svm.cpp

支持向量机是一种专门用于样本分类的算法,本程序用VC++实现了SVM算法

	int nSV = 0;
	int nBSV = 0;
	for(int i=0;i<prob->l;i++)
	{
		if(fabs(alpha[i]) > 0)
		{
			++nSV;
			if(prob->y[i] > 0)
			{
				if(fabs(alpha[i]) >= si.upper_bound_p)
					++nBSV;
			}
			else
			{
				if(fabs(alpha[i]) >= si.upper_bound_n)
					++nBSV;
			}
		}
	}

	info("nSV = %d, nBSV = %d\n",nSV,nBSV);

	decision_function f;
	f.alpha = alpha;
	f.rho = si.rho;
	return f;
}

//
// svm_model
//
struct svm_model
{
	svm_parameter param;	// parameter
	int nr_class;		// number of classes, = 2 in regression/one class svm
	int l;			// total #SV
	svm_node **SV;		// SVs (SV[l])
	double **sv_coef;	// coefficients for SVs in decision functions (sv_coef[n-1][l])
	double *rho;		// constants in decision functions (rho[n*(n-1)/2])

	// for classification only

	int *label;		// label of each class (label[n])
	int *nSV;		// number of SVs for each class (nSV[n])
				// nSV[0] + nSV[1] + ... + nSV[n-1] = l
	// XXX
	int free_sv;		// 1 if svm_model is created by svm_load_model
				// 0 if svm_model is created by svm_train
};

//
// Interface functions
//
double *svm_train(const svm_problem *prob, const svm_parameter *param)
{
	svm_model *model = Malloc(svm_model,1);
	model->param = *param;
	model->free_sv = 0;	// XXX
	double * outalpha = Malloc(double , (prob->l+1));

	if(param->svm_type == ONE_CLASS ||
	   param->svm_type == EPSILON_SVR ||
	   param->svm_type == NU_SVR)
	{
		// regression or one-class-svm
		model->nr_class = 2;
		model->label = NULL;
		model->nSV = NULL;
		model->sv_coef = Malloc(double *,1);
		decision_function f = svm_train_one(prob,param,0,0);
		model->rho = Malloc(double,1);
		model->rho[0] = f.rho;

		int nSV = 0;
		int i;
		for(i=0;i<prob->l;i++)
			if(fabs(f.alpha[i]) > 0) ++nSV;
		model->l = nSV;
		model->SV = Malloc(svm_node *,nSV);
		model->sv_coef[0] = Malloc(double,nSV);
		int j = 0;
		for(i=0;i<prob->l;i++)
			if(fabs(f.alpha[i]) > 0)
			{
				model->SV[j] = prob->x[i];
				model->sv_coef[0][j] = f.alpha[i];
				++j;
			}		

		free(f.alpha);
	}
	else
	{
		// classification
		// find out the number of classes
		int l = prob->l;
		int max_nr_class = 16;
		int nr_class = 0;
		int *label = Malloc(int,max_nr_class);
		int *count = Malloc(int,max_nr_class);
		int *index = Malloc(int,l);

		int i;
		for(i=0;i<l;i++)
		{
			int this_label = (int)prob->y[i];
			int j;
			for(j=0;j<nr_class;j++)
				if(this_label == label[j])
				{
					++count[j];
					break;
				}
			index[i] = j;
			if(j == nr_class)
			{
				if(nr_class == max_nr_class)
				{
					max_nr_class *= 2;
					label = (int *)realloc(label,max_nr_class*sizeof(int));
					count = (int *)realloc(count,max_nr_class*sizeof(int));
				}
				label[nr_class] = this_label;
				count[nr_class] = 1;
				++nr_class;
			}
		}

		// group training data of the same class

		int *start = Malloc(int,nr_class);
		start[0] = 0;
		for(i=1;i<nr_class;i++)
			start[i] = start[i-1]+count[i-1];

		svm_node **x = Malloc(svm_node *,l);

		int *y = Malloc(int , l);  //保存序号
		for(i=0;i<l;i++)
		{
			x[start[index[i]]] = prob->x[i];
			y[start[index[i]]] = i;
			++start[index[i]];
		}
		
		start[0] = 0;
		for(i=1;i<nr_class;i++)
			start[i] = start[i-1]+count[i-1];

