Description Usage Arguments Details Value Note Author(s) References See Also Examples
Support Vector Machines are an excellent tool for classification,
novelty detection, and regression. ksvm
supports the
well known Csvc, nusvc, (classification) oneclasssvc (novelty)
epssvr, nusvr (regression) formulations along with
native multiclass classification formulations and
the boundconstraint SVM formulations.
ksvm
also supports classprobabilities output and
confidence intervals for regression.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  ## S4 method for signature 'formula'
ksvm(x, data = NULL, ..., subset, na.action = na.omit, scaled = TRUE)
## S4 method for signature 'vector'
ksvm(x, ...)
## S4 method for signature 'matrix'
ksvm(x, y = NULL, scaled = TRUE, type = NULL,
kernel ="rbfdot", kpar = "automatic",
C = 1, nu = 0.2, epsilon = 0.1, prob.model = FALSE,
class.weights = NULL, cross = 0, fit = TRUE, cache = 40,
tol = 0.001, shrinking = TRUE, ...,
subset, na.action = na.omit)
## S4 method for signature 'kernelMatrix'
ksvm(x, y = NULL, type = NULL,
C = 1, nu = 0.2, epsilon = 0.1, prob.model = FALSE,
class.weights = NULL, cross = 0, fit = TRUE, cache = 40,
tol = 0.001, shrinking = TRUE, ...)
## S4 method for signature 'list'
ksvm(x, y = NULL, type = NULL,
kernel = "stringdot", kpar = list(length = 4, lambda = 0.5),
C = 1, nu = 0.2, epsilon = 0.1, prob.model = FALSE,
class.weights = NULL, cross = 0, fit = TRUE, cache = 40,
tol = 0.001, shrinking = TRUE, ...,
na.action = na.omit)

x 
a symbolic description of the model to be fit. When not
using a formula x can be a matrix or vector containing the training
data
or a kernel matrix of class 
data 
an optional data frame containing the training data, when using a formula. By default the data is taken from the environment which ‘ksvm’ is called from. 
y 
a response vector with one label for each row/component of 
scaled 
A logical vector indicating the variables to be
scaled. If 
type 

kernel 
the kernel function used in training and predicting.
This parameter can be set to any function, of class kernel, which
computes the inner product in feature space between two
vector arguments (see
Setting the kernel parameter to "matrix" treats The kernel parameter can also be set to a user defined function of class kernel by passing the function name as an argument. 
kpar 
the list of hyperparameters (kernel parameters). This is a list which contains the parameters to be used with the kernel function. For valid parameters for existing kernels are :
Hyperparameters for user defined kernels can be passed through the
kpar parameter as well. In the case of a Radial Basis kernel function (Gaussian)
kpar can also be set to the string "automatic" which uses the heuristics in

C 
cost of constraints violation (default: 1) this is the ‘C’constant of the regularization term in the Lagrange formulation. 
nu 
parameter needed for 
epsilon 
epsilon in the insensitiveloss function used for

