matlab怎么实现支持向量机的回归拟合

SVM应用于回归拟合分析时，其基本思想不再是寻找一个最优分类面使得两类样本分开，而是寻找一个最优分类面使得所有训练样本离该最优分类面的误差最小

%% 清空环境变量

clear

clc

%% 导入数据

load concrete_data.mat

% 随机产生训练集和测试集

n = randperm(size(attributes,2));

% 训练集——80个样本

p_train = attributes(:,n(1:80))';

t_train = strength(:,n(1:80))';

% 测试集——23个样本

p_test = attributes(:,n(81:end))';

t_test = strength(:,n(81:end))';

%% 数据归一化

% 训练集

[pn_train,inputps] = mapminmax(p_train');

pn_train = pn_train';

pn_test = mapminmax('apply',p_test',inputps);

pn_test = pn_test';

% 测试集

[tn_train,outputps] = mapminmax(t_train');

tn_train = tn_train';

tn_test = mapminmax('apply',t_test',outputps);

tn_test = tn_test';

%% SVM模型创建/训练

% 寻找最佳c参数/g参数

[c,g] = meshgrid(-10:0.5:10,-10:0.5:10);

[m,n] = size(c);

cg = zeros(m,n);

eps = 10^(-4);

v = 5;

bestc = 0;

bestg = 0;

error = Inf;

for i = 1:m

    for j = 1:n

        cmd = ['-v ',num2str(v),' -t 2',' -c ',num2str(2^c(i,j)),' -g ',num2str(2^g(i,j) ),' -s 3 -p 0.1'];

        cg(i,j) = svmtrain(tn_train,pn_train,cmd);

        if cg(i,j) < error

            error = cg(i,j);

            bestc = 2^c(i,j);

            bestg = 2^g(i,j);

        end

        if abs(cg(i,j) - error) <= eps && bestc > 2^c(i,j)

            error = cg(i,j);

            bestc = 2^c(i,j);

            bestg = 2^g(i,j);

        end

    end

end

% 创建/训练SVM  

cmd = [' -t 2',' -c ',num2str(bestc),' -g ',num2str(bestg),' -s 3 -p 0.01'];

model = svmtrain(tn_train,pn_train,cmd);

%% SVM仿真预测

[Predict_1,error_1] = svmpredict(tn_train,pn_train,model);

[Predict_2,error_2] = svmpredict(tn_test,pn_test,model);

% 反归一化

predict_1 = mapminmax('reverse',Predict_1,outputps);

predict_2 = mapminmax('reverse',Predict_2,outputps);

% 结果对比

result_1 = [t_train predict_1];

result_2 = [t_test predict_2];

%% 绘图

figure(1)

plot(1:length(t_train),t_train,'r-*',1:length(t_train),predict_1,'b:o')

grid on

legend('真实值','预测值')

xlabel('样本编号')

ylabel('耐压强度')

string_1 = {'训练集预测结果对比';

           ['mse = ' num2str(error_1(2)) ' R^2 = ' num2str(error_1(3))]};

title(string_1)

figure(2)

plot(1:length(t_test),t_test,'r-*',1:length(t_test),predict_2,'b:o')

grid on

legend('真实值','预测值')

xlabel('样本编号')

ylabel('耐压强度')

string_2 = {'测试集预测结果对比';

           ['mse = ' num2str(error_2(2)) ' R^2 = ' num2str(error_2(3))]};

title(string_2)

%% BP 神经网络

% 数据转置

pn_train = pn_train';

tn_train = tn_train';

pn_test = pn_test';

tn_test = tn_test';

% 创建BP神经网络

net = newff(pn_train,tn_train,10);

% 设置训练参数

net.trainParam.epcohs = 1000;

net.trainParam.goal = 1e-3;

net.trainParam.show = 10;

net.trainParam.lr = 0.1;

% 训练网络

net = train(net,pn_train,tn_train);

% 仿真测试

tn_sim = sim(net,pn_test);

% 均方误差

E = mse(tn_sim - tn_test);

% 决定系数

N = size(t_test,1);

R2=(N*sum(tn_sim.*tn_test)-sum(tn_sim)*sum(tn_test))^2/((N*sum((tn_sim).^2)-(sum(tn_sim))^2)*(N*sum((tn_test).^2)-(sum(tn_test))^2)); 

% 反归一化

t_sim = mapminmax('reverse',tn_sim,outputps);

% 绘图

figure(3)

plot(1:length(t_test),t_test,'r-*',1:length(t_test),t_sim,'b:o')

grid on

legend('真实值','预测值')

xlabel('样本编号')

ylabel('耐压强度')

string_3 = {'测试集预测结果对比(BP神经网络)';

           ['mse = ' num2str(E) ' R^2 = ' num2str(R2)]};

title(string_3)