svm.java

SVM是一种常用的模式分类机器学习算法

			}
		}
		
		if (iter>=max_iter)
			System.err.print("Reaching maximal iterations in two-class probability estimates\n");
		probAB[0]=A;probAB[1]=B;
	}

	private static double sigmoid_predict(double decision_value, double A, double B)
	{
		double fApB = decision_value*A+B;
		if (fApB >= 0)
			return Math.exp(-fApB)/(1.0+Math.exp(-fApB));
		else
			return 1.0/(1+Math.exp(fApB)) ;
	}

	// Method 2 from the multiclass_prob paper by Wu, Lin, and Weng
	private static void multiclass_probability(int k, double[][] r, double[] p)
	{
		int t,j;
		int iter = 0, max_iter=Math.max(100,k);
		double[][] Q=new double[k][k];
		double[] Qp= new double[k];
		double pQp, eps=0.005/k;
	
		for (t=0;t<k;t++)
		{
			p[t]=1.0/k;  // Valid if k = 1
			Q[t][t]=0;
			for (j=0;j<t;j++)
			{
				Q[t][t]+=r[j][t]*r[j][t];
				Q[t][j]=Q[j][t];
			}
			for (j=t+1;j<k;j++)
			{
				Q[t][t]+=r[j][t]*r[j][t];
				Q[t][j]=-r[j][t]*r[t][j];
			}
		}
		for (iter=0;iter<max_iter;iter++)
		{
			// stopping condition, recalculate QP,pQP for numerical accuracy
			pQp=0;
			for (t=0;t<k;t++)
			{
				Qp[t]=0;
				for (j=0;j<k;j++)
					Qp[t]+=Q[t][j]*p[j];
				pQp+=p[t]*Qp[t];
			}
			double max_error=0;
			for (t=0;t<k;t++)
			{
				double error=Math.abs(Qp[t]-pQp);
				if (error>max_error)
					max_error=error;
			}
			if (max_error<eps) break;
		
			for (t=0;t<k;t++)
			{
				double diff=(-Qp[t]+pQp)/Q[t][t];
				p[t]+=diff;
				pQp=(pQp+diff*(diff*Q[t][t]+2*Qp[t]))/(1+diff)/(1+diff);
				for (j=0;j<k;j++)
				{
					Qp[j]=(Qp[j]+diff*Q[t][j])/(1+diff);
					p[j]/=(1+diff);
				}
			}
		}
		if (iter>=max_iter)
			System.err.print("Exceeds max_iter in multiclass_prob\n");
	}

	// Cross-validation decision values for probability estimates
	private static void svm_binary_svc_probability(svm_problem prob, svm_parameter param, double Cp, double Cn, double[] probAB)
	{
		int i;
		int nr_fold = 5;
		int[] perm = new int[prob.l];
		double[] dec_values = new double[prob.l];

		// random shuffle
		for(i=0;i<prob.l;i++) perm[i]=i;
		for(i=0;i<prob.l;i++)
		{
			int j = i+(int)(Math.random()*(prob.l-i));
			do {int _=perm[i]; perm[i]=perm[j]; perm[j]=_;} while(false);
		}
		for(i=0;i<nr_fold;i++)
		{
			int begin = i*prob.l/nr_fold;
			int end = (i+1)*prob.l/nr_fold;
			int j,k;
			svm_problem subprob = new svm_problem();

			subprob.l = prob.l-(end-begin);
			subprob.x = new svm_node[subprob.l][];
			subprob.y = new double[subprob.l];
			
			k=0;
			for(j=0;j<begin;j++)
			{
				subprob.x[k] = prob.x[perm[j]];
				subprob.y[k] = prob.y[perm[j]];
				++k;
			}
			for(j=end;j<prob.l;j++)
			{
				subprob.x[k] = prob.x[perm[j]];
				subprob.y[k] = prob.y[perm[j]];
				++k;
			}
			int p_count=0,n_count=0;
			for(j=0;j<k;j++)
				if(subprob.y[j]>0)
					p_count++;
				else
					n_count++;
			
