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.
svmmaj(X,y,lambda=1,...)
# S3 method for default
svmmaj(X, y, lambda=1, weights.obs = 1, weights.var= 1, scale = 'none',
spline.knots=0L, spline.degree=1L, kernel=vanilladot, kernel.sigma=1, kernel.degree=1,
kernel.scale=1, kernel.offset=0, hinge='absolute', hinge.k=5, convergence=1e-8,
print.step=FALSE, initial.point=NULL, increase.step = 20, eps=1e-8,
check.positive=TRUE,na.action=na.omit,...)plotWeights(object,plotdim=c(3,3))
# S3 method for svmmaj
plot(x,titletext=NULL,...)
A data frame (or object coercible by as.data.frame
to a data frame) consisting the attribues, the class of each attribute can be either numeric,
logical or factor.
A factor (or object coercible by factor to a factor) consisting the
class labels.
Regularization parameter of the penalty term.
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.
Vector of length k with weights for each attribute.
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.
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
link[base]{unique}. spline.knots = 0 and spline.degree=1
in case of no splines.
The polynomial degree of the splines, for no splines:
spline.knots = 0 and spline.degree=1.
Specifies which kernel function to be used (see dots of
package kernlab). Default kernel is the linear kernel .
The kernel parameter sigma for the RBF kernel (see rbfdot).
Default value is 1.
The degree parameter of the polynomial kernel (see polydot).
The scale parameter of the polynomial kernel (see polydot).
The offset used in a polynomial kernel (polydot).
Specifies which hinge term to be used. Possible values are:
absolute, quadratic, huber.
The parameter of the huber hinge, if the huber hinge is used.
Specifies the convergence criterion of the algorithm. Default is 1e-08.
print.step=TRUE shows the progress of the iteration.
Initial solution.
The iteration number from which relaxed update will be used.
The relaxation of the majorization function for absolute hinge: .25 * eps^-1 is the
maximum steepness of the majorization function.
Specifies whether a check has to be made for positive input values.
Generic function for handling NA values.
The model returned from svmmaj.
The model returned from svmmaj used to plot the distribution of the
objects per class using plot.svmmaj.
An optional title for plot.svmmaj.
A vector of the form c(nr, nc). Subsequent figures will be drawn
in an nr-by-nc array on the device.
Other arguments passed to methods.
Returns a svmmaj-class, of which the methods plot, plotWeights, summary and predict can be applied.
(see also predict.svmmaj)
The returning object consist of the following values:
The function specifications which has been called.
The regularization parameter of the penalty term which has been used.
The corresponding loss function value of the final solution.
Number of iterations needed to evaluate the algorithm.
The attribute matrix of dim(X) = c(n,k).
The vector of length n with the actual class labels. These labels can be numeric [0 1] or
two strings.
A vector of length n with the predicted class labels of each object, derived from q.tilde
The attribute matrix X after standardization and (if specified) spline transformation.
The applied normalization parameters (see normalize).
The spline knots which has been used (see isb).
Denotes the number of spline basis of each explanatory variable in X.
The decomposition matrices used in estimating the model.
The hinge function which has been used (see hinge).
If identified, the beta parameters for the linear combination (only available for linear kernel).
A vector of length n with predicted values of each object including the intercept.
Number of support vectors.
P.J.F. Groenen, G. Nalbantov and J.C. Bioch (2008) SVM-Maj: a majorization approah to linear support vector machines with different hinge errors.
dots for the computations of the kernels.
predict.svmmaj
normalize
isb
hinge
# NOT RUN {
attach(diabetes)
## using default settings
model1 <- model <- svmmaj(X,y,hinge='quadratic', lambda=1)
summary(model1)
weights.obs = list(positive=2,negative=1)
## using radial basis kernel
model2 <- svmmaj(X,y,hinge='quadratic', lambda=1, weights.obs=weights.obs,
standardize='interval',kernel=rbfdot,
kernel.sigma=1)
summary(model2)
## I-spline basis
model3 <- svmmaj(X,y,,weights.obs=weights.obs,spline.knots=3,spline.degree=2)
plotWeights(model3,plotdim=c(2,4))
# }
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