Conformal Isometric Feature Mapping

Conformal Isomap(C-Isomap) is a variant of a celebrated method of Isomap. It aims at, rather than preserving full isometry, maintaining infinitestimal angles - conformality - in that it alters geodesic distance to reflect scale information.

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

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.

References

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.

Author

Kisung You

Examples

# \donttest{
## generate data
set.seed(100)
X <- aux.gensamples(dname="cswiss",n=100)

## 1. original Isomap
output1 <- do.isomap(X,ndim=2)

## 2. C-Isomap
output2 <- do.cisomap(X,ndim=2)

## 3. C-Isomap on a binarized graph
output3 <- do.cisomap(X,ndim=2,weight=FALSE)

## Visualize three different projections
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(output1$Y, main="Isomap")
plot(output2$Y, main="C-Isomap")
plot(output3$Y, main="Binarized C-Isomap")

par(opar)
# }