Locality Preserving Projection

do.lpp is a linear approximation to Laplacian Eigenmaps. More precisely, it aims at finding a linear approximation to the eigenfunctions of the Laplace-Beltrami operator on the graph-approximated data manifold.

do.lpp(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  symmetric = c("union", "intersect", "asymmetric"),
  preprocess = c("center", "scale", "cscale", "whiten", "decorrelate"),
  t = 1
)

Arguments

X

an \((n\times p)\) matrix or data frame whose rows are observations

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.

symmetric

one of "intersect", "union" or "asymmetric" is supported. Default is "union". 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 for heat kernel in \((0,\infty)\).

Value

a named list containing

Y

an \((n\times ndim)\) matrix whose rows are embedded observations.

projection

a \((p\times ndim)\) whose columns are basis for projection.

trfinfo

a list containing information for out-of-sample prediction.

References

He X (2005). Locality Preserving Projections. PhD Thesis, University of Chicago, Chicago, IL, USA.

Author

Kisung You

Examples

## use iris dataset
data(iris)
set.seed(100)
subid <- sample(1:150, 50)
X     <- as.matrix(iris[subid,1:4])
lab   <- as.factor(iris[subid,5])

## try different kernel bandwidths
out1 <- do.lpp(X, t=0.1)
out2 <- do.lpp(X, t=1)
out3 <- do.lpp(X, t=10)

## Visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=lab, pch=19, main="LPP::bandwidth=0.1")
plot(out2$Y, col=lab, pch=19, main="LPP::bandwidth=1")
plot(out3$Y, col=lab, pch=19, main="LPP::bandwidth=10")

par(opar)