		// calculate weighted C

		double *weighted_C = Malloc(double, nr_class);
		for(i=0;i<nr_class;i++)
			weighted_C[i] = param->C;
		for(i=0;i<param->nr_weight;i++)
		{	
			int j;
			for(j=0;j<nr_class;j++)
				if(param->weight_label[i] == label[j])
					break;
			if(j == nr_class)
				fprintf(stderr,"warning: class label %d specified in weight is not found\n", param->weight_label[i]);
			else
				weighted_C[j] *= param->weight[i];
		}

		// train n*(n-1)/2 models
		
		bool *nonzero = Malloc(bool,l);
		for(i=0;i<l;i++)
			nonzero[i] = false;
		decision_function *f = Malloc(decision_function,nr_class*(nr_class-1)/2);

		int p = 0;
		for(i=0;i<nr_class;i++)
			for(int j=i+1;j<nr_class;j++)
			{
				svm_problem sub_prob;
				int si = start[i], sj = start[j];
				int ci = count[i], cj = count[j];
				sub_prob.l = ci+cj;
				sub_prob.x = Malloc(svm_node *,sub_prob.l);
				sub_prob.y = Malloc(double,sub_prob.l);
				int k;
				for(k=0;k<ci;k++)
				{
					sub_prob.x[k] = x[si+k];
					sub_prob.y[k] = +1;
				}
				for(k=0;k<cj;k++)
				{
					sub_prob.x[ci+k] = x[sj+k];
					sub_prob.y[ci+k] = -1;
				}
				
				f[p] = svm_train_one(&sub_prob,param,weighted_C[i],weighted_C[j]);
				for(k=0;k<ci;k++)
					if(!nonzero[si+k] && fabs(f[p].alpha[k]) > 0)
						nonzero[si+k] = true;
				for(k=0;k<cj;k++)
					if(!nonzero[sj+k] && fabs(f[p].alpha[ci+k]) > 0)
						nonzero[sj+k] = true;
				free(sub_prob.x);
				free(sub_prob.y);
				++p;
			}

		// build output

		model->nr_class = nr_class;
		
		model->label = Malloc(int,nr_class);
		for(i=0;i<nr_class;i++)
			model->label[i] = label[i];
		
		model->rho = Malloc(double,nr_class*(nr_class-1)/2);
		for(i=0;i<nr_class*(nr_class-1)/2;i++)
			model->rho[i] = f[i].rho;

		int total_sv = 0;
		int *nz_count = Malloc(int,nr_class);
		model->nSV = Malloc(int,nr_class);
		for(i=0;i<nr_class;i++)
		{
			int nSV = 0;
			for(int j=0;j<count[i];j++)
				if(nonzero[start[i]+j])
				{	
					++nSV;
					++total_sv;
				}
			model->nSV[i] = nSV;
			nz_count[i] = nSV;
		}
		
		info("Total nSV = %d\n",total_sv);

		model->l = total_sv;
		model->SV = Malloc(svm_node *,total_sv);
		p = 0;
		for(i=0;i<l;i++)
			if(nonzero[i]) model->SV[p++] = x[i];

		int *nz_start = Malloc(int,nr_class);
		nz_start[0] = 0;
		for(i=1;i<nr_class;i++)
			nz_start[i] = nz_start[i-1]+nz_count[i-1];

		model->sv_coef = Malloc(double *,nr_class-1);
		for(i=0;i<nr_class-1;i++)
			model->sv_coef[i] = Malloc(double,total_sv);
		p = 0;
		for(i=0;i<nr_class;i++)
			for(int j=i+1;j<nr_class;j++)
			{
				// classifier (i,j): coefficients with
				// i are in sv_coef[j-1][nz_start[i]...],
				// j are in sv_coef[i][nz_start[j]...]

