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    then the components of svm_problem are:    l = 5    y -> 1 2 1 2 3    x -> [ ] -> (2,0.1) (3,0.2) (-1,?)	 [ ] -> (2,0.1) (3,0.3) (4,-1.2) (-1,?)	 [ ] -> (1,0.4) (-1,?)	 [ ] -> (2,0.1) (4,1.4) (5,0.5) (-1,?)	 [ ] -> (1,-0.1) (2,-0.2) (3,0.1) (4,1.1) (5,0.1) (-1,?)    where (index,value) is stored in the structure `svm_node':	struct svm_node	{		int index;		double value;	};    index = -1 indicates the end of one vector.     struct svm_parameter describes the parameters of an SVM model:	struct svm_parameter	{		int svm_type;		int kernel_type;		int degree;	/* for poly */		double gamma;	/* for poly/rbf/sigmoid */		double coef0;	/* for poly/sigmoid */		/* these are for training only */		double cache_size; /* in MB */		double eps;	/* stopping criteria */		double C;	/* for C_SVC, EPSILON_SVR, and NU_SVR */		int nr_weight;		/* for C_SVC */		int *weight_label;	/* for C_SVC */		double* weight;		/* for C_SVC */		double nu;	/* for NU_SVC, ONE_CLASS, and NU_SVR */		double p;	/* for EPSILON_SVR */		int shrinking;	/* use the shrinking heuristics */		int probability; /* do probability estimates */	};    svm_type can be one of C_SVC, NU_SVC, ONE_CLASS, EPSILON_SVR, NU_SVR.    C_SVC:		C-SVM classification    NU_SVC:		nu-SVM classification    ONE_CLASS:		one-class-SVM    EPSILON_SVR:	epsilon-SVM regression    NU_SVR:		nu-SVM regression    kernel_type can be one of LINEAR, POLY, RBF, SIGMOID.    LINEAR:	u'*v    POLY:	(gamma*u'*v + coef0)^degree    RBF:	exp(-gamma*|u-v|^2)    SIGMOID:	tanh(gamma*u'*v + coef0)    PRECOMPUTED: kernel values in training_set_file    cache_size is the size of the kernel cache, specified in megabytes.    C is the cost of constraints violation. (we usually use 1 to 1000)    eps is the stopping criterion. (we usually use 0.00001 in nu-SVC,    0.001 in others). nu is the parameter in nu-SVM, nu-SVR, and    one-class-SVM. p is the epsilon in epsilon-insensitive loss function    of epsilon-SVM regression. shrinking = 1 means shrinking is conducted;    = 0 otherwise. probability = 1 means model with probability    information is obtained; = 0 otherwise.    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.    *NOTE* Because svm_model contains pointers to svm_problem, you can    not free the memory used by svm_problem if you are still using the    svm_model produced by svm_train().- Function: double svm_predict(const struct svm_model *model,                               const struct svm_node *x);    This function does classification or regression on a test vector x    given a model.    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. For an one-class model, +1 or -1 is    returned.- Function: void svm_cross_validation(const struct svm_problem *prob,	const struct svm_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 svm_prob is same as that for svm_train(). - Function: int svm_get_svm_type(const struct svm_model *model);    This function gives svm_type of the model. Possible values of    svm_type are defined in svm.h.- Function: int svm_get_nr_class(const svm_model *model);    For a classification model, this function gives the number of    classes. For a regression or an one-class model, 2 is returned.- Function: void svm_get_labels(const svm_model *model, int* label)        For a classification model, this function outputs the name of    labels into an array called label. For regression and one-class    models, label is unchanged.- Function: double svm_get_svr_probability(const struct svm_model *model);    For a regression model with probability information, this function    outputs a value sigma > 0. For test data, we consider the    probability model: target value = predicted value + z, z: Laplace    distribution e^(-|z|/sigma)/(2sigma)    If the model is not for svr or does not contain required    information, 0 is returned.- Function: void svm_predict_values(const svm_model *model, 				    const svm_node *x, double* dec_values)    This function gives decision values on a test vector x given a    model.    For a classification model with nr_class classes, this function    gives nr_class*(nr_class-1)/2 decision values in the array    dec_values, where nr_class can be obtained from the function    svm_get_nr_class. The order is label[0] vs. label[1], ...,    label[0] vs. label[nr_class-1], label[1] vs. label[2], ...,    label[nr_class-2] vs. label[nr_class-1], where label can be    obtained from the function svm_get_labels.    For a regression model, label[0] is the function value of x    calculated using the model. For one-class model, label[0] is +1 or    -1.- Function: double svm_predict_probability(const struct svm_model *model, 	    const struct svm_node *x, double* prob_estimates);        This function does classification or regression on a test vector x    given a model with probability information.    