Rdimtools (version 1.0.6)

do.plp: Piecewise Laplacian-based Projection (PLP)

Description

do.plp is an implementation of Piecewise Laplacian-based Projection (PLP) that adopts two-stage reduction scheme with local approximation.

Usage

do.plp(
  X,
  ndim = 2,
  preprocess = c("null", "center", "scale", "cscale", "whiten", "decorrelate"),
  type = c("proportion", 0.2)
)

Arguments

X

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

ndim

an integer-valued target dimension.

preprocess

an additional option for preprocessing the data. Default is "null". See also aux.preprocess for more details.

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.

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.

Notes

Random Control Points : The performance of embedding using PLP heavily relies on selection of control points, which is contingent on the performance of \(k\)-means clustering.

User Interruption : PLP is actually an interactive algorithm that a user should be able to intervene intermittently. Such functionality is, however, sacrificed in this version.

Details

First step is to select \(\sqrt{n}\) number of control points using \(k\)-means algorithm. After selecting control points that play similar roles as representatives of the entire data points, it performs classical multidimensional scaling.

For the rest of the data other than control points, Laplacian Eigenmaps (do.lapeig) is then applied to high-dimensional data points lying in neighborhoods of each control point. Embedded low-dimensional local manifold is then aligned to match their coordinates as of their counterparts from classical MDS.

References

paulovich_piece_2011Rdimtools

Examples

# NOT RUN {
## use iris data
data(iris)
X     = as.matrix(iris[,1:4])
label = as.integer(iris$Species)

## try with 3 levels of connectivity
out1 = do.plp(X, type=c("proportion", 0.1))
out2 = do.plp(X, type=c("proportion", 0.2))
out3 = do.plp(X, type=c("proportion", 0.5))

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, main="PLP::10% connected")
plot(out2$Y, col=label, main="PLP::20% connected")
plot(out3$Y, col=label, main="PLP::50% connected")
par(opar)
# }
# NOT RUN {
# }