SVM應用于回歸擬合分析時，其基本思想不再是尋找一個最優分類面使得兩類樣本分開，而是尋找一個最優分類面使得所有訓練樣本離該最優分類面的誤差最小

%% 清空環境變量

clear

clc

%% 導入數據

load concrete_data.mat

% 隨機產生訓練集和測試集

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

% 訓練集——80個樣本

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

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

% 測試集——23個樣本

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

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

%% 數據歸一化

% 訓練集

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

pn_train = pn_train';

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

pn_test = pn_test';

% 測試集

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

tn_train = tn_train';

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

tn_test = tn_test';

%% SVM模型創建/訓練

% 尋找最佳c參數/g參數

[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

% 創建/訓練SVM  

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

model = svmtrain(tn_train,pn_train,cmd);

%% SVM仿真預測

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

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

% 反歸一化

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

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

% 結果對比

result_1 = [t_train predict_1];

result_2 = [t_test predict_2];

%% 繪圖

figure(1)

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

grid on

legend('真實值','預測值')

xlabel('樣本編號')

ylabel('耐壓強度')

string_1 = {'訓練集預測結果對比';

           ['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('真實值','預測值')

xlabel('樣本編號')

ylabel('耐壓強度')

string_2 = {'測試集預測結果對比';

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

title(string_2)

%% BP 神經網絡

% 數據轉置

pn_train = pn_train';

tn_train = tn_train';

pn_test = pn_test';

tn_test = tn_test';

% 創建BP神經網絡

net = newff(pn_train,tn_train,10);

% 設置訓練參數

net.trainParam.epcohs = 1000;

net.trainParam.goal = 1e-3;

net.trainParam.show = 10;

net.trainParam.lr = 0.1;

% 訓練網絡

net = train(net,pn_train,tn_train);

% 仿真測試

tn_sim = sim(net,pn_test);

% 均方誤差

E = mse(tn_sim - tn_test);

% 決定系數

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)); 

% 反歸一化

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

% 繪圖

figure(3)

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

grid on

legend('真實值','預測值')

xlabel('樣本編號')

ylabel('耐壓強度')

string_3 = {'測試集預測結果對比(BP神經網絡)';

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

title(string_3)