Support Vector Machines taking initial alpha values

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Description

alphasvm is used to train a support vector machine. It can be used to carry out general regression and classification (of nu and epsilon-type), as well as density-estimation. A formula interface is provided.

Print alphasvm object

Summary alphasvm object

Print summary.alphasvm object

Usage

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alphasvm(x, ...)

## S3 method for class 'formula'
alphasvm(formula, data = NULL, ..., subset,
  na.action = stats::na.omit, scale = FALSE)

## Default S3 method:
alphasvm(x, y = NULL, scale = FALSE, type = NULL,
  kernel = "radial", degree = 3, gamma = if (is.vector(x)) 1 else
  1/ncol(x), coef0 = 0, cost = 1, nu = 0.5, class.weights = NULL,
  cachesize = 40, tolerance = 0.001, epsilon = 0.1, shrinking = TRUE,
  cross = 0, probability = FALSE, fitted = TRUE, alpha = NULL,
  mute = TRUE, ..., subset, na.action = stats::na.omit)

## S3 method for class 'alphasvm'
print(x, ...)

## S3 method for class 'alphasvm'
summary(object, ...)

## S3 method for class 'summary.alphasvm'
print(x, ...)

Arguments

x

a data matrix, a vector, or a sparse matrix (object of class Matrix provided by the Matrix package, or of class matrix.csr provided by the SparseM package, or of class simple_triplet_matrix provided by the slam package).

...

additional parameters for the low level fitting function svm.default

formula

a symbolic description of the model to be fit.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which 'svm' is called from.

subset

An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)

na.action

A function to specify the action to be taken if NAs are found. The default action is stats::na.omit, which leads to rejection of cases with missing values on any required variable. An alternative is stats::na.fail, which causes an error if NA cases are found. (NOTE: If given, this argument must be named.)

scale

A logical vector indicating the variables to be scaled. If scale is of length 1, the value is recycled as many times as needed. Per default, data are scaled internally (both x and y variables) to zero mean and unit variance. The center and scale values are returned and used for later predictions.

y

a response vector with one label for each row/component of x. Can be either a factor (for classification tasks) or a numeric vector (for regression).

type

svm can be used as a classification machine. The default setting for type is C-classification, but may be set to nu-classification as well.

kernel

the kernel used in training and predicting. You might consider changing some of the following parameters, depending on the kernel type.

linear:

u'*v

polynomial:

(gamma*u'*v + coef0)^degree

radial basis:

exp(-gamma*|u-v|^2)

sigmoid:

tanh(gamma*u'*v + coef0)

degree

parameter needed for kernel of type polynomial (default: 3)

gamma

parameter needed for all kernels except linear (default: 1/(data dimension))

coef0

parameter needed for kernels of type polynomial and sigmoid (default: 0)

cost

cost of constraints violation (default: 1)—it is the ‘C’-constant of the regularization term in the Lagrange formulation.

nu

parameter needed for nu-classification

class.weights

a named vector of weights for the different classes, used for asymmetric class sizes. Not all factor levels have to be supplied (default weight: 1). All components have to be named.

cachesize

cache memory in MB (default 40)

tolerance

tolerance of termination criterion (default: 0.001)

epsilon

epsilon in the insensitive-loss function (default: 0.1)

shrinking

option whether to use the shrinking-heuristics (default: TRUE)

cross

if a integer value k>0 is specified, a k-fold cross validation on the training data is performed to assess the quality of the model: the accuracy rate for classification and the Mean Squared Error for regression

probability

logical indicating whether the model should allow for probability predictions.

fitted

logical indicating whether the fitted values should be computed and included in the model or not (default: TRUE)

alpha

Initial values for the coefficients (default: NULL). A numerical vector for binary classification or a nx(k-1) matrix for a k-class-classification problem.

mute

a logical value indicating whether to print training information from svm.

object

An object of class alphasvm

Details

For multiclass-classification with k levels, k>2, libsvm uses the ‘one-against-one’-approach, in which k(k-1)/2 binary classifiers are trained; the appropriate class is found by a voting scheme.

libsvm internally uses a sparse data representation, which is also high-level supported by the package SparseM.

If the predictor variables include factors, the formula interface must be used to get a correct model matrix.

plot.svm allows a simple graphical visualization of classification models.

The probability model for classification fits a logistic distribution using maximum likelihood to the decision values of all binary classifiers, and computes the a-posteriori class probabilities for the multi-class problem using quadratic optimization. The probabilistic regression model assumes (zero-mean) laplace-distributed errors for the predictions, and estimates the scale parameter using maximum likelihood.

Author(s)

Tong He (based on package e1071 by David Meyer and C/C++ code by Cho-Jui Hsieh in Divide-and-Conquer kernel SVM (DC-SVM) )

References

Examples

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data(svmguide1)
svmguide1.t = svmguide1[[2]]
svmguide1 = svmguide1[[1]]

model = alphasvm(x = svmguide1[,-1], y = svmguide1[,1], scale = TRUE)
preds = predict(model, svmguide1.t[,-1])
table(preds, svmguide1.t[,1])

data(iris)
attach(iris)

# default with factor response:
model = alphasvm(Species ~ ., data = iris)

# get new alpha
new.alpha = matrix(0, nrow(iris),2)
new.alpha[model$index,] = model$coefs

model2 = alphasvm(Species ~ ., data = iris, alpha = new.alpha)
preds = predict(model2, as.matrix(iris[,-5]))
table(preds, iris[,5])