Rdimtools (version 1.0.0)

do.lapeig: Laplacian Eigenmaps

Description

do.lapeig performs Laplacian Eigenmaps (LE) to discover low-dimensional manifold embedded in high-dimensional data space using graph laplacians. This is a classic algorithm employing spectral graph theory.

Usage

do.lapeig(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  symmetric = c("union", "intersect", "asymmetric"),
  preprocess = c("null", "center", "scale", "cscale", "whiten", "decorrelate"),
  weighted = TRUE,
  kernelscale = 1
)

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.

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 "null". See also aux.preprocess for more details.

weighted

TRUE for weighted graph laplacian and FALSE for combinatorial laplacian where connectivity is represented as 1 or 0 only.

kernelscale

kernel scale parameter. Default value is 1.0.

Value

a named list containing

Y

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

eigvals

a vector of eigenvalues for laplacian matrix.

trfinfo

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

References

belkin_laplacian_2003Rdimtools

Examples

# NOT RUN {
## generate swiss-roll dataset of size 100
X <- aux.gensamples(n=100)

## two types of graph laplacians using 20% of neighbors
out1 <- do.lapeig(X,ndim=2,type=c("proportion",0.05),kernelscale=10) # weighted version
out2 <- do.lapeig(X,ndim=2,type=c("proportion",0.05),weighted=FALSE) # combinatorial

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(out1$Y, main="weighted")
plot(out2$Y, main="combinatorial")
par(opar)
# }
# NOT RUN {
# }