			if(p_count==0 && n_count==0)
				for(j=begin;j<end;j++)
					dec_values[perm[j]] = 0;
			else if(p_count > 0 && n_count == 0)
				for(j=begin;j<end;j++)
					dec_values[perm[j]] = 1;
			else if(p_count == 0 && n_count > 0)
				for(j=begin;j<end;j++)
					dec_values[perm[j]] = -1;
			else
			{
				svm_parameter subparam = (svm_parameter)param.clone();
				subparam.probability=0;
				subparam.C=1.0;
				subparam.nr_weight=2;
				subparam.weight_label = new int[2];
				subparam.weight = new double[2];
				subparam.weight_label[0]=+1;
				subparam.weight_label[1]=-1;
				subparam.weight[0]=Cp;
				subparam.weight[1]=Cn;
				svm_model submodel = svm_train(subprob,subparam);
				for(j=begin;j<end;j++)
				{
					double[] dec_value=new double[1];
					svm_predict_values(submodel,prob.x[perm[j]],dec_value);
					dec_values[perm[j]]=dec_value[0];
					// ensure +1 -1 order; reason not using CV subroutine
					dec_values[perm[j]] *= submodel.label[0];
				}		
			}
		}		
		sigmoid_train(prob.l,dec_values,prob.y,probAB);
	}

	// Return parameter of a Laplace distribution 
	private static double svm_svr_probability(svm_problem prob, svm_parameter param)
	{
		int i;
		int nr_fold = 5;
		double[] ymv = new double[prob.l];
		double mae = 0;

		svm_parameter newparam = (svm_parameter)param.clone();
		newparam.probability = 0;
		svm_cross_validation(prob,newparam,nr_fold,ymv);
		for(i=0;i<prob.l;i++)
		{
			ymv[i]=prob.y[i]-ymv[i];
			mae += Math.abs(ymv[i]);
		}		
		mae /= prob.l;
		double std=Math.sqrt(2*mae*mae);
		int count=0;
		mae=0;
		for(i=0;i<prob.l;i++)
			if (Math.abs(ymv[i]) > 5*std) 
				count=count+1;
			else 
				mae+=Math.abs(ymv[i]);
		mae /= (prob.l-count);
		System.err.print("Prob. model for test data: target value = predicted value + z,\nz: Laplace distribution e^(-|z|/sigma)/(2sigma),sigma="+mae+"\n");
		return mae;
	}

	// label: label name, start: begin of each class, count: #data of classes, perm: indices to the original data
	// perm, length l, must be allocated before calling this subroutine
	private static void svm_group_classes(svm_problem prob, int[] nr_class_ret, int[][] label_ret, int[][] start_ret, int[][] count_ret, int[] perm)
	{
		int l = prob.l;
		int max_nr_class = 16;
		int nr_class = 0;
		int[] label = new int[max_nr_class];
		int[] count = new int[max_nr_class];
		int[] data_label = new 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;
				}
			}
			data_label[i] = j;
			if(j == nr_class)
			{
				if(nr_class == max_nr_class)
				{
					max_nr_class *= 2;
					int[] new_data = new int[max_nr_class];
					System.arraycopy(label,0,new_data,0,label.length);
					label = new_data;
					new_data = new int[max_nr_class];
					System.arraycopy(count,0,new_data,0,count.length);
					count = new_data;					
				}
				label[nr_class] = this_label;
				count[nr_class] = 1;
				++nr_class;
			}
		}

		int[] start = new int[nr_class];
		start[0] = 0;
		for(i=1;i<nr_class;i++)
			start[i] = start[i-1]+count[i-1];
		for(i=0;i<l;i++)
		{
			perm[start[data_label[i]]] = i;
			++start[data_label[i]];
		}
		start[0] = 0;
		for(i=1;i<nr_class;i++)
			start[i] = start[i-1]+count[i-1];

		nr_class_ret[0] = nr_class;
		label_ret[0] = label;
		start_ret[0] = start;
		count_ret[0] = count;
	}

