[ossvm] OSSVM implementation for binary classification

This commit provides the OSSVM implementation as proposed by [1].  For
usage through LibSVM’s executable, it provides the additional `-l`
option for the lambda regularization parameters described in
Equation (11) of the paper [1].  The `-l` option is only accepted when
the kernel type is RBF, i.e., when `-t 2` is provided.

Note: Although in the paper [1] it is presented that the lambda
regularization parameter can be up to `C * mp`, in which `C` is the
SVM cost parameter and `mp` is the number of positive training
instances on the training set, to facilitate usage, `-l` option
accepts a value in the interval `[0, 1)` which is linearly mapped to
the interval `[0, C*mp)`.  Value of the lambda parameters equals to 1
is not accepted, as explained in the second paragraph after
Proposition 1 in the paper [1].

This commit also adjusts the Python wrap for usage.

[1] Mendes Júnior, Pedro Ribeiro; Boult, Terrance E.; Wainer, Jacques;
and Rocha, Anderson de Rezende (2021), “Open-Set Support Vector
Machines”, to appear in IEEE Transactions on Systems, Man, and
Cybernetics: Systems. URL: https://pedrormjunior.github.io/OSSVM.html

README

@@ -153,6 +153,7 @@ options:
 -g gamma : set gamma in kernel function (default 1/num_features)
 -r coef0 : set coef0 in kernel function (default 0)
 -c cost : set the parameter C of C-SVC, epsilon-SVR, and nu-SVR (default 1)
+-l lamb : set the parameter lambda of SSVM (C-SVC) for open-set recognition (default -1)
 -n nu : set the parameter nu of nu-SVC, one-class SVM, and nu-SVR (default 0.5)
 -p epsilon : set the epsilon in loss function of epsilon-SVR (default 0.1)
 -m cachesize : set cache memory size in MB (default 100)
@@ -385,6 +386,7 @@ to classify new data.
 		double cache_size; /* in MB */
 		double eps;	/* stopping criteria */
 		double C;	/* for C_SVC, EPSILON_SVR, and NU_SVR */
+		double lamb;	/* for SSVM (open-set recognition) */
 		int nr_weight;		/* for C_SVC */
 		int *weight_label;	/* for C_SVC */
 		double* weight;		/* for C_SVC */

python/svm.py

@@ -224,10 +224,10 @@ def __init__(self, y, x, isKernel=False):
 
 class svm_parameter(Structure):
 	_names = ["svm_type", "kernel_type", "degree", "gamma", "coef0",
-			"cache_size", "eps", "C", "nr_weight", "weight_label", "weight",
+			"cache_size", "eps", "C", "lamb", "nr_weight", "weight_label", "weight",
 			"nu", "p", "shrinking", "probability"]
 	_types = [c_int, c_int, c_int, c_double, c_double,
-			c_double, c_double, c_double, c_int, POINTER(c_int), POINTER(c_double),
+			c_double, c_double, c_double, c_double, c_int, POINTER(c_int), POINTER(c_double),
 			c_double, c_double, c_int, c_int]
 	_fields_ = genFields(_names, _types)
 
@@ -255,6 +255,7 @@ def set_to_default_values(self):
 		self.nu = 0.5
 		self.cache_size = 100
 		self.C = 1
+		self.lamb = -1
 		self.eps = 0.001
 		self.p = 0.1
 		self.shrinking = 1
@@ -304,6 +305,9 @@ def parse_options(self, options):
 			elif argv[i] == "-c":
 				i = i + 1
 				self.C = float(argv[i])
+			elif argv[i] == "-l":
+				i = i + 1
+				self.lamb = float(argv[i])
 			elif argv[i] == "-e":
 				i = i + 1
 				self.eps = float(argv[i])

python/svmutil.py

@@ -74,6 +74,7 @@ def svm_train(arg1, arg2=None, arg3=None):
 	    -g gamma : set gamma in kernel function (default 1/num_features)
 	    -r coef0 : set coef0 in kernel function (default 0)
 	    -c cost : set the parameter C of C-SVC, epsilon-SVR, and nu-SVR (default 1)
+	    -l lamb : set the parameter lamb of SSVM (C-SVC) for open-set recognition (default -1)
 	    -n nu : set the parameter nu of nu-SVC, one-class SVM, and nu-SVR (default 0.5)
 	    -p epsilon : set the epsilon in loss function of epsilon-SVR (default 0.1)
 	    -m cachesize : set cache memory size in MB (default 100)

