print.q.svmmaj: SVM-Maj Algorithm

Description

SVM-Maj is an algorithm to compute a support vector machine (SVM) solution. In its most simple form, it aims at finding hyperplane that optimally separates two given classes. This objective is equivalent to finding a linear combination of k predictor variables to predict the two classes for n observations. SVM-Maj minimizes the standard support vector machine (SVM) loss function. The algorithm uses three efficient updates for three different situations: primal method which is efficient in the case of n > k, the decomposition method, used when the matrix of predictor variables is not of full rank, and a dual method, that is efficient when n < k. Apart from the standard absolute hinge error, SVM-Maj can also handle the quadratic and the Huber hinge.

Usage

# S3 method for q.svmmaj
print(x, ...)
svmmaj(
  X,
  y,
  lambda = 1,
  weights.obs = 1,
  weights.var = 1,
  scale = c("interval", "zscore", "none"),
  spline.knots = 0,
  spline.degree = 1L,
  kernel = vanilladot,
  kernel.sigma = 1,
  kernel.scale = 1,
  kernel.degree = 1,
  kernel.offset = 1,
  hinge = c("absolute", "quadratic", "huber", "logitistic"),
  hinge.delta = 1e-08,
  options = setSVMoptions(),
  initial.point = NULL,
  verbose = FALSE,
  na.action = na.omit,
  ...
)
# S3 method for default
svmmaj(
  X,
  y,
  lambda = 1,
  weights.obs = 1,
  weights.var = 1,
  scale = c("interval", "zscore", "none"),
  spline.knots = 0,
  spline.degree = 1L,
  kernel = vanilladot,
  kernel.sigma = 1,
  kernel.scale = 1,
  kernel.degree = 1,
  kernel.offset = 1,
  hinge = c("absolute", "quadratic", "huber", "logitistic"),
  hinge.delta = 1e-08,
  options = setSVMoptions(),
  initial.point = NULL,
  verbose = FALSE,
  na.action = na.omit,
  ...
)

Value

Returns a svmmaj-class object, of which the methods plot,

plotWeights, summary and predict can be applied. (see also predict.svmmaj and

print.svmmaj)

Arguments

x: the svmmaj object as result of svmmaj
...: Other arguments passed to methods.
X: A data frame (or object coercible by as.data.frame to a data frame) consisting the attributes, the class of each attribute can be either numeric, logical or factor.
y: A factor (or object coercible by factor to a factor) consisting the class labels.
lambda: Regularization parameter of the penalty term.
weights.obs: a vector of length n with the nonnegative weight for the residual of each object (with length n). If the length is 2, then it specifies the weight per class.
weights.var: a vector of length k with weights for each attribute.
scale: Specifies whether the columns of attribute matrix X needs to be standardized into zscores or to the interval [0 1]. Possible values are: none, zscore and interval. Moreover, the standardization parameters can be given instead.
spline.knots: equals the number of internal knots of the spline basis. When the number of knots exceeds the number of (categorical) values of an explanatory variable, the duplicate knots will be removed using unique. For no splines, use spline.knots = 0.
spline.degree: equals the polynomial degree of the splines, for no splines:spline.degree = 1.
kernel: Specifies which kernel function to be used (see dots of package kernlab). Default kernel is the linear kernel.
kernel.sigma: additional parameters used for the kernel function (see dots)
kernel.scale: additional parameters used for the kernel function (see dots)
kernel.degree: additional parameters used for the kernel function (see dots)
kernel.offset: additional parameters used for the kernel function (see dots)
hinge: Specifies with hinge function from getHinge should be used.
hinge.delta: The parameter of the huber hinge (only if hinge = 'huber').
options: additional settings used in the svmmaj algorithm
initial.point: Initial solution.
verbose: TRUE shows the progress of the iteration.
na.action: Generic function for handling NA values.

Author

Hok San Yip, Patrick J.F. Groenen, Georgi Nalbantov

Details

The following settings can be added as element in the options parameter: decomposition Specifies whether the QR decomposition should be used for efficient updates. Possible values are 'svd' for Singular value decomposition (Eigenvalue decomposition for non-linear kernel) or 'chol' for Cholesky (or QR decomposition in case of linear kernel)

convergence Specifies the convergence criterion of the algorithm. Default is 1e-08. increase.step The iteration number from which relaxed update will be used. eps The relaxation of the majorization function for absolute hinge: .25 * eps^-1 is the maximum steepness of the majorization function.

check.positive Specifies whether a check has to be made for positive input values. max.iter maximum number of iterations to use

References

P.J.F. Groenen, G. Nalbantov and J.C. Bioch (2008) SVM-Maj: a majorization approach to linear support vector machines with different hinge errors.

Examples

Run this code


## using default settings
model1 <- svmmaj(
  diabetes$X, diabetes$y,
  hinge = "quadratic", lambda = 1
)
summary(model1)

weights.obs <- list(positive = 2, negative = 1)
## using radial basis kernel
library(kernlab)
model2 <- svmmaj(
  diabetes$X, diabetes$y,
  hinge = "quadratic", lambda = 1,
  weights.obs = weights.obs, scale = "interval",
  kernel = rbfdot,
  kernel.sigma = 1
)
summary(model2)
## I-spline basis
library(ggplot2)
model3 <- svmmaj(
  diabetes$X, diabetes$y,
  weight.obs = weight.obs,
  spline.knots = 3, spline.degree = 2
)
plotWeights(model3, plotdim = c(2, 4))

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