alphasvm: Support Vector Machines taking initial alpha values

In hetong007/SwarmSVM: Ensemble Learning Algorithms Based on Support Vector Machines

Support Vector Machines taking initial alpha values

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.

Usage

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,
  nclass = NULL,
  ...,
  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.
nclass	the number of classes in total.
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

• Chang, Chih-Chung and Lin, Chih-Jen:
  LIBSVM: a library for Support Vector Machines
  https://www.csie.ntu.edu.tw/~cjlin/libsvm/

• Exact formulations of models, algorithms, etc. can be found in the document:
  Chang, Chih-Chung and Lin, Chih-Jen:
  LIBSVM: a library for Support Vector Machines
  https://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.ps.gz

• More implementation details and speed benchmarks can be found on: Rong-En Fan and Pai-Hsune Chen and Chih-Jen Lin:
  Working Set Selection Using the Second Order Information for Training SVM
  https://www.csie.ntu.edu.tw/~cjlin/papers/quadworkset.pdf

Examples

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])

hetong007/SwarmSVM documentation built on Jan. 10, 2023, 12:52 a.m.