lssvm {kernlab} | 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 kernelMatrix or a list of character vectors. |
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 x . Can be either
a factor (for classification tasks) or a numeric vector (for
classification or regression - currently nor suported -). |
scaled |
A logical vector indicating the variables to be
scaled. If scaled is of length 1, the value is recycled as
many times as needed and all non-binary variables are scaled.
Per default, data are scaled internally to zero mean and unit
variance. The center and scale values are returned and used for later predictions. |
type |
Type of problem. Either "classification" or "regression".
Depending on whether y is a factor or not, the default
setting for type is "classification" or "regression" respectively,
but can be overwritten by setting an explicit value. (regression is
currently not supported) |
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:
x as a kernel
matrix calling the kernelMatrix interface.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 hyper-parameters (kernel parameters).
This is a list which contains the parameters to be used with the
kernel function. For valid parameters for existing kernels are :
kpar can also be set to the string "automatic" which uses the heuristics in
sigest to calculate a good sigma value for the
Gaussian RBF or Laplace kernel, from the data. (default = "automatic").
|
tau |
the regularization parameter (default 0.01) |
reduced |
if set to FALSE the full linear problem of the
lssvm is solved, when TRUE a reduced method using csi is used. |
rank |
the maximal rank of the decomposed kernel matrix, see
csi |
delta |
number of columns of cholesky performed in advance, see
csi (default 40) |
tol |
tolerance of termination criterion for the csi
function, lower tolerance leads to more preciese approximation but
may increase the training time and the decomposed matrix size (default: 0.0001) |
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 k-fold 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 NA s are
found. The default action is na.omit , which leads to rejection of cases
with missing values on any required variable. An alternative
is na.fail , which causes an error if NA cases
are found. (NOTE: If given, this argument must be named.) |
... |
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
least-squares cost function. The current implementation approximates
the kernel matrix by an incomplete Cholesky factorization optained 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 "lssvm" |
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
## 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)