svmadmm (version 0.2)

svm.admm: linear/nonlinear svm solver based ADMM and IADMM algorithms

Description

svm.admm is a simple function for solving large-scale regularized linear/nonlinear classification by using ADMM and IADMM algorithms. This function provides linear L2-regularized primal classification (both ADMM and IADMM are available), kernel L2-regularized dual classification (IADMM) as well as L1-regularized primal classification (both ADMM and IADMM are available). The training of the models perform well practice.

Usage

svm.admm(x.tr, y.tr, type = 0, kernel = "radial", sigma = 1/ncol(x.tr),
  degree = 1, scale = 1, offset = 1, algo = "iadmm", lambda = 1,
  rho = 1, eps = 0.01)

Arguments

x.tr

a n*p data matrix. Each row stands for an example (sample, point) and each column stands for a dimension (feature, variable).

y.tr

a n-length vector. The values correspond to class labels.

type

svmadmm can provide 3 types of linear/kernel models. The default value for type is 0. See details below. Valid options are:

• 0 -- L2-regularized kernel svm (dual)
• 1 -- L2-regularized linear svm (primal)

kernel

the kernel used in training and predicting when type is 0. The default value for kernel is radial. See details below. Valid options are:

• radial-- The Gaussian RBF kernel k(x,x') = exp(-sigma \|x - x

sigma

The inverse kernel width used by the Gaussian.

degree

The degree of the polynomial kernel function. This has to be an positive integer.

scale

The scaling parameter of the polynomial kernel is a convenient way of normalizing patterns without the need to modify the data itself.

offset

The offset used in a polynomial kernel.

algo

the algorithm to solve the problem w.r.t. type.

lambda

regularization constant (default: 1). Rules the trade-off between regularization and correct classification on data.

rho

regularization constant (default: 1).

eps

epsilon in the termination condition.

Value

• An list containing the fitted model, including:
• alpha
  A solution for dual form svm classification.
• beta
  A solution for primal form svm classifciation, also are the model weights.
• type
  An integer correspinding to type.
• kernel
  A function to define the kernel.
• x.tr
  The training input data.
• y.tr
  The training output data.

Details

svmadmm internally computing kernel matrix when type is 0, which is based by the package kernlab.

Examples

library(svmadmm)
n = 100
p = 10
x = matrix(runif(2 * n * p, -1, 1), nrow = 2 * n)
y = sign(x[, 1])
y.ind = sample(1 : (2 * n), n / 10, replace = FALSE)
y[y.ind] = - y[y.ind]
x.tr = x[1 : n, ]
y.tr = y[1 : n]
x.te = x[-(1 : n), ]
y.te = y[-(1 : n)]
model = svm.admm(x.tr, y.tr)
fit = svm.predict(x.te, model)