Extended Locality Preserving Projection

Extended Locality Preserving Projection (EXTLPP) is an unsupervised dimension reduction algorithm with a bit of flavor in adopting discriminative idea by nature. It raises a question on the data points at moderate distance in that a Z-shaped function is introduced in defining similarity derived from Euclidean distance.

do.extlpp(
  X,
  ndim = 2,
  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.

ndim

an integer-valued target dimension.

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

Shikkenawis G, Mitra SK (2012). “Improving the Locality Preserving Projection for Dimensionality Reduction.” In 2012 Third International Conference on Emerging Applications of Information Technology, 161--164.

See also

do.lpp

Author

Kisung You

Examples

## generate data
set.seed(100)
X <- aux.gensamples(n=75)

## run Extended LPP with different neighborhood graph
out1 <- do.extlpp(X, numk=5)
out2 <- do.extlpp(X, numk=10)
out3 <- do.extlpp(X, numk=25)

## Visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="EXTLPP::k=5")
plot(out2$Y, main="EXTLPP::k=10")
plot(out3$Y, main="EXTLPP::k=25")

par(opar)