				int si = start[i];
				int sj = start[j];
				int ci = count[i];
				int cj = count[j];
				
				int q = nz_start[i];
				int k;
				for(k=0;k<ci;k++)
					if(nonzero[si+k])
					{	model->sv_coef[j-1][q++] = f[p].alpha[k];
						outalpha[y[k]] = f[p].alpha[k];
					}
					else
					{   outalpha[y[k]] = 0;}
				q = nz_start[j];
				for(k=0;k<cj;k++)
					if(nonzero[sj+k])
					{	model->sv_coef[i][q++] = f[p].alpha[ci+k];
						outalpha[y[ci+k]] = f[p].alpha[ci+k];
					}
					else
					{
						outalpha[y[ci+k]] = 0;
					}
				++p;
				outalpha[prob->l]=model->rho[0];
			}
	//	for(i=0;i<l;i++)
	//		printf("outalpha[%d] = %e \n",i,outalpha[i]);
		free(label);
		free(count);
		free(index);
		free(start);
		free(x);
		free(weighted_C);
		free(nonzero);
		for(i=0;i<nr_class*(nr_class-1)/2;i++)
			free(f[i].alpha);
		free(f);
		free(nz_count);
		free(nz_start);
	}
	return outalpha;
}

/*double svm_predict(const svm_model *model, const svm_node *x)
{
	if(model->param.svm_type == ONE_CLASS ||
	   model->param.svm_type == EPSILON_SVR ||
	   model->param.svm_type == NU_SVR)
	{
		double *sv_coef = model->sv_coef[0];
		double sum = 0;
		for(int i=0;i<model->l;i++)
			sum += sv_coef[i] * Kernel::k_function(x,model->SV[i],model->param);
		sum -= model->rho[0];
		if(model->param.svm_type == ONE_CLASS)
			return (sum>0)?1:-1;
		else
			return sum;
	}
	else
	{
		int i;
		int nr_class = model->nr_class;
		int l = model->l;
		
		double *kvalue = Malloc(double,l);
		for(i=0;i<l;i++)
			kvalue[i] = Kernel::k_function(x,model->SV[i],model->param);

		int *start = Malloc(int,nr_class);
		start[0] = 0;
		for(i=1;i<nr_class;i++)
			start[i] = start[i-1]+model->nSV[i-1];

		int *vote = Malloc(int,nr_class);
		for(i=0;i<nr_class;i++)
			vote[i] = 0;
		int p=0;
		for(i=0;i<nr_class;i++)
			for(int j=i+1;j<nr_class;j++)
			{
				double sum = 0;
				int si = start[i];
				int sj = start[j];
				int ci = model->nSV[i];
				int cj = model->nSV[j];
				
				int k;
				double *coef1 = model->sv_coef[j-1];
				double *coef2 = model->sv_coef[i];
				for(k=0;k<ci;k++)
					sum += coef1[si+k] * kvalue[si+k];
				for(k=0;k<cj;k++)
					sum += coef2[sj+k] * kvalue[sj+k];
				sum -= model->rho[p++];
				if(sum > 0)
					++vote[i];
				else
					++vote[j];
			}

		int vote_max_idx = 0;
		for(i=1;i<nr_class;i++)
			if(vote[i] > vote[vote_max_idx])
				vote_max_idx = i;
		free(kvalue);
		free(start);
		free(vote);
		return model->label[vote_max_idx];
	}
}
*/
const char *svm_type_table[] =
{
	"c_svc","nu_svc","one_class","epsilon_svr","nu_svr",NULL
};

const char *kernel_type_table[]=
{
	"linear","polynomial","rbf","sigmoid",NULL
};

/*int svm_save_model(const char *model_file_name, const svm_model *model)
{
	FILE *fp = fopen(model_file_name,"w");
	if(fp==NULL) return -1;

	const svm_parameter& param = model->param;

	fprintf(fp,"svm_type %s\n", svm_type_table[param.svm_type]);
	fprintf(fp,"kernel_type %s\n", kernel_type_table[param.kernel_type]);

	if(param.kernel_type == POLY)
		fprintf(fp,"degree %g\n", param.degree);

	if(param.kernel_type == POLY || param.kernel_type == RBF || param.kernel_type == SIGMOID)
		fprintf(fp,"gamma %g\n", param.gamma);

	if(param.kernel_type == POLY || param.kernel_type == SIGMOID)
		fprintf(fp,"coef0 %g\n", param.coef0);

	int nr_class = model->nr_class;
	int l = model->l;
	fprintf(fp, "nr_class %d\n", nr_class);
	fprintf(fp, "total_sv %d\n",l);
	
