Package {LiblineaR}

a nxp data matrix. Each row stands for an example (sample, point) and each column stands for a dimension (feature, variable). A vector will be transformed to a n x 1 matrix. Sparse matrices of class matrix.csr, matrix.csc and matrix.coo from package SparseM are accepted. Sparse matrices of class dgCMatrix, dgRMatrix or dgTMatrix from package Matrix are also accepted. Note that C code at the core of LiblineaR package corresponds to a row-based sparse format. Hence, dgCMatrix, dgTMatrix, matrix.csc and matrix.csr inputs are first transformed into matrix.csr or dgRMatrix formats, which requires small extra computation time.

a response vector for prediction tasks with one value for each of the n rows of data. For classification, the values correspond to class labels and can be a 1xn matrix, a simple vector or a factor. For regression, the values correspond to the values to predict, and can be a 1xn matrix or a simple vector.

LiblineaR can produce 10 types of (generalized) linear models, by combining several types of loss functions and regularization schemes. The regularization can be L1 or L2, and the losses can be the regular L2-loss for SVM (hinge loss), L1-loss for SVM, or the logistic loss for logistic regression. The default value for type is 0. See details below. Valid options are:

for multi-class classification

• 0 – L2-regularized logistic regression (primal)

• 1 – L2-regularized L2-loss support vector classification (dual)

• 2 – L2-regularized L2-loss support vector classification (primal)

• 3 – L2-regularized L1-loss support vector classification (dual)

• 4 – support vector classification by Crammer and Singer

• 5 – L1-regularized L2-loss support vector classification

• 6 – L1-regularized logistic regression

• 7 – L2-regularized logistic regression (dual)

for regression

• 11 – L2-regularized L2-loss support vector regression (primal)

• 12 – L2-regularized L2-loss support vector regression (dual)

• 13 – L2-regularized L1-loss support vector regression (dual)

for outlier/novelty detection

• 21 – one-class support vector machine (dual). Unsupervised: target is still required (its length must match the number of rows of data) but its values are ignored – only data is used. Requires bias <= 0 (no bias term is supported for this solver). See nu below. predict returns 1 for inliers and -1 for outliers (see predict.LiblineaR); decisionValues=TRUE additionally returns the raw signed distance to the decision boundary.

cost of constraints violation (default: 1). Rules the trade-off between regularization and correct classification on data. It can be seen as the inverse of a regularization constant. See information on the 'C' constant in details below. A usually good baseline heuristics to tune this constant is provided by the heuristicC function of this package.

set tolerance of termination criterion for optimization. If NULL, the LIBLINEAR defaults are used, which are:

if type is 0, 2, 5 or 6

epsilon=0.01

if type is 1, 3, 4, 7, 12 or 13

epsilon=0.1

The meaning of epsilon is as follows:

if type is 0 or 2:

|f'(w)|_{2} \le \code{epsilon} \times \min (pos,neg) / l \times |f'(w_{0})|_{2}, where f is the primal function and pos/neg are # of positive/negative data (default 0.01)

if type is 11:

|f'(w)|_{2} \le \code{epsilon} \times |f'(w_{0})|_{2}, where f is the primal function (default 0.001)

if type is 1, 3, 4 or 7:

Dual maximal violation \le \code{epsilon} (default 0.1)

if type is 5 or 6:

|f'(w)|_\infty \le \code{epsilon}\times \min(pos,neg)/l\ |f'(w_{0})|_\infty, where f is the primal function (default 0.01)

if type is 12 or 13:

|f'(\alpha)|_1 \le \code{epsilon}\times |f'(\alpha_{0})|_1, where f is the dual function (default 0.1)

set tolerance margin (epsilon) in regression loss function of SVR. Not used for classification methods.

if bias > 0, instance data becomes [data; bias]; if <= 0, no bias term added (default 1).

