nonlinear_ISOMAP: Isometric Feature Mapping

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

Isometric Feature Mapping

Description

do.isomap is an efficient implementation of a well-known Isomap method by Tenenbaum et al (2000). Its novelty comes from applying classical multidimensional scaling on nonlinear manifold, which is approximated as a graph.

Usage

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

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 Isomap on weighted graph, or FALSE otherwise.
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.

Author(s)

Kisung You

References

\insertRef

silva_global_2003Rdimtools

Examples

## generate data
set.seed(100)
X <- aux.gensamples(n=123)

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

## 2. constructing 25%-connected graph
output2 <- do.isomap(X,ndim=2,type=c("proportion",0.25),weight=FALSE)

## 3. constructing 25%-connected with binarization
output3 <- do.isomap(X,ndim=2,type=c("proportion",0.50),weight=FALSE)

## Visualize three different projections
opar = par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, main="10%")
plot(output2$Y, main="25%")
plot(output3$Y, main="25%+Binary")
par(opar)

kisungyou/Rdimtools documentation built on Jan. 2, 2023, 9:55 a.m.