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LIBLINEAR is a simple package for solving large-scale regularized linear
classification, regression and outlier detection. It currently supports
- L2-regularized logistic regression/L2-loss support vector classification/L1-loss support vector classification
- L1-regularized L2-loss support vector classification/L1-regularized logistic regression
- L2-regularized L2-loss support vector regression/L1-loss support vector regression
- one-class support vector machine.
This document explains the usage of LIBLINEAR.
To get started, please read the ``Quick Start'' section first.
For developers, please check the ``Library Usage'' section to learn
how to integrate LIBLINEAR in your software.
Table of Contents
=================
- When to use LIBLINEAR but not LIBSVM
- Quick Start
- Installation
- `train' Usage
- `predict' Usage
- `svm-scale' Usage
- Examples
- Library Usage
- Building Windows Binaries
- MATLAB/OCTAVE interface
- Python Interface
- Additional Information
When to use LIBLINEAR but not LIBSVM
====================================
There are some large data for which with/without nonlinear mappings
gives similar performances. Without using kernels, one can
efficiently train a much larger set via linear classification/regression.
These data usually have a large number of features. Document classification
is an example.
Warning: While generally liblinear is very fast, its default solver
may be slow under certain situations (e.g., data not scaled or C is
large). See Appendix B of our SVM guide about how to handle such
cases.
http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf
Warning: If you are a beginner and your data sets are not large, you
should consider LIBSVM first.
LIBSVM page:
http://www.csie.ntu.edu.tw/~cjlin/libsvm
Quick Start
===========
See the section ``Installation'' for installing LIBLINEAR.
After installation, there are programs `train' and `predict' for
training and testing, respectively.
About the data format, please check the README file of LIBSVM. Note
that feature index must start from 1 (but not 0).
A sample classification data included in this package is `heart_scale'.
Type `train heart_scale', and the program will read the training
data and output the model file `heart_scale.model'. If you have a test
set called heart_scale.t, then type `predict heart_scale.t
heart_scale.model output' to see the prediction accuracy. The `output'
file contains the predicted class labels.
For more information about `train' and `predict', see the sections
`train' Usage and `predict' Usage.
To obtain good performances, sometimes one needs to scale the
data. Please check the program `svm-scale' of LIBSVM. For large and
sparse data, use `-l 0' to keep the sparsity.
Installation
============
On Unix systems, type `make' to build the `train', `predict',
and `svm-scale' programs. Run them without arguments to show the usages.
On other systems, consult `Makefile' to build them (e.g., see
'Building Windows binaries' in this file).
This software uses some level-1 BLAS subroutines. The needed functions are
included in this package. If a BLAS library is available on your
machine, you may use it by modifying the Makefile: Unmark the following line
#LIBS = -lblas
and mark
LIBS = blas/blas.a
The tool `svm-scale', borrowed from LIBSVM, is for scaling input data file.
`train' Usage
=============
Usage: train [options] training_set_file [model_file]
options:
-s type : set type of solver (default 1)
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 detection
21 -- one-class support vector machine (dual)
-c cost : set the parameter C (default 1)
-p epsilon : set the epsilon in loss function of epsilon-SVR (default 0.1)
-n nu : set the parameter nu of one-class SVM (default 0.5)
-e epsilon : set tolerance of termination criterion
-s 0 and 2
|f'(w)|_2 <= eps*min(pos,neg)/l*|f'(w0)|_2,
where f is the primal function and pos/neg are # of
positive/negative data (default 0.01)
-s 11
|f'(w)|_2 <= eps*|f'(w0)|_2 (default 0.0001)
-s 1, 3, 4, 7, and 21
Dual maximal violation <= eps; similar to libsvm (default 0.1 except 0.01 for -s 21)
-s 5 and 6
|f'(w)|_1 <= eps*min(pos,neg)/l*|f'(w0)|_1,
where f is the primal function (default 0.01)
-s 12 and 13
|f'(alpha)|_1 <= eps |f'(alpha0)|,
where f is the dual function (default 0.1)
-B bias : if bias >= 0, instance x becomes [x; bias]; if < 0, no bias term added (default -1)
-R : not regularize the bias; must with -B 1 to have the bias; DON'T use this unless you know what it is
(for -s 0, 2, 5, 6, 11)
-wi weight: weights adjust the parameter C of different classes (see README for details)
-v n: n-fold cross validation mode
-C : find parameters (C for -s 0, 2 and C, p for -s 11)
-q : quiet mode (no outputs)
Option -v randomly splits the data into n parts and calculates cross
validation accuracy on them.
