linear_LPFDA: Locality Preserving Fisher Discriminant Analysis

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

Locality Preserving Fisher Discriminant Analysis

Description

Locality Preserving Fisher Discriminant Analysis (LPFDA) is a supervised variant of LPP. It can also be seemed as an improved version of LDA where the locality structure of the data is preserved. The algorithm aims at getting a subspace projection matrix by solving a generalized eigenvalue problem.

Usage

do.lpfda(
  X,
  label,
  ndim = 2,
  type = c("proportion", 0.1),
  preprocess = c("center", "scale", "cscale", "whiten", "decorrelate"),
  t = 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.
t	bandwidth parameter for heat kernel in (0,∞).

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

zhao_locality_2009Rdimtools

Examples

## generate data of 3 types with clear 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 proportion of connected edges
out1 = do.lpfda(X, label, type=c("proportion",0.10))
out2 = do.lpfda(X, label, type=c("proportion",0.25))
out3 = do.lpfda(X, label, type=c("proportion",0.50))

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

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