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.
an \((n\times p)\) matrix or data frame whose rows are observations and columns represent independent variables.
an integer-valued target dimension.
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.
one of "intersect"
, "union"
or "asymmetric"
is supported. Default is "union"
. See also aux.graphnbd
for more details.
TRUE
to perform Isomap on weighted graph, or FALSE
otherwise.
an additional option for preprocessing the data.
Default is "center". See also aux.preprocess
for more details.
a named list containing
an \((n\times ndim)\) matrix whose rows are embedded observations.
a list containing information for out-of-sample prediction.
Silva VD, Tenenbaum JB (2003). “Global Versus Local Methods in Nonlinear Dimensionality Reduction.” In Becker S, Thrun S, Obermayer K (eds.), Advances in Neural Information Processing Systems 15, 721--728. MIT Press.
# \donttest{
## 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)
# }