Curvilinear Distance Analysis

Source: R/nonlinear_CRDA.R

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.

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.

References

Lee JA, Lendasse A, Verleysen M (2002). “Curvilinear Distance Analysis versus Isomap.” In ESANN.

Lee JA, Lendasse A, Verleysen M (2004). “Nonlinear Projection with Curvilinear Distances: Isomap versus Curvilinear Distance Analysis.” Neurocomputing, 57, 49--76.

See also

do.isomap, do.crca

Author

Kisung You

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)