C++代码实现MATLAB中的fitcsvm函数功能

// ============================================================// fitcsvm 的独立 C++ 实现（SMO + RBF 核，无第三方依赖）// 编译: g++ -std=c++17 svm_standalone.cpp -o svm_standalone// 运行: ./svm_standalone// ============================================================#include<iostream>#include<vector>#include<cmath>#include<iomanip>structSample{doublex[2];doubley;};classSVM{public:doubleC=1.0,gamma=1.0,tol=1e-3;std::vector<Sample>D;std::vector<double>alpha;doubleb=0;// RBF 核: K(a,c) = exp(-gamma * ||a-c||^2)doubleK(constSample&a,constSample&c)const{doubled=0;for(intk=0;k<2;++k)d+=(a.x[k]-c.x[k])*(a.x[k]-c.x[k]);returnstd::exp(-gamma*d);}// 决策函数 f(x) = sum_i alpha_i * y_i * K(x_i, x) + bdoubledec(constSample&x)const{doubles=0;for(inti=0;i<(int)D.size();++i)s+=alpha[i]*D[i].y*K(D[i],x);returns+b;}// SMO 训练voidtrain(conststd::vector<Sample>&data){D=data;intn=(int)D.size();alpha.assign(n,0.0);b=0.0;for(intiter=0;iter<200;++iter){intchanged=0;for(inti=0;i<n;++i){doubleEi=dec(D[i])-D[i].y;// KKT 违反检查if(!((D[i].y*Ei<-tol&&alpha[i]<C)||(D[i].y*Ei>tol&&alpha[i]>0)))continue;for(intj=0;j<n;++j){if(j==i)continue;doubleEj=dec(D[j])-D[j].y;doubleai=alpha[i],aj=alpha[j];// 计算 alpha_j 的上下界 L, HdoubleL,H;if(D[i].y!=D[j].y){L=std::max(0.0,aj-ai);H=std::min(C,C+aj-ai);}else{L=std::max(0.0,ai+aj-C);H=std::min(C,ai+aj);}if(L>=H)continue;doubleeta=2*K(D[i],D[j])-K(D[i],D[i])-K(D[j],D[j]);if(eta>=0)continue;// 更新 alpha_jdoubleajN=aj-D[j].y*(Ei-Ej)/eta;if(ajN>H)ajN=H;if(ajN<L)ajN=L;if(std::fabs(ajN-aj)<1e-5)continue;// 更新 alpha_idoubleaiN=ai+D[i].y*D[j].y*(aj-ajN);// 更新偏置 bdoubleb1=b-Ei-D[i].y*(aiN-ai)*K(D[i],D[i])-D[j].y*(ajN-aj)*K(D[i],D[j]);doubleb2=b-Ej-D[i].y*(aiN-ai)*K(D[i],D[j])-D[j].y*(ajN-aj)*K(D[j],D[j]);if(aiN>0&&aiN<C)b=b1;elseif(ajN>0&&ajN<C)b=b2;elseb=(b1+b2)/2;alpha[i]=aiN;alpha[j]=ajN;++changed;break;}}if(changed==0)break;}}doublepredict(constSample&x)const{returndec(x)>0?1.0:-1.0;}intnumSV()const{intc=0;for(doublea:alpha)if(a>1e-8)++c;returnc;}};intmain(){// ---------- 1. 训练数据（XOR 分布） ----------std::vector<Sample>train={{{1.0,1.0},1.0},{{-1.0,1.0},-1.0},{{-1.0,-1.0},-1.0},{{1.0,-1.0},1.0}};std::cout<<std::fixed<<std::setprecision(2);std::cout<<"=== Training Data ===\n";for(inti=0;i<(int)train.size();++i)std::cout<<" Sample "<<i<<": y="<<(train[i].y>0?"+1":"-1")<<" x=["<<train[i].x[0]<<", "<<train[i].x[1]<<"]\n";std::cout<<"\n";// ---------- 2. 配置参数（对应 fitcsvm 的 Name-Value） ----------SVM svm;svm.C=1.0;// 'BoxConstraint'svm.gamma=5.0;// 1 / (2 * KernelScale^2)svm.tol=1e-3;std::cout<<"=== SVM Parameters ===\n";std::cout<<" C = "<<svm.C<<"\n";std::cout<<" gamma = "<<svm.gamma<<"\n";std::cout<<" tol = "<<svm.tol<<"\n\n";// ---------- 3. 训练 ----------std::cout<<">>> Training ...\n";svm.train(train);std::cout<<">>> Training done.\n\n";// ---------- 4. 模型信息 ----------std::cout<<std::setprecision(4);std::cout<<"=== Model Info ===\n";std::cout<<" Support vectors = "<<svm.numSV()<<"\n";std::cout<<" Bias (b) = "<<svm.b<<"\n";std::cout<<" Alphas = [";for(inti=0;i<(int)svm.alpha.size();++i)std::cout<<svm.alpha[i]<<(i+1<(int)svm.alpha.size()?", ":"");std::cout<<"]\n\n";// ---------- 5. 预测 ----------std::cout<<"=== Predictions ===\n";std::vector<Sample>tests={{{1.0,1.0},1.0},{{-1.0,-1.0},-1.0},{{0.5,0.5},1.0},{{-0.5,-0.5},-1.0}};for(constauto&t:tests){doubled=svm.dec(t);doublep=svm.predict(t);std::cout<<" x=["<<std::setw(5)<<t.x[0]<<", "<<std::setw(5)<<t.x[1]<<"]"<<" decision="<<std::setw(8)<<d<<" predicted="<<(p>0?"+1":"-1")<<" expected="<<(t.y>0?"+1":"-1")<<(p==t.y?" [OK]":" [X]")<<"\n";}std::cout<<"\n>>> Done.\n";return0;}