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) or use the pre-built

binaries (Windows binaries are in the directory `windows').

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;

};

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.

*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.

Building Windows Binaries

=========================

Windows binaries are available in the directory `windows'. To re-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