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 according to the corresponding class label. Not used in regression mode.

if an integer value k>0 is specified, a k-fold cross validation on data is performed to assess the quality of the model via a measure of the accuracy. Note that this metric might not be appropriate if classes are largely unbalanced. Default is 0.

if TRUE, information are printed. Default is FALSE.

if findC is TRUE runs a cross-validation of cross folds to find the best cost (C) value (works only for type 0, 2 and 11). Cross validation is conducted many times under parameters C = start_C, 2*start_C, 4*start_C, 8*start_C, ..., and finds the best one with the highest cross validation accuracy (or, for type 11, the lowest cross-validation mean squared error, additionally searching svr_eps the same way). The procedure stops when the models of all folds become stable or C reaches the maximal value of 1024.

if useInitC is TRUE (default) cost is used as the smallest start_C value of the search range (findC has to be TRUE). If useInitC is FALSE, then the procedure calculates a small enough start_C itself. For type=11, useInitC additionally governs the svr_eps search: when TRUE, svr_eps sets an upper anchor point for where the (always-descending, always ending at 0) svr_eps sweep begins – LIBLINEAR's own find_parameters() always tests every value from that anchor down to 0 and keeps whichever minimizes cross-validation error, so a small svr_eps relative to the scale of target can collapse the sweep to testing only svr_eps=0. When FALSE, the full default 20-step sweep (anchored at the largest abs(target) value) is used instead.

if FALSE, the bias term is excluded from the L1/L2 regularization penalty (upstream LIBLINEAR's -R flag). Default is TRUE (the bias term is regularized like every other coefficient, matching this package's behavior prior to this argument's introduction). Only valid combined with bias == 1 exactly, and only for type 0, 2, 5, 6 or 11; using FALSE elsewhere, or with a different bias, raises an error. Upstream LIBLINEAR's own documentation advises against using this unless you specifically know why you need it.

the nu parameter of one-class SVM (type 21 only, ignored otherwise): an upper bound on the fraction of training examples that may be treated as outliers, and a lower bound on the fraction of examples that end up as support vectors. Must be in (0, 1). Default is 0.5, matching upstream LIBLINEAR's own default.

for backwards compatibility, parameter labels may be provided instead of target. A warning will then be issued, or an error if both are present. Other extra parameters are ignored.

A string describing the type of model fitted, as determined by type.

An integer corresponding to type.

A matrix with the model weights. If bias >0, W contains p+1 columns, the last being the bias term. The columns are named according to the names of data, if provided, or "Wx" where "x" ranges from 1 to the number of dimensions. The bias term is named "Bias".If the number of classes is 2, or if in regression mode rather than classification, the matrix only has one row. If the number of classes is k>2 (classification), it has k rows. Each row i corresponds then to a linear model discriminating between class i and all the other classes. If there are more than 2 classes, rows are named according to the class i which is opposed to the other classes.

The value of bias

A vector containing the class names. This entry is not returned in case of regression models.

a nxp data matrix. Each row stands for an example (sample, point) and each column stands for a dimension (feature, variable). A vector will be transformed to a n x 1 matrix. Sparse matrices of class matrix.csr, matrix.csc and matrix.coo from package SparseM are accepted, as are dgCMatrix, dgRMatrix and dgTMatrix from package Matrix – the same classes accepted by LiblineaR and predict.LiblineaR.

Object of class "LiblineaR", created by LiblineaR.

An n x p matrix containing the new input data. A vector will be transformed to a n x 1 matrix. Sparse matrices of class matrix.csr, matrix.csc and matrix.coo from package SparseM are accepted. Sparse matrices of class dgCMatrix, dgRMatrix or dgTMatrix from package Matrix are also accepted. Note that C code at the core of LiblineaR package corresponds to a row-based sparse format. Hence, dgCMatrix, dgTMatrix, matrix.csc and matrix.csr inputs are first transformed into matrix.csr or dgRMatrix formats, which requires small extra computation time.

Logical indicating whether class probabilities should be computed and returned. Only possible if the model was fitted with type=0, type=6 or type=7, i.e. a Logistic Regression. Default is FALSE.

Logical indicating whether model decision values should be computed and returned. Only possible for classification models (type<10) and one-class SVM (type=21, where the decision value is the signed distance to the decision boundary, i.e. w %*% x - rho; positive means inlier). Not possible for regression models (type 11-13). Default is FALSE.

Currently not used

A vector of predicted labels (regression: predicted values; one-class SVM, type=21: 1 for inliers, -1 for outliers).

An n x k matrix (k number of classes) of the class probabilities. The columns of this matrix are named after class labels.

An n x k matrix (k number of classes) of the model decision values. The columns of this matrix are named after class labels (for one-class SVM, k=1 and the column is unnamed, since there are no class labels for this solver).