do.crca {Rdimtools}

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.

Author(s)

Kisung You

References

Demartines P, Herault J (1997). “Curvilinear Component Analysis: A Self-Organizing Neural Network for Nonlinear Mapping of Data Sets.” IEEE Transactions on Neural Networks, 8(1), 148–154.

Hérault J, Jausions-Picaud C, Guérin-Dugué A (1999). “Curvilinear Component Analysis for High-Dimensional Data Representation: I. Theoretical Aspects and Practical Use in the Presence of Noise.” In Goos G, Hartmanis J, van Leeuwen J, Mira J, Sánchez-Andrés JV (eds.), Engineering Applications of Bio-Inspired Artificial Neural Networks, volume 1607, 625–634. Springer Berlin Heidelberg, Berlin, Heidelberg. ISBN 978-3-540-66068-2 978-3-540-48772-2.

See Also

do.crda

Examples

## use 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 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$Y, col=label, pch=19, main="alpha=1.0")
plot(out2$Y, col=label, pch=19, main="alpha=5.0")
plot(out3$Y, col=label, pch=19, main="alpha=10.0")
par(opar)