nonlinear_CRDA: Curvilinear Distance Analysis

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

Curvilinear Distance Analysis

Description

Curvilinear Distance Analysis (CRDA) is a variant of Curvilinear Component Analysis in that the input pairwise distance is altered by curvilinear distance on a data manifold. Like in Isomap, it first generates neighborhood graph and finds shortest path on a constructed graph so that the shortest-path length plays as an approximate geodesic distance on nonlinear manifolds.

Usage

do.crda(
  X,
  ndim = 2,
  type = c("proportion", 0.1),
  symmetric = "union",
  weight = TRUE,
  lambda = 1,
  alpha = 1,
  maxiter = 1000,
  tolerance = 1e-06
)

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 CRDA on weighted graph, or FALSE otherwise.
lambda	threshold value.
alpha	initial value for updating.
maxiter	maximum number of iterations allowed.
tolerance	stopping criterion for maximum absolute discrepancy between two distance matrices.

Value

a named list containing

Y

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

niter

the number of iterations until convergence.

trfinfo

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

Author(s)

Kisung You

References

\insertRef

lee_curvilinear_2002Rdimtools

\insertRef

lee_nonlinear_2004Rdimtools

See Also

do.isomap, do.crca

Examples

## load iris data
data(iris)
set.seed(100)
subid = sample(1:150,50)
X     = as.matrix(iris[subid,1:4])
label = as.factor(iris[subid,5])

## different settings of connectivity
out1 <- do.crda(X, type=c("proportion",0.10))
out2 <- do.crda(X, type=c("proportion",0.25))
out3 <- do.crda(X, type=c("proportion",0.50))

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, pch=19, main="10% connected")
plot(out2$Y, col=label, pch=19, main="25% connected")
plot(out3$Y, col=label, pch=19, main="50% connected")
par(opar)

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