nonlinear_LLE: Locally Linear Embedding

In Rdimtools: Dimension Reduction and Estimation Methods

Locally Linear Embedding

Description

Locally-Linear Embedding (LLE) was introduced approximately at the same time as Isomap. Its idea was motivated to describe entire data manifold by making a chain of local patches in that low-dimensional embedding should resemble the connectivity pattern of patches. do.lle also provides an automatic choice of regularization parameter based on an optimality criterion suggested by authors.

Usage

do.lle(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  symmetric = "union",
  weight = TRUE,
  preprocess = c("null", "center", "scale", "cscale", "decorrelate", "whiten"),
  regtype = FALSE,
  regparam = 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.
weight	TRUE to perform LLE on weighted graph, or FALSE otherwise.
preprocess	an additional option for preprocessing the data. Default is "null". See also aux.preprocess for more details.
regtype	TRUE for automatic regularization parameter selection, FALSE otherwise as default.
regparam	regularization parameter.

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.

eigvals

a vector of eigenvalues from computation of embedding matrix.

Author(s)

Kisung You

References

\insertRef

roweis_nonlinear_2000Rdimtools

Examples

## generate swiss-roll data
set.seed(100)
X = aux.gensamples(n=100)

## 1. connecting 10% of data for graph construction.
output1 <- do.lle(X,ndim=2,type=c("proportion",0.10))

## 2. constructing 20%-connected graph
output2 <- do.lle(X,ndim=2,type=c("proportion",0.20))

## 3. constructing 50%-connected with bigger regularization parameter
output3 <- do.lle(X,ndim=2,type=c("proportion",0.5),regparam=10)

## Visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, main="5%")
plot(output2$Y, main="10%")
plot(output3$Y, main="50%+Binary")
par(opar)

Rdimtools documentation built on Nov. 5, 2025, 5:28 p.m.