Rdimtools (version 1.0.0)

do.crca: Curvilinear Component Analysis

Description

Curvilinear Component Analysis (CRCA) is a type of self-organizing algorithms for manifold learning. Like MDS, it aims at minimizing a cost function (Stress) based on pairwise proximity. Parameter lambda is a heaviside function for penalizing distance pair of embedded data, and alpha controls learning rate similar to that of subgradient method in that at each iteration \(t\) the gradient is weighted by \(\alpha /t\).

Usage

do.crca(X, ndim = 2, 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.

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

demartines_curvilinear_1997Rdimtools

herault_curvilinear_1999Rdimtools

See Also

do.crda

Examples

# NOT RUN {
## generate sample data
X <- aux.gensamples(n=200)

## different initial learning rates
out1 <- do.crca(X,alpha=1)
out2 <- do.crca(X,alpha=5)
out3 <- do.crca(X,alpha=10)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="alpha=1.0")
plot(out2$Y, main="alpha=5.0")
plot(out3$Y, main="alpha=10.0")
par(opar)
# }
# NOT RUN {

# }