LASSO is a popular regularization scheme in linear regression in pursuit of sparsity in coefficient vector
that has been widely used. The method can be used in feature selection in that given the regularization parameter,
it first solves the problem and takes indices of estimated coefficients with the largest magnitude as
meaningful features by solving
$$\textrm{min}_{\beta} ~ \frac{1}{2}\|X\beta-y\|_2^2 + \lambda \|\beta\|_1$$
where \(y\) is response in our method.
do.lasso(X, response, ndim = 2, lambda = 1)Arguments
- X
an \((n\times p)\) matrix whose rows are observations and columns represent independent variables.
- response
a length-\(n\) vector of response variable.
- ndim
an integer-valued target dimension.
- lambda
sparsity 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.
References
Tibshirani R (1996). “Regression Shrinkage and Selection via the Lasso.” Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267--288.
Examples
# \donttest{
## generate swiss roll with auxiliary dimensions
## it follows reference example from LSIR paper.
set.seed(1)
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.lasso(X, y, lambda=0.1)
out2 = do.lasso(X, y, lambda=1)
out3 = do.lasso(X, y, lambda=10)
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="LASSO::lambda=0.1")
plot(out2$Y, main="LASSO::lambda=1")
plot(out3$Y, main="LASSO::lambda=10")
par(opar)
# }