Option -C conducts cross validation under different parameters and finds
the best one. This option is supported only by -s 0, -s 2 (for finding
C) and -s 11 (for finding C, p). If the solver is not specified, -s 2
is used.
Formulations:
For L2-regularized logistic regression (-s 0), we solve
min_w w^Tw/2 + C \sum log(1 + exp(-y_i w^Tx_i))
For L2-regularized L2-loss SVC dual (-s 1), we solve
min_alpha 0.5(alpha^T (Q + I/2/C) alpha) - e^T alpha
s.t. 0 <= alpha_i,
For L2-regularized L2-loss SVC (-s 2), we solve
min_w w^Tw/2 + C \sum max(0, 1- y_i w^Tx_i)^2
For L2-regularized L1-loss SVC dual (-s 3), we solve
min_alpha 0.5(alpha^T Q alpha) - e^T alpha
s.t. 0 <= alpha_i <= C,
For L1-regularized L2-loss SVC (-s 5), we solve
min_w \sum |w_j| + C \sum max(0, 1- y_i w^Tx_i)^2
For L1-regularized logistic regression (-s 6), we solve
min_w \sum |w_j| + C \sum log(1 + exp(-y_i w^Tx_i))
For L2-regularized logistic regression (-s 7), we solve
min_alpha 0.5(alpha^T Q alpha) + \sum alpha_i*log(alpha_i) + \sum (C-alpha_i)*log(C-alpha_i) - a constant
s.t. 0 <= alpha_i <= C,
where
Q is a matrix with Q_ij = y_i y_j x_i^T x_j.
For L2-regularized L2-loss SVR (-s 11), we solve
min_w w^Tw/2 + C \sum max(0, |y_i-w^Tx_i|-epsilon)^2
For L2-regularized L2-loss SVR dual (-s 12), we solve
min_beta 0.5(beta^T (Q + lambda I/2/C) beta) - y^T beta + \sum |beta_i|
For L2-regularized L1-loss SVR dual (-s 13), we solve
min_beta 0.5(beta^T Q beta) - y^T beta + \sum |beta_i|
s.t. -C <= beta_i <= C,
where
Q is a matrix with Q_ij = x_i^T x_j.
For one-class SVM dual (-s 21), we solve
min_alpha 0.5(alpha^T Q alpha)
s.t. 0 <= alpha_i <= 1 and \sum alpha_i = nu*l,
where
Q is a matrix with Q_ij = x_i^T x_j.
If bias >= 0, w becomes [w; w_{n+1}] and x becomes [x; bias]. For
example, L2-regularized logistic regression (-s 0) becomes
min_w w^Tw/2 + (w_{n+1})^2/2 + C \sum log(1 + exp(-y_i [w; w_{n+1}]^T[x_i; bias]))
Some may prefer not having (w_{n+1})^2/2 (i.e., bias variable not
regularized). For primal solvers (-s 0, 2, 5, 6, 11), we provide an
option -R to remove (w_{n+1})^2/2. However, -R is generally not needed
as for most data with/without (w_{n+1})^2/2 give similar performances.
The primal-dual relationship implies that -s 1 and -s 2 give the same
model, -s 0 and -s 7 give the same, and -s 11 and -s 12 give the same.
We implement 1-vs-the rest multi-class strategy for classification.
In training i vs. non_i, their C parameters are (weight from -wi)*C
and C, respectively. If there are only two classes, we train only one
model. Thus weight1*C vs. weight2*C is used. See examples below.
