SparseSVM_solver: Solve given Sparse SVM problem in parametric simplex method
In PRIMAL: Parametric Simplex Method for Sparse Learning

Description Usage Arguments Value See Also Examples

Solve given Sparse SVM problem in parametric simplex method

1	SparseSVM_solver(X, y, max_it = 50, lambda_threshold = 0.01)

`X`	`x` is an `n` by `d` data matrix
`y`	`y` is a length `n` response vector
`max_it`	This is the number of the maximum path length one would like to achieve. The default length is `50`.
`lambda_threshold`	The parametric simplex method will stop when the calculated parameter is smaller than lambda. The default value is `0.01`.

An object with S3 class "primal" is returned:

`data`	The `n` by `d` data matrix from the input
`response`	The length `n` response vector from the input
`beta`	A matrix of regression estimates whose columns correspond to regularization parameters for parametric simplex method.
`beta0`	A vector of regression estimates whose index correspond to regularization parameters for parametric simplex method.
`df`	The degree of freecom (number of nonzero coefficients) along the solution path.
`value`	The sequence of optimal value of the object function corresponded to the sequence of lambda.
`iterN`	The number of iteration in the program.
`lambda`	The sequence of regularization parameters `lambda` obtained in the program.
`type`	The type of the problem, such as `Dantzig` and `SparseSVM`.

primal-package

## SparseSVM
## We set the X matrix to be normal random matrix and Y is a vector consists of -1 and 1
## with the number of iteration to be 1000.
## Generate the design matrix and coefficient vector
n = 200 # sample number
d = 100 # sample dimension
c = 0.5 # correlation parameter
s = 20  # support size of coefficient
set.seed(1024)
X = matrix(rnorm(n*d),n,d)+c*rnorm(n)
## Generate response and solve the solution path
Y <- sample(c(-1,1),n,replace = TRUE)
## Sparse SVM solved with parametric simplex method
fit.SVM = SparseSVM_solver(X, Y, max_it = 1000, lambda_threshold = 0.01)
## lambdas used
print(fit.SVM$lambda)
## Visualize the solution path
plot(fit.SVM)