	{
		fprintf(fp, "rho");
		for(int i=0;i<nr_class*(nr_class-1)/2;i++)
			fprintf(fp," %g",model->rho[i]);
		fprintf(fp, "\n");
	}
	
	if(model->label)
	{
		fprintf(fp, "label");
		for(int i=0;i<nr_class;i++)
			fprintf(fp," %d",model->label[i]);
		fprintf(fp, "\n");
	}

	if(model->nSV)
	{
		fprintf(fp, "nr_sv");
		for(int i=0;i<nr_class;i++)
			fprintf(fp," %d",model->nSV[i]);
		fprintf(fp, "\n");
	}

	fprintf(fp, "SV\n");
	const double * const *sv_coef = model->sv_coef;
	const svm_node * const *SV = model->SV;

	for(int i=0;i<l;i++)
	{
		for(int j=0;j<nr_class-1;j++)
			fprintf(fp, "alpha:%.16g \n",sv_coef[j][i]);

		const svm_node *p = SV[i];
		while(p->index != -1)
		{
			fprintf(fp,"%d:%.8g ",p->index,p->value);
			p++;
		}
		fprintf(fp, "\n");
	}

	fclose(fp);
	return 0;
}
*/
/*svm_model *svm_load_model(const char *model_file_name)
{
	FILE *fp = fopen(model_file_name,"rb");
	if(fp==NULL) return NULL;
	
	// read parameters

	svm_model *model = Malloc(svm_model,1);
	svm_parameter& param = model->param;
	model->rho = NULL;
	model->label = NULL;
	model->nSV = NULL;

	char cmd[81];
	while(1)
	{
		fscanf(fp,"%80s",cmd);

		if(strcmp(cmd,"svm_type")==0)
		{
			fscanf(fp,"%80s",cmd);
			int i;
			for(i=0;svm_type_table[i];i++)
			{
				if(strcmp(svm_type_table[i],cmd)==0)
				{
					param.svm_type=i;
					break;
				}
			}
			if(svm_type_table[i] == NULL)
			{
				fprintf(stderr,"unknown svm type.\n");
				free(model->rho);
				free(model->label);
				free(model->nSV);
				free(model);
				return NULL;
			}
		}
		else if(strcmp(cmd,"kernel_type")==0)
		{		
			fscanf(fp,"%80s",cmd);
			int i;
			for(i=0;kernel_type_table[i];i++)
			{
				if(strcmp(kernel_type_table[i],cmd)==0)
				{
					param.kernel_type=i;
					break;
				}
			}
			if(kernel_type_table[i] == NULL)
			{
				fprintf(stderr,"unknown kernel function.\n");
				free(model->rho);
				free(model->label);
				free(model->nSV);
				free(model);
				return NULL;
			}
		}
		else if(strcmp(cmd,"degree")==0)
			fscanf(fp,"%lf",&param.degree);
		else if(strcmp(cmd,"gamma")==0)
			fscanf(fp,"%lf",&param.gamma);
		else if(strcmp(cmd,"coef0")==0)
			fscanf(fp,"%lf",&param.coef0);
		else if(strcmp(cmd,"nr_class")==0)
			fscanf(fp,"%d",&model->nr_class);
		else if(strcmp(cmd,"total_sv")==0)
			fscanf(fp,"%d",&model->l);
		else if(strcmp(cmd,"rho")==0)
		{
			int n = model->nr_class * (model->nr_class-1)/2;
			model->rho = Malloc(double,n);
			for(int i=0;i<n;i++)
				fscanf(fp,"%lf",&model->rho[i]);
		}
		else if(strcmp(cmd,"label")==0)
		{
			int n = model->nr_class;
			model->label = Malloc(int,n);
			for(int i=0;i<n;i++)
				fscanf(fp,"%d",&model->label[i]);
		}
		else if(strcmp(cmd,"nr_sv")==0)
		{
			int n = model->nr_class;
			model->nSV = Malloc(int,n);
			for(int i=0;i<n;i++)
				fscanf(fp,"%d",&model->nSV[i]);
		}
		else if(strcmp(cmd,"SV")==0)
		{
			while(1)
			{
				int c = getc(fp);
				if(c==EOF || c=='\n') break;	
			}
			break;
		}
		else
		{
			fprintf(stderr,"unknown text in model file\n");
			free(model->rho);
			free(model->label);
			free(model->nSV);
			free(model);
			return NULL;
		}
	}

