lssvm  R Documentation 
The lssvm
function is an
implementation of the Least Squares SVM. lssvm
includes a
reduced version of Least Squares SVM using a decomposition of the
kernel matrix which is calculated by the csi
function.
## S4 method for signature 'formula' lssvm(x, data=NULL, ..., subset, na.action = na.omit, scaled = TRUE) ## S4 method for signature 'vector' lssvm(x, ...) ## S4 method for signature 'matrix' lssvm(x, y, scaled = TRUE, kernel = "rbfdot", kpar = "automatic", type = NULL, tau = 0.01, reduced = TRUE, tol = 0.0001, rank = floor(dim(x)[1]/3), delta = 40, cross = 0, fit = TRUE, ..., subset, na.action = na.omit) ## S4 method for signature 'kernelMatrix' lssvm(x, y, type = NULL, tau = 0.01, tol = 0.0001, rank = floor(dim(x)[1]/3), delta = 40, cross = 0, fit = TRUE, ...) ## S4 method for signature 'list' lssvm(x, y, scaled = TRUE, kernel = "stringdot", kpar = list(length=4, lambda = 0.5), type = NULL, tau = 0.01, reduced = TRUE, tol = 0.0001, rank = floor(dim(x)[1]/3), delta = 40, cross = 0, fit = TRUE, ..., subset)
x 
a symbolic description of the model to be fit, a matrix or
vector containing the training data when a formula interface is not
used or a 
data 
an optional data frame containing the variables in the model. By default the variables are taken from the environment which ‘lssvm’ 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 
Type of problem. Either "classification" or "regression".
Depending on whether 
kernel 
the kernel function used in training and predicting. This parameter can be set to any function, of class kernel, which computes a dot product between two vector arguments. kernlab provides the most popular kernel functions which can be used by setting the kernel parameter to the following strings:
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.

tau 
the regularization parameter (default 0.01) 
reduced 
if set to 
rank 
the maximal rank of the decomposed kernel matrix, see

delta 
number of columns of cholesky performed in advance, see

tol 
tolerance of termination criterion for the 
fit 
indicates whether the fitted values should be computed and included in the model or not (default: 'TRUE') 
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 Mean Squared Error for regression 
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 
... 
additional parameters 
Least Squares Support Vector Machines are reformulation to the
standard SVMs that lead to solving linear KKT systems.
The algorithm is based on the minimization of a classical penalized
leastsquares cost function. The current implementation approximates
the kernel matrix by an incomplete Cholesky factorization obtained by
the csi
function, thus the solution is an approximation
to the exact solution of the lssvm optimization problem. The quality
of the solution depends on the approximation and can be influenced by
the "rank" , "delta", and "tol" parameters.
An S4 object of class "lssvm"
containing the fitted model,
Accessor functions can be used to access the slots of the object (see
examples) which include:
alpha 
the parameters of the 
coef 
the model coefficients (identical to alpha) 
b 
the model offset. 
xmatrix 
the training data used by the model 
Alexandros Karatzoglou
alexandros.karatzoglou@ci.tuwien.ac.at
J. A. K. Suykens and J. Vandewalle
Least Squares Support Vector Machine Classifiers
Neural Processing Letters vol. 9, issue 3, June 1999
ksvm
, gausspr
, csi
## simple example data(iris) lir < lssvm(Species~.,data=iris) lir lirr < lssvm(Species~.,data= iris, reduced = FALSE) lirr ## Using the kernelMatrix interface iris < unique(iris) rbf < rbfdot(0.5) k < kernelMatrix(rbf, as.matrix(iris[,5])) klir < lssvm(k, iris[, 5]) klir pre < predict(klir, k)
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