One of drawbacks of Neighborhood Preserving Embedding (NPE) is the small-sample-size problem under high-dimensionality of original data, where singular matrices to be decomposed suffer from rank deficiency. Instead of applying PCA as a preprocessing step, Complete NPE (CNPE) transforms the singular generalized eigensystem computation of NPE into two eigenvalue decomposition problems.

do.cnpe(
X,
ndim = 2,
type = c("proportion", 0.1),
preprocess = c("center", "scale", "cscale", "decorrelate", "whiten")
)

## Arguments

X

an $$(n\times p)$$ matrix or data frame whose rows are observations and columns represent independent variables.

ndim

an integer-valued target dimension.

type

a vector of neighborhood graph construction. Following types are supported; c("knn",k), c("enn",radius), and c("proportion",ratio). Default is c("proportion",0.1), connecting about 1/10 of nearest data points among all data points. See also aux.graphnbd for more details.

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

Wang Y, Wu Y (2010). “Complete Neighborhood Preserving Embedding for Face Recognition.” Pattern Recognition, 43(3), 1008--1015.

Kisung You

## Examples

# \donttest{
## generate data of 3 types with clear difference
dt1  = aux.gensamples(n=20)-50
dt2  = aux.gensamples(n=20)
dt3  = aux.gensamples(n=20)+50
lab  = rep(1:3, each=20)

## merge the data
X      = rbind(dt1,dt2,dt3)

## try different numbers for neighborhood size
out1 = do.cnpe(X, type=c("proportion",0.10))
out2 = do.cnpe(X, type=c("proportion",0.25))
out3 = do.cnpe(X, type=c("proportion",0.50))

## visualize
plot(out1$Y, col=lab, pch=19, main="CNPE::10% connected") plot(out2$Y, col=lab, pch=19, main="CNPE::25% connected")