svm-train.c

@@ -29,6 +29,7 @@ void exit_with_help()
 	"-g gamma : set gamma in kernel function (default 1/num_features)\n"
 	"-r coef0 : set coef0 in kernel function (default 0)\n"
 	"-c cost : set the parameter C of C-SVC, epsilon-SVR, and nu-SVR (default 1)\n"
+	"-l lamb : set the parameter lambda of SSVM (C-SVC) for open-set recognition (default -1)\n"
 	"-n nu : set the parameter nu of nu-SVC, one-class SVM, and nu-SVR (default 0.5)\n"
 	"-p epsilon : set the epsilon in loss function of epsilon-SVR (default 0.1)\n"
 	"-m cachesize : set cache memory size in MB (default 100)\n"
@@ -172,6 +173,7 @@ void parse_command_line(int argc, char **argv, char *input_file_name, char *mode
 	param.nu = 0.5;
 	param.cache_size = 100;
 	param.C = 1;
+	param.lamb = -1;
 	param.eps = 1e-3;
 	param.p = 0.1;
 	param.shrinking = 1;
@@ -213,6 +215,9 @@ void parse_command_line(int argc, char **argv, char *input_file_name, char *mode
 			case 'c':
 				param.C = atof(argv[i]);
 				break;
+			case 'l':
+				param.lamb = atof(argv[i]);
+				break;
 			case 'e':
 				param.eps = atof(argv[i]);
 				break;

svm.cpp

@@ -1447,9 +1447,10 @@ static void solve_c_svc(
 
 	int i;
 
+	double alpha_epsilon = param->lamb >= 0 ? param->lamb * param->C : 0;
 	for(i=0;i<l;i++)
 	{
-		alpha[i] = 0;
+		alpha[i] = prob->y[i] > 0 ? alpha_epsilon : 0;
 		minus_ones[i] = -1;
 		if(prob->y[i] > 0) y[i] = +1; else y[i] = -1;
 	}
@@ -2669,6 +2670,8 @@ int svm_save_model(const char *model_file_name, const svm_model *model)
 	if(param.kernel_type == POLY || param.kernel_type == SIGMOID)
 		fprintf(fp,"coef0 %.17g\n", param.coef0);
 
+	fprintf(fp,"lamb %g\n", param.lamb);
+
 	int nr_class = model->nr_class;
 	int l = model->l;
 	fprintf(fp, "nr_class %d\n", nr_class);
@@ -2825,6 +2828,8 @@ bool read_model_header(FILE *fp, svm_model* model)
 			FSCANF(fp,"%lf",&param.gamma);
 		else if(strcmp(cmd,"coef0")==0)
 			FSCANF(fp,"%lf",&param.coef0);
+		else if(strcmp(cmd,"lamb")==0)
+			FSCANF(fp,"%lf",&param.lamb);
 		else if(strcmp(cmd,"nr_class")==0)
 			FSCANF(fp,"%d",&model->nr_class);
 		else if(strcmp(cmd,"total_sv")==0)
@@ -3086,6 +3091,15 @@ const char *svm_check_parameter(const svm_problem *prob, const svm_parameter *pa
 		if(param->C <= 0)
 			return "C <= 0";
 
+	if(param->lamb < 0 && param->lamb != -1)
+		return "lamb < 0 and lamb != -1";
+	if(param->lamb >= 1)
+		return "lamb >= 1";
+	if(param->lamb >= 0 && svm_type != C_SVC)
+		return "lamb >= 0 and svm_type != C_SVC";
+	if(param->lamb >= 0 && kernel_type != RBF)
+		return "lamb > 0 and kernel_type != RBF";
+
 	if(svm_type == NU_SVC ||
 	   svm_type == ONE_CLASS ||
 	   svm_type == NU_SVR)

svm.h

@@ -37,6 +37,7 @@ struct svm_parameter
 	double cache_size; /* in MB */
 	double eps;	/* stopping criteria */
 	double C;	/* for C_SVC, EPSILON_SVR and NU_SVR */
+	double lamb;	/* for SSVM (open-set recognition) */
 	int nr_weight;		/* for C_SVC */
 	int *weight_label;	/* for C_SVC */
 	double* weight;		/* for C_SVC */