prob.model 
if set to 
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. 
cache 
cache memory in MB (default 40) 
tol 
tolerance of termination criterion (default: 0.001) 
shrinking 
option whether to use the shrinkingheuristics
(default: 
cross 
if a integer value k>0 is specified, a kfold 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 
fit 
indicates whether the fitted values should be computed
and included in the model or not (default: 
... 
additional parameters for the low level fitting function 
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 
ksvm
uses John Platt's SMO algorithm for solving the SVM QP problem an
most SVM formulations. On the spocsvc
, kbbsvc
, Cbsvc
and
epsbsvr
formulations a chunking algorithm based on the TRON QP
solver is used.
For multiclassclassification with k classes, k > 2, ksvm
uses the
‘oneagainstone’approach, in which k(k1)/2 binary classifiers are
trained; the appropriate class is found by a voting scheme,
The spocsvc
and the kbbsvc
formulations deal with the
multiclassclassification problems by solving a single quadratic problem involving all the classes.
If the predictor variables include factors, the formula interface must be used to get a
correct model matrix.
In classification when prob.model
is TRUE
a 3fold cross validation is
performed on the data and a sigmoid function is fitted on the
resulting decision values f.
The data can be passed to the ksvm
function in a matrix
or a
data.frame
, in addition ksvm
also supports input in the form of a
kernel matrix of class kernelMatrix
or as a list of character
vectors where a string kernel has to be used.
The plot
function for binary classification ksvm
objects
displays a contour plot of the decision values with the corresponding
support vectors highlighted.
The predict function can return class probabilities for
classification problems by setting the type
parameter to
"probabilities".
The problem of model selection is partially addressed by an empirical
observation for the RBF kernels (Gaussian , Laplace) where the optimal values of the
sigma width parameter are shown to lie in between the 0.1 and 0.9
quantile of the \x x'\ statistics. When using an RBF kernel
and setting kpar
to "automatic", ksvm
uses the sigest
function
to estimate the quantiles and uses the median of the values.
An S4 object of class "ksvm"
containing the fitted model,
Accessor functions can be used to access the slots of the object (see
examples) which include:
alpha 
The resulting support vectors, (alpha vector) (possibly scaled). 
alphaindex 
The index of the resulting support vectors in the data
matrix. Note that this index refers to the preprocessed data (after
the possible effect of 
coef 
The corresponding coefficients times the training labels. 
b 
The negative intercept. 
nSV 
The number of Support Vectors 
obj 
The value of the objective function. In case of oneagainstone classification this is a vector of values 
error 
Training error 
cross 
Cross validation error, (when cross > 0) 
prob.model 
Contains the width of the Laplacian fitted on the residuals in case of regression, or the parameters of the sigmoid fitted on the decision values in case of classification. 
Data is scaled internally by default, usually yielding better results.
Alexandros Karatzoglou (SMO optimizers in C++ by ChihChung Chang & ChihJen Lin)
[email protected]
Chang ChihChung, Lin ChihJen
LIBSVM: a library for Support Vector Machines
http://www.csie.ntu.edu.tw/~cjlin/libsvm
ChihWei Hsu, ChihJen Lin
BSVM
http://www.csie.ntu.edu.tw/~cjlin/bsvm/
J. Platt
Probabilistic outputs for support vector machines and comparison to regularized likelihood methods
Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B. Schoelkopf and D. Schuurmans, Eds. Cambridge, MA: MIT Press, 2000.
http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.1639
H.T. Lin, C.J. Lin and R. C. Weng
A note on Platt's probabilistic outputs for support vector machines
http://www.csie.ntu.edu.tw/~htlin/paper/doc/plattprob.pdf
C.W. Hsu and C.J. Lin
A comparison on methods for multiclass support vector machines
IEEE Transactions on Neural Networks, 13(2002) 415425.
http://www.csie.ntu.edu.tw/~cjlin/papers/multisvm.ps.gz
K. Crammer, Y. Singer
On the learnability and design of output codes for multiclass prolems
Computational Learning Theory, 3546, 2000.
http://webee.technion.ac.il/people/koby/publications/ecocmlj02.pdf
J. Weston, C. Watkins
Multiclass support vector machines
In M. Verleysen, Proceedings of ESANN99 Brussels, 1999
http://citeseer.ist.psu.edu/8884.html
predict.ksvm
, ksvmclass
, couple
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96  ## simple example using the spam data set
data(spam)
## create test and training set
index < sample(1:dim(spam)[1])
spamtrain < spam[index[1:floor(dim(spam)[1]/2)], ]
spamtest < spam[index[((ceiling(dim(spam)[1]/2)) + 1):dim(spam)[1]], ]
## train a support vector machine
filter < ksvm(type~.,data=spamtrain,kernel="rbfdot",
kpar=list(sigma=0.05),C=5,cross=3)
filter
## predict mail type on the test set
mailtype < predict(filter,spamtest[,58])
## Check results
table(mailtype,spamtest[,58])
## Another example with the famous iris data
data(iris)
## Create a kernel function using the build in rbfdot function
rbf < rbfdot(sigma=0.1)
rbf
## train a bound constraint support vector machine
irismodel < ksvm(Species~.,data=iris,type="Cbsvc",
kernel=rbf,C=10,prob.model=TRUE)
irismodel
## get fitted values
fitted(irismodel)
## Test on the training set with probabilities as output
predict(irismodel, iris[,5], type="probabilities")
## Demo of the plot function
x < rbind(matrix(rnorm(120),,2),matrix(rnorm(120,mean=3),,2))
y < matrix(c(rep(1,60),rep(1,60)))
svp < ksvm(x,y,type="Csvc")
plot(svp,data=x)
### Use kernelMatrix
K < as.kernelMatrix(crossprod(t(x)))
svp2 < ksvm(K, y, type="Csvc")
svp2
# test data
xtest < rbind(matrix(rnorm(20),,2),matrix(rnorm(20,mean=3),,2))
# test kernel matrix i.e. inner/kernel product of test data with
# Support Vectors
Ktest < as.kernelMatrix(crossprod(t(xtest),t(x[SVindex(svp2), ])))
predict(svp2, Ktest)
#### Use custom kernel
k < function(x,y) {(sum(x*y) +1)*exp(0.001*sum((xy)^2))}
class(k) < "kernel"
data(promotergene)
## train svm using custom kernel
gene < ksvm(Class~.,data=promotergene[c(1:20, 80:100),],kernel=k,
C=5,cross=5)
gene
#### Use text with string kernels
data(reuters)
is(reuters)
tsv < ksvm(reuters,rlabels,kernel="stringdot",
kpar=list(length=5),cross=3,C=10)
tsv
## regression
# create data
x < seq(20,20,0.1)
y < sin(x)/x + rnorm(401,sd=0.03)
# train support vector machine
regm < ksvm(x,y,epsilon=0.01,kpar=list(sigma=16),cross=3)
plot(x,y,type="l")
lines(x,predict(regm,x),col="red")

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