,
  t = 1,
  numk = max(ceiling(nrow(X)/10), 2),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  ktype = c("gaussian", 1),
  kcentering = TRUE
)

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.

ktype

a vector containing name of a kernel and corresponding parameters. See also aux.kernelcov for complete description of Kernel Trick.

kcentering

a logical; TRUE to use centered Kernel matrix, FALSE otherwise.

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.

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

# \donttest{
## generate data of 2 types with clear difference
set.seed(100)
diff = 25
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.klde(X, label, numk=5)
out2 <- do.klde(X, label, numk=10)
out3 <- do.klde(X, label, numk=20)

## visualize
opar = par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, pch=19, main="k=5")
plot(out2$Y, col=label, pch=19, main="k=10")
plot(out3$Y, col=label, pch=19, main="k=20")

par(opar)
# }