We also implement multi-class SVM by Crammer and Singer (-s 4):
min_{w_m, \xi_i} 0.5 \sum_m ||w_m||^2 + C \sum_i \xi_i
s.t. w^T_{y_i} x_i - w^T_m x_i >= \e^m_i - \xi_i \forall m,i
where e^m_i = 0 if y_i = m,
e^m_i = 1 if y_i != m,
Here we solve the dual problem:
min_{\alpha} 0.5 \sum_m ||w_m(\alpha)||^2 + \sum_i \sum_m e^m_i alpha^m_i
s.t. \alpha^m_i <= C^m_i \forall m,i , \sum_m \alpha^m_i=0 \forall i
where w_m(\alpha) = \sum_i \alpha^m_i x_i,
and C^m_i = C if m = y_i,
C^m_i = 0 if m != y_i.
`predict' Usage
===============
Usage: predict [options] test_file model_file output_file
options:
-b probability_estimates: whether to output probability estimates, 0 or 1 (default 0); currently for logistic regression only
-q : quiet mode (no outputs)
Note that -b is only needed in the prediction phase. This is different
from the setting of LIBSVM.
`svm-scale' Usage
=================
See LIBSVM README.
Examples
========
> train data_file
Train linear SVM with L2-loss function.
> train -s 0 data_file
Train a logistic regression model.
> train -s 21 -n 0.1 data_file
Train a linear one-class SVM which selects roughly 10% data as outliers.
> train -v 5 -e 0.001 data_file
Do five-fold cross-validation using L2-loss SVM.
Use a smaller stopping tolerance 0.001 than the default
0.1 if you want more accurate solutions.
> train -C data_file
...
Best C = 0.000488281 CV accuracy = 83.3333%
> train -c 0.000488281 data_file
Conduct cross validation many times by L2-loss SVM and find the
parameter C which achieves the best cross validation accuracy. Then
use the selected C to train the data for getting a model.
> train -C -s 0 -v 3 -c 0.5 -e 0.0001 data_file
For parameter selection by -C, users can specify other
solvers (currently -s 0, -s 2 and -s 11 are supported) and
different number of CV folds. Further, users can use
the -c option to specify the smallest C value of the
search range. This option is useful when users want to
rerun the parameter selection procedure from a specified
C under a different setting, such as a stricter stopping
tolerance -e 0.0001 in the above example. Similarly, for
-s 11, users can use the -p option to specify the
maximal p value of the search range.
> train -c 10 -w1 2 -w2 5 -w3 2 four_class_data_file
Train four classifiers:
positive negative Cp Cn
class 1 class 2,3,4. 20 10
class 2 class 1,3,4. 50 10
class 3 class 1,2,4. 20 10
class 4 class 1,2,3. 10 10
> train -c 10 -w3 1 -w2 5 two_class_data_file
If there are only two classes, we train ONE model.
The C values for the two classes are 10 and 50.
> predict -b 1 test_file data_file.model output_file
Output probability estimates (for logistic regression only).
Library Usage
=============
These functions and structures are declared in the header file `linear.h'.
You can see `train.c' and `predict.c' for examples showing how to use them.
We define LIBLINEAR_VERSION and declare `extern int liblinear_version; '
in linear.h, so you can check the version number.
- Function: model* train(const struct problem *prob,
const struct parameter *param);
This function constructs and returns a linear classification
or regression model according to the given training data and
parameters.
struct problem describes the problem:
struct problem
{
int l, n;
double *y;
struct feature_node **x;
double bias;
};
where `l' is the number of training data. If bias >= 0, we assume
that one additional feature is added to the end of each data
instance. `n' is the number of feature (including the bias feature
if bias >= 0). `y' is an array containing the target values. (integers
in classification, real numbers in regression) And `x' is an array
of pointers, each of which points to a sparse representation (array
of feature_node) of one training vector.
For example, if we have the following training data:
LABEL ATTR1 ATTR2 ATTR3 ATTR4 ATTR5
----- ----- ----- ----- ----- -----
1 0 0.1 0.2 0 0
2 0 0.1 0.3 -1.2 0
1 0.4 0 0 0 0
2 0 0.1 0 1.4 0.5
3 -0.1 -0.2 0.1 1.1 0.1
and bias = 1, then the components of problem are:
l = 5
n = 6
y -> 1 2 1 2 3
x -> [ ] -> (2,0.1) (3,0.2) (6,1) (-1,?)
[ ] -> (2,0.1) (3,0.3) (4,-1.2) (6,1) (-1,?)