	//
	// Interface functions
	//
	public static svm_model svm_train(svm_problem prob, svm_parameter param)
	{
		svm_model model = new svm_model();
		model.param = param;

		if(param.svm_type == svm_parameter.ONE_CLASS ||
		   param.svm_type == svm_parameter.EPSILON_SVR ||
		   param.svm_type == svm_parameter.NU_SVR)
		{
			// regression or one-class-svm
			model.nr_class = 2;
			model.label = null;
			model.nSV = null;
			model.probA = null; model.probB = null;
			model.sv_coef = new double[1][];

			if(param.probability == 1 &&
			   (param.svm_type == svm_parameter.EPSILON_SVR ||
			    param.svm_type == svm_parameter.NU_SVR))
			{
				model.probA = new double[1];
				model.probA[0] = svm_svr_probability(prob,param);
			}

			decision_function f = svm_train_one(prob,param,0,0);
			model.rho = new double[1];
			model.rho[0] = f.rho;

			int nSV = 0;
			int i;
			for(i=0;i<prob.l;i++)
				if(Math.abs(f.alpha[i]) > 0) ++nSV;
			model.l = nSV;
			model.SV = new svm_node[nSV][];
			model.sv_coef[0] = new double[nSV];
			int j = 0;
			for(i=0;i<prob.l;i++)
				if(Math.abs(f.alpha[i]) > 0)
				{
					model.SV[j] = prob.x[i];
					model.sv_coef[0][j] = f.alpha[i];
					++j;
				}
		}
		else
		{
			// classification
			int l = prob.l;
			int[] tmp_nr_class = new int[1];
			int[][] tmp_label = new int[1][];
			int[][] tmp_start = new int[1][];
			int[][] tmp_count = new int[1][];			
			int[] perm = new int[l];

			// group training data of the same class
			svm_group_classes(prob,tmp_nr_class,tmp_label,tmp_start,tmp_count,perm);
			int nr_class = tmp_nr_class[0];			
			int[] label = tmp_label[0];
			int[] start = tmp_start[0];
			int[] count = tmp_count[0];
			svm_node[][] x = new svm_node[l][];
			int i;
			for(i=0;i<l;i++)
				x[i] = prob.x[perm[i]];

			// calculate weighted C

			double[] weighted_C = new 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)
					System.err.print("warning: class label "+param.weight_label[i]+" specified in weight is not found\n");
				else
					weighted_C[j] *= param.weight[i];
			}

			// train k*(k-1)/2 models

			boolean[] nonzero = new boolean[l];
			for(i=0;i<l;i++)
				nonzero[i] = false;
			decision_function[] f = new decision_function[nr_class*(nr_class-1)/2];

			double[] probA=null,probB=null;
			if (param.probability == 1)
			{
				probA=new double[nr_class*(nr_class-1)/2];
				probB=new double[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 = new svm_problem();
					int si = start[i], sj = start[j];
					int ci = count[i], cj = count[j];
					sub_prob.l = ci+cj;
					sub_prob.x = new svm_node[sub_prob.l][];
					sub_prob.y = new 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;
					}

					if(param.probability == 1)
					{
						double[] probAB=new double[2];
						svm_binary_svc_probability(sub_prob,param,weighted_C[i],weighted_C[j],probAB);
						probA[p]=probAB[0];
						probB[p]=probAB[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] && Math.abs(f[p].alpha[k]) > 0)
							nonzero[si+k] = true;
					for(k=0;k<cj;k++)
						if(!nonzero[sj+k] && Math.abs(f[p].alpha[ci+k]) > 0)
							nonzero[sj+k] = true;
					++p;
				}

			// build output

			model.nr_class = nr_class;

			model.label = new int[nr_class];
			for(i=0;i<nr_class;i++)
				model.label[i] = label[i];

			model.rho = new double[nr_class*(nr_class-1)/2];
			for(i=0;i<nr_class*(nr_class-1)/2;i++)
				model.rho[i] = f[i].rho;

			if(param.probability == 1)
			{
				model.probA = new double[nr_class*(nr_class-1)/2];
				model.probB = new double[nr_class*(nr_class-1)/2];
				for(i=0;i<nr_class*(nr_class-1)/2;i++)
				{
					model.probA[i] = probA[i];
					model.probB[i] = probB[i];
				}
			}
			else
			{
				model.probA=null;
				model.probB=null;
			}

			int nnz = 0;
			int[] nz_count = new int[nr_class];
			model.nSV = new 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;
						++nnz;
					}
				model.nSV[i] = nSV;
				nz_count[i] = nSV;
			}