	// read sv_coef and SV

	int elements = 0;
	long pos = ftell(fp);

	while(1)
	{
		int c = fgetc(fp);
		switch(c)
		{
			case '\n':
				// count the '-1' element
			case ':':
				++elements;
				break;
			case EOF:
				goto out;
			default:
				;
		}
	}
out:
	fseek(fp,pos,SEEK_SET);

	int m = model->nr_class - 1;
	int l = model->l;
	model->sv_coef = Malloc(double *,m);
	int i;
	for(i=0;i<m;i++)
		model->sv_coef[i] = Malloc(double,l);
	model->SV = Malloc(svm_node*,l);
	svm_node *x_space = Malloc(svm_node,elements);

	int j=0;
	for(i=0;i<l;i++)
	{
		model->SV[i] = &x_space[j];
		for(int k=0;k<m;k++)
			fscanf(fp,"%lf",&model->sv_coef[k][i]);
		while(1)
		{
			int c;
			do {
				c = getc(fp);
				if(c=='\n') goto out2;
			} while(isspace(c));
			ungetc(c,fp);
			fscanf(fp,"%d:%lf",&(x_space[j].index),&(x_space[j].value));
			++j;
		}	
out2:
		x_space[j++].index = -1;
	}

	fclose(fp);

	model->free_sv = 1;	// XXX
	return model;
}
*/
/*void svm_destroy_model(svm_model* model)
{
	if(model->free_sv)
		free((void *)(model->SV[0]));
	for(int i=0;i<model->nr_class-1;i++)
		free(model->sv_coef[i]);
	free(model->SV);
	free(model->sv_coef);
	free(model->rho);
	free(model->label);
	free(model->nSV);
	free(model);
}
*/
/*const char *svm_check_parameter(const svm_problem *prob, const svm_parameter *param)
{
	// svm_type

	int svm_type = param->svm_type;
	if(svm_type != C_SVC &&
	   svm_type != NU_SVC &&
	   svm_type != ONE_CLASS &&
	   svm_type != EPSILON_SVR &&
	   svm_type != NU_SVR)
		return "unknown svm type";
	
	// kernel_type
	
	int kernel_type = param->kernel_type;
	if(kernel_type != LINEAR &&
	   kernel_type != POLY &&
	   kernel_type != RBF &&
	   kernel_type != SIGMOID)
		return "unknown kernel type";

	// cache_size,eps,C,nu,p,shrinking

	if(param->cache_size <= 0)
		return "cache_size <= 0";

	if(param->eps <= 0)
		return "eps <= 0";

	if(svm_type == C_SVC ||
	   svm_type == EPSILON_SVR ||
	   svm_type == NU_SVR)
		if(param->C <= 0)
			return "C <= 0";

	if(svm_type == NU_SVC ||
	   svm_type == ONE_CLASS ||
	   svm_type == NU_SVR)
		if(param->nu < 0 || param->nu > 1)
			return "nu < 0 or nu > 1";

	if(svm_type == EPSILON_SVR)
		if(param->p < 0)
			return "p < 0";

	if(param->shrinking != 0 &&
	   param->shrinking != 1)
		return "shrinking != 0 and shrinking != 1";


	// check whether nu-svc is feasible
	
	if(svm_type == NU_SVC)
	{
		int l = prob->l;
		int max_nr_class = 16;
		int nr_class = 0;
		int *label = Malloc(int,max_nr_class);
		int *count = Malloc(int,max_nr_class);

		int i;
		for(i=0;i<l;i++)
		{
			int this_label = (int)prob->y[i];
			int j;
			for(j=0;j<nr_class;j++)
				if(this_label == label[j])
				{
					++count[j];
					break;
				}
			if(j == nr_class)
			{
				if(nr_class == max_nr_class)
				{
					max_nr_class *= 2;
					label = (int *)realloc(label,max_nr_class*sizeof(int));
					count = (int *)realloc(count,max_nr_class*sizeof(int));
				}
				label[nr_class] = this_label;
				count[nr_class] = 1;
				++nr_class;
			}
		}
	
		for(i=0;i<nr_class;i++)
		{
			int n1 = count[i];
			for(int j=i+1;j<nr_class;j++)
			{
				int n2 = count[j];
				if(param->nu*(n1+n2)/2 > min(n1,n2))
				{
					free(label);
					free(count);
					return "specified nu is infeasible";
				}
			}
		}
	}

	return NULL;
}
*/