[ ] -> (1,0.4) (6,1) (-1,?)
[ ] -> (2,0.1) (4,1.4) (5,0.5) (6,1) (-1,?)
[ ] -> (1,-0.1) (2,-0.2) (3,0.1) (4,1.1) (5,0.1) (6,1) (-1,?)
struct parameter describes the parameters of a linear classification
or regression model:
struct parameter
{
int solver_type;
/* these are for training only */
double eps; /* stopping tolerance */
double C;
double nu; /* one-class SVM only */
int nr_weight;
int *weight_label;
double* weight;
double p;
double *init_sol;
int regularize_bias;
bool w_recalc; /* for -s 1, 3; may be extended to -s 12, 13, 21 */
};
solver_type can be one of L2R_LR, L2R_L2LOSS_SVC_DUAL, L2R_L2LOSS_SVC, L2R_L1LOSS_SVC_DUAL, MCSVM_CS, L1R_L2LOSS_SVC, L1R_LR, L2R_LR_DUAL, L2R_L2LOSS_SVR, L2R_L2LOSS_SVR_DUAL, L2R_L1LOSS_SVR_DUAL, ONECLASS_SVM.
for classification
L2R_LR L2-regularized logistic regression (primal)
L2R_L2LOSS_SVC_DUAL L2-regularized L2-loss support vector classification (dual)
L2R_L2LOSS_SVC L2-regularized L2-loss support vector classification (primal)
L2R_L1LOSS_SVC_DUAL L2-regularized L1-loss support vector classification (dual)
MCSVM_CS support vector classification by Crammer and Singer
L1R_L2LOSS_SVC L1-regularized L2-loss support vector classification
L1R_LR L1-regularized logistic regression
L2R_LR_DUAL L2-regularized logistic regression (dual)
for regression
L2R_L2LOSS_SVR L2-regularized L2-loss support vector regression (primal)
L2R_L2LOSS_SVR_DUAL L2-regularized L2-loss support vector regression (dual)
L2R_L1LOSS_SVR_DUAL L2-regularized L1-loss support vector regression (dual)
for outlier detection
ONECLASS_SVM one-class support vector machine (dual)
C is the cost of constraints violation.
p is the sensitiveness of loss of support vector regression.
nu in ONECLASS_SVM approximates the fraction of data as outliers.
eps is the stopping criterion.
nr_weight, weight_label, and weight are used to change the penalty
for some classes (If the weight for a class is not changed, it is
set to 1). This is useful for training classifier using unbalanced
input data or with asymmetric misclassification cost.
nr_weight is the number of elements in the array weight_label and
weight. Each weight[i] corresponds to weight_label[i], meaning that
the penalty of class weight_label[i] is scaled by a factor of weight[i].
If you do not want to change penalty for any of the classes,
just set nr_weight to 0.
init_sol includes the initial weight vectors (supported for only some
solvers). See the explanation of the vector w in the model
structure.
regularize_bias is the flag for bias regularization. By default it is set
to be 1. If you don't want to regularize the bias, set it to 0 with
specifying the bias in the problem structure to be 1. (DON'T use it unless
you know what it is.)
w_recalc is the flag for recalculating w after optimization
with a dual-based solver. This may further reduces the weight density
when the data is sparse. The default value is set as false for time
efficiency. Currently it only takes effect in -s 1 and 3.
*NOTE* To avoid wrong parameters, check_parameter() should be
called before train().
struct model stores the model obtained from the training procedure:
struct model
{
struct parameter param;
int nr_class; /* number of classes */
int nr_feature;
double *w;
int *label; /* label of each class */
double bias;
double rho; /* one-class SVM only */
};
param describes the parameters used to obtain the model.
nr_class is the number of classes for classification. It is a
non-negative integer with special cases of 0 (no training data at
all) and 1 (all training data in one class). For regression and
one-class SVM, nr_class = 2.
nr_feature is the number of features.
The array w gives feature weights. Its size is
nr_feature*nr_class but is nr_feature if nr_class = 2 and the
solver is not MCSVM_CS (see more explanation below). We use one
against the rest for multi-class classification, so each feature
index corresponds to nr_class weight values. Weights are
organized in the following way
+------------------+------------------+------------+
| nr_class weights | nr_class weights | ...
| for 1st feature | for 2nd feature |
+------------------+------------------+------------+
The array label stores class labels.
