Extended Supervised Locality Preserving Projection

Extended LPP and Supervised LPP are two variants of the celebrated Locality Preserving Projection (LPP) algorithm for dimension reduction. Their combination, Extended Supervised LPP, is a combination of two algorithmic novelties in one that it reflects discriminant information with realistic distance measure via Z-score function.

do.eslpp(
  X,
  label,
  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.
label: a length-\(n\) vector of data class labels.
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

Zheng Z, Yang F, Tan W, Jia J, Yang J (2007). “Gabor Feature-Based Face Recognition Using Supervised Locality Preserving Projection.” Signal Processing, 87(10), 2473--2483.

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.

Author

Kisung You

Examples

## generate data of 2 types with clear difference
set.seed(100)
diff = 50
dt1  = aux.gensamples(n=50)-diff;
dt2  = aux.gensamples(n=50)+diff;

## merge the data and create a label correspondingly
Y      = rbind(dt1,dt2)
label  = rep(1:2, each=50)

## compare LPP, SLPP and ESLPP
outLPP   <- do.lpp(Y)
outSLPP  <- do.slpp(Y, label)
outESLPP <- do.eslpp(Y, label)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(outLPP$Y,   col=label, pch=19, main="LPP")
plot(outSLPP$Y,  col=label, pch=19, main="SLPP")
plot(outESLPP$Y, col=label, pch=19, main="ESLPP")

par(opar)