			System.out.print("Total nSV = "+nnz+"\n");

			model.l = nnz;
			model.SV = new svm_node[nnz][];
			p = 0;
			for(i=0;i<l;i++)
				if(nonzero[i]) model.SV[p++] = x[i];

			int[] nz_start = new 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 = new double[nr_class-1][];
			for(i=0;i<nr_class-1;i++)
				model.sv_coef[i] = new double[nnz];

			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];
					q = nz_start[j];
					for(k=0;k<cj;k++)
						if(nonzero[sj+k])
							model.sv_coef[i][q++] = f[p].alpha[ci+k];
					++p;
				}
		}
		return model;
	}
	
	// Stratified cross validation
	public static void svm_cross_validation(svm_problem prob, svm_parameter param, int nr_fold, double[] target)
	{
		int i;
		int[] fold_start = new int[nr_fold+1];
		int l = prob.l;
		int[] perm = new int[l];
		
		// stratified cv may not give leave-one-out rate
		// Each class to l folds -> some folds may have zero elements
		if((param.svm_type == svm_parameter.C_SVC ||
		    param.svm_type == svm_parameter.NU_SVC) && nr_fold < l)
		{
			int[] tmp_nr_class = new int[1];
			int[][] tmp_label = new int[1][];
			int[][] tmp_start = new int[1][];
			int[][] tmp_count = new int[1][];

			svm_group_classes(prob,tmp_nr_class,tmp_label,tmp_start,tmp_count,perm);

			int nr_class = tmp_nr_class[0];
			int[] label = tmp_label[0];
			int[] start = tmp_start[0];
			int[] count = tmp_count[0]; 		

			// random shuffle and then data grouped by fold using the array perm
			int[] fold_count = new int[nr_fold];
			int c;
			int[] index = new int[l];
			for(i=0;i<l;i++)
				index[i]=perm[i];
			for (c=0; c<nr_class; c++)
				for(i=0;i<count[c];i++)
				{
					int j = i+(int)(Math.random()*(count[c]-i));
					do {int _=index[start[c]+j]; index[start[c]+j]=index[start[c]+i]; index[start[c]+i]=_;} while(false);
				}
			for(i=0;i<nr_fold;i++)
			{
				fold_count[i] = 0;
				for (c=0; c<nr_class;c++)
					fold_count[i]+=(i+1)*count[c]/nr_fold-i*count[c]/nr_fold;
			}
			fold_start[0]=0;
			for (i=1;i<=nr_fold;i++)
				fold_start[i] = fold_start[i-1]+fold_count[i-1];
			for (c=0; c<nr_class;c++)
				for(i=0;i<nr_fold;i++)
				{
					int begin = start[c]+i*count[c]/nr_fold;
					int end = start[c]+(i+1)*count[c]/nr_fold;
					for(int j=begin;j<end;j++)
					{
						perm[fold_start[i]] = index[j];
						fold_start[i]++;
					}
				}
			fold_start[0]=0;
			for (i=1;i<=nr_fold;i++)
				fold_start[i] = fold_start[i-1]+fold_count[i-1];
		}
		else
		{
			for(i=0;i<l;i++) perm[i]=i;
			for(i=0;i<l;i++)
			{
				int j = i+(int)(Math.random()*(l-i));
				do {int _=perm[i]; perm[i]=perm[j]; perm[j]=_;} while(false);
			}
			for(i=0;i<=nr_fold;i++)
				fold_start[i]=i*l/nr_fold;
		}

		for(i=0;i<nr_fold;i++)
		{
			int begin = fold_start[i];
			int end = fold_start[i+1];
			int j,k;
			svm_problem subprob = new svm_problem();

			subprob.l = l-(end-begin);
			subprob.x = new svm_node[subprob.l][];
			subprob.y = new double[subprob.l];

			k=0;