When nr_class = 1 or 2, classification solvers (MCSVM_CS
excluded) return a single vector of weights by considering
label[0] as positive in training.
If bias >= 0, x becomes [x; bias]. The number of features is
increased by one, so w is a (nr_feature+1)*nr_class array. The
value of bias is stored in the variable bias.
rho is the bias term used in one-class SVM only.
- Function: void cross_validation(const problem *prob, const parameter *param, int nr_fold, double *target);
This function conducts cross validation. Data are separated to
nr_fold folds. Under given parameters, sequentially each fold is
validated using the model from training the remaining. Predicted
labels in the validation process are stored in the array called
target.
The format of prob is same as that for train().
- Function: void find_parameters(const struct problem *prob,
const struct parameter *param, int nr_fold, double start_C,
double start_p, double *best_C, double *best_p, double *best_score);
This function is similar to cross_validation. However, instead of
conducting cross validation under specified parameters. For -s 0, 2, it
conducts cross validation 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. For -s 11, it conducts cross
validation many times with a two-fold loop. The outer loop considers a
default sequence of p = 19/20*max_p, ..., 1/20*max_p, 0 and
under each p value the inner loop considers a sequence of parameters
C = start_C, 2*start_C, 4*start_C, ..., and finds the best one with the
lowest mean squared error.
If start_C <= 0, then this procedure calculates a small enough C
for prob as the start_C. The procedure stops when the models of
all folds become stable or C reaches max_C.
If start_p <= 0, then this procedure calculates a maximal p for prob as
the start_p. Otherwise, the procedure starts with the first
i/20*max_p <= start_p so the outer sequence is i/20*max_p,
(i-1)/20*max_p, ..., 0.
The best C, the best p, and the corresponding accuracy (or MSE) are
assigned to *best_C, *best_p and *best_score, respectively. For
classification, *best_p is not used, and the returned value is -1.
- Function: double predict(const model *model_, const feature_node *x);
For a classification model, the predicted class for x is returned.
For a regression model, the function value of x calculated using
the model is returned.
- Function: double predict_values(const struct model *model_,
const struct feature_node *x, double* dec_values);
This function gives nr_w decision values in the array dec_values.
nr_w=1 if regression is applied or the number of classes is two. An exception is
multi-class SVM by Crammer and Singer (-s 4), where nr_w = 2 if there are two classes. For all other situations, nr_w is the
number of classes.
We implement one-vs-the rest multi-class strategy (-s 0,1,2,3,5,6,7)
and multi-class SVM by Crammer and Singer (-s 4) for multi-class SVM.
The class with the highest decision value is returned.
- Function: double predict_probability(const struct model *model_,
const struct feature_node *x, double* prob_estimates);
This function gives nr_class probability estimates in the array
prob_estimates. nr_class can be obtained from the function
get_nr_class. The class with the highest probability is
returned. Currently, we support only the probability outputs of
logistic regression.
- Function: int get_nr_feature(const model *model_);
The function gives the number of attributes of the model.
- Function: int get_nr_class(const model *model_);
The function gives the number of classes of the model.
For a regression model, 2 is returned.
- Function: void get_labels(const model *model_, int* label);
This function outputs the name of labels into an array called label.
For a regression model, label is unchanged.
- Function: double get_decfun_coef(const struct model *model_, int feat_idx,
int label_idx);
This function gives the coefficient for the feature with feature index =
feat_idx and the class with label index = label_idx. Note that feat_idx
starts from 1, while label_idx starts from 0. If feat_idx is not in the
valid range (1 to nr_feature), then a zero value will be returned. For
classification models, if label_idx is not in the valid range (0 to
nr_class-1), then a zero value will be returned; for regression models
and one-class SVM models, label_idx is ignored.
- Function: double get_decfun_bias(const struct model *model_, int label_idx);
This function gives the bias term corresponding to the class with the
label_idx. For classification models, if label_idx is not in a valid range
(0 to nr_class-1), then a zero value will be returned; for regression
models, label_idx is ignored. This function cannot be called for a one-class
SVM model.
