Locally Discriminating Projection

Locally Discriminating Projection (LDP) is a supervised linear dimension reduction method. It utilizes both label/class information and local neighborhood information to discover the intrinsic structure of the data. It can be considered as an extension of LPP in a supervised manner.

do.ldp(
  X,
  label,
  ndim = 2,
  type = c("proportion", 0.1),
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  beta = 10
)

Arguments

X

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

label

a length-\(n\) vector of data class labels.

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.

beta

bandwidth parameter for heat kernel in \((0,\infty)\).

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

Zhao H, Sun S, Jing Z, Yang J (2006). “Local Structure Based Supervised Feature Extraction.” Pattern Recognition, 39(8), 1546--1550.

Author

Kisung You

Examples

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

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

## try different neighborhood sizes
out1 = do.ldp(X, label, type=c("proportion",0.10))
out2 = do.ldp(X, label, type=c("proportion",0.25))
out3 = do.ldp(X, label, type=c("proportion",0.50))

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, pch=19, main="10% connectivity")
plot(out2$Y, col=label, pch=19, main="25% connectivity")
plot(out3$Y, col=label, pch=19, main="50% connectivity")

par(opar)