do.enet {Rdimtools}

Elastic Net Regularization

Description

Elastic Net is a regularized regression method by solving

\textrm{min}_{\beta} ~ \frac{1}{2}\|X\beta-y\|_2^2 + \lambda_1 \|\beta \|_1 + \lambda_2 \|\beta \|_2^2

where y iis response variable in our method. The method can be used in feature selection like LASSO.

Usage

do.enet(X, response, ndim = 2, lambda1 = 1, lambda2 = 1)

Arguments

X

an (n\times p) matrix or data frame whose rows are observations and columns represent independent variables.

response

a length-n vector of response variable.

ndim

an integer-valued target dimension.

lambda1

\ell_1 regularization parameter in (0,\infty).

lambda2

\ell_2 regularization parameter in (0,\infty).

Value

a named Rdimtools S3 object containing

Y

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

featidx

a length-ndim vector of indices with highest scores.

projection

a (p\times ndim) whose columns are basis for projection.

algorithm

name of the algorithm.

Author(s)

Kisung You

References

Zou H, Hastie T (2005). “Regularization and Variable Selection via the Elastic Net.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301–320.

Examples

## generate swiss roll with auxiliary dimensions
## it follows reference example from LSIR paper.
set.seed(100)
n = 123
theta = runif(n)
h     = runif(n)
t     = (1+2*theta)*(3*pi/2)
X     = array(0,c(n,10))
X[,1] = t*cos(t)
X[,2] = 21*h
X[,3] = t*sin(t)
X[,4:10] = matrix(runif(7*n), nrow=n)

## corresponding response vector
y = sin(5*pi*theta)+(runif(n)*sqrt(0.1))

## try different regularization parameters
out1 = do.enet(X, y, lambda1=0.01)
out2 = do.enet(X, y, lambda1=1)
out3 = do.enet(X, y, lambda1=100)

## extract embeddings
Y1 = out1$Y; Y2 = out2$Y; Y3 = out3$Y

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(Y1, pch=19, main="ENET::lambda1=0.01")
plot(Y2, pch=19, main="ENET::lambda1=1")
plot(Y3, pch=19, main="ENET::lambda1=100")
par(opar)