Locality Preserving Fisher Discriminant Analysis

Source: R/linear_LPFDA.R

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.

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 \((0,\infty)\).

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 X, Tian X (2009). “Locality Preserving Fisher Discriminant Analysis for Face Recognition.” In Huang D, Jo K, Lee H, Kang H, Bevilacqua V (eds.), Emerging Intelligent Computing Technology and Applications, 261--269.

Author

Kisung You

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)