For a classification model with probability information, this    function gives nr_class probability estimates in the array    prob_estimates. nr_class can be obtained from the function    svm_get_nr_class. The class with the highest probability is    returned. For all other situations, the array prob_estimates is    unchanged and the returned value is the same as that of    svm_predict.- Function: const char *svm_check_parameter(const struct svm_problem *prob,                                            const struct svm_parameter *param);    This function checks whether the parameters are within the feasible    range of the problem. This function should be called before calling    svm_train(). It returns NULL if the parameters are feasible,     otherwise an error message is returned. - Function: int svm_check_probability_model(const struct svm_model *model);    This function checks whether the model contains required    information to do probability estimates. If so, it returns    +1. Otherwise, 0 is returned. This function should be called    before calling svm_get_svr_probability and    svm_predict_probability.- Function: int svm_save_model(const char *model_file_name,			       const struct svm_model *model);    This function saves a model to a file; returns 0 on success, or -1    if an error occurs.- Function: struct svm_model *svm_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 svm_destroy_model(struct svm_model *model);    This function frees the memory used by a model.- Function: void svm_destroy_param(struct svm_parameter *param);    This function frees the memory used by a parameter set.Java Version============The pre-compiled java class archive `libsvm.jar' and its source files arein the java directory. To run the programs, usejava -classpath libsvm.jar svm_train <arguments>java -classpath libsvm.jar svm_predict <arguments>java -classpath libsvm.jar svm_toyYou may need to add Java runtime library (like classes.zip) to the classpath.You may need to increase maximum Java heap size.Library usages are similar to the C version. These functions are available:public class svm {	public static svm_model svm_train(svm_problem prob, svm_parameter param);	public static void svm_cross_validation(svm_problem prob, svm_parameter param, int nr_fold, double[] target);	public static int svm_get_svm_type(svm_model model);	public static int svm_get_nr_class(svm_model model);	public static void svm_get_labels(svm_model model, int[] label);	public static double svm_get_svr_probability(svm_model model);	public static void svm_predict_values(svm_model model, svm_node[] x, double[] dec_values);	public static double svm_predict(svm_model model, svm_node[] x);	public static double svm_predict_probability(svm_model model, svm_node[] x, double[] prob_estimates);	public static void svm_save_model(String model_file_name, svm_model model) throws IOException	public static svm_model svm_load_model(String model_file_name) throws IOException	public static String svm_check_parameter(svm_problem prob, svm_parameter param);	public static int svm_check_probability_model(svm_model model);}The library is in the "libsvm" package.Note that in Java version, svm_node[] is not ended with a node whose index = -1.Building Windows Binaries=========================Windows binaries are in the directory `windows'. To build them viaVisual C++, use the following steps:1. Open a dos command box and change to libsvm directory. Ifenvironment variables of VC++ have not been set, type"C:\Program Files\Microsoft Visual Studio .NET 2003\Vc7\bin\vcvars32.bat"You may have to modify the above according which version of VC++orwhere it is installed.2. Typenmake -f Makefile.win clean all3. (optional) To build python interface, download and install Python.Edit Makefile.win and change PYTHON_INC and PYTHON_LIB to your pythoninstallation. Typenmake -f Makefile.win python and then copy windows\python\svmc.dll to the python directory.Another way is to build them from Visual C++ environment. See detailsin libsvm faq.Additional Tools: Model Selection, Sub-sampling, etc.====================================================See the README file in the tools directory.Python Interface================See the README file in python directory.Additional Information======================If you find LIBSVM helpful, please cite it asChih-Chung Chang and Chih-Jen Lin, LIBSVM: a library for support vector machines, 2001.Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvmLIBSVM implementation document is available athttp://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdfFor any questions and comments, please send your email tocjlin@csie.ntu.edu.twAcknowledgments:This work was supported in part by the National Science Council of Taiwan via the grant NSC 89-2213-E-002-013.The authors thank their group members and usersfor many helpful discussions and comments. They are listed inhttp://www.csie.ntu.edu.tw/~cjlin/libsvm/acknowledgements