- Function: double get_decfun_rho(const struct model *model_);
This function gives rho, the bias term used in one-class SVM only. This
function can only be called for a one-class SVM model.
- Function: const char *check_parameter(const struct problem *prob,
const struct parameter *param);
This function checks whether the parameters are within the feasible
range of the problem. This function should be called before calling
train() and cross_validation(). It returns NULL if the
parameters are feasible, otherwise an error message is returned.
- Function: int check_probability_model(const struct model *model);
This function returns 1 if the model supports probability output;
otherwise, it returns 0.
- Function: int check_regression_model(const struct model *model);
This function returns 1 if the model is a regression model; otherwise
it returns 0.
- Function: int check_oneclass_model(const struct model *model);
This function returns 1 if the model is a one-class SVM model; otherwise
it returns 0.
- Function: int save_model(const char *model_file_name,
const struct model *model_);
This function saves a model to a file; returns 0 on success, or -1
if an error occurs.
- Function: struct model *load_model(const char *model_file_name);
This function returns a pointer to the model read from the file,
or a null pointer if the model could not be loaded.
- Function: void free_model_content(struct model *model_ptr);
This function frees the memory used by the entries in a model structure.
- Function: void free_and_destroy_model(struct model **model_ptr_ptr);
This function frees the memory used by a model and destroys the model
structure.
- Function: void destroy_param(struct parameter *param);
This function frees the memory used by a parameter set.
- Function: void set_print_string_function(void (*print_func)(const char *));
Users can specify their output format by a function. Use
set_print_string_function(NULL);
for default printing to stdout.
Please note that this function is not thread-safe. When multiple threads load or
use the same dynamic library (for example, liblinear.so.6), they actually share the
same memory space of the dynamic library, which results in all threads modifying
the same static function pointer, liblinear_print_string, in linear.cpp when they
call this function.
For example, suppose we have threads A and B. They call this function sequentially
and pass their own thread-local print_func into it. After that, they both call (*liblinear_print_string)(str)
once. When the last thread finishes setting it (say B), liblinear_print_string
is set to B.print_func. Now, if thread A wants to access liblinear_print_string,
it is actually accessing B.print_func rather than A.print_func, which is incorrect
since we expect to use the functionality of A.print_func.
Even if A.print_func and B.print_func have identical functionality, it is still risky.
Suppose liblinear_print_string is now set to B.print_func, and B deletes B.print_func
after finishing its work. Later, thread A calls liblinear_print_string, but the address
points to, which is B.print_func, has already been deleted. This invalid memory access
will crash the program. To mitigate this issue, in this example, you should ensure that
A.print_func and B.print_func remain valid after threads finish their work. For example,
in Python, you can assign them as global variables.
Building Windows Binaries
=========================
Starting from version 2.48, we no longer provide pre-built Windows binaries,
to build them via Visual C++, use the following steps:
1. Open a dos command box and change to liblinear directory. If
environment variables of VC++ have not been set, type
"C:\Program Files (x86)\Microsoft Visual Studio\2019\Community\VC\Auxiliary\Build\vcvars64.bat"
You may have to modify the above command according which version of
VC++ or where it is installed.
2. Type
nmake -f Makefile.win clean all
3. (optional) To build shared library liblinear.dll, type
nmake -f Makefile.win lib
4. (Optional) To build 32-bit windows binaries, you must
(1) Setup "C:\Program Files (x86)\Microsoft Visual Studio\2019\Community\VC\Auxiliary\Build\vcvars32.bat" instead of vcvars64.bat
(2) Change CFLAGS in Makefile.win: /D _WIN64 to /D _WIN32
MATLAB/OCTAVE Interface
=======================
Please check the file README in the directory `matlab'.
Python Interface
================
Please check the file README in the directory `python'.
Additional Information
======================
If you find LIBLINEAR helpful, please cite it as
R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang, and C.-J. Lin.
LIBLINEAR: A Library for Large Linear Classification, Journal of
Machine Learning Research 9(2008), 1871-1874. Software available at
http://www.csie.ntu.edu.tw/~cjlin/liblinear
For any questions and comments, please send your email to
cjlin@csie.ntu.edu.tw
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