function fitting.rar_RBF svm matlab_SVM拟合函数_svm一维_一维神经网络_网络感知

clc; clear all; close all; qid=1; kernel='gaussian' %polynomial gaussian sigmoid dev=0.000008; % dev=0.11; tt=0; tt=tt+1; sigma=1; switch qid case 1 f=@(x)(1./sqrt(x)); xtrain=1:0.25:100; dtrain=f(xtrain); xtest=xtrain+0.5*(xtrain(2)-xtrain(1)); dtest=f(xtest); case 2 f=@(x)sin(x); xtrain=0:0.04*pi:4*pi; dtrain=f(xtrain); xtest=xtrain+0.5*(xtrain(2)-xtrain(1)); dtest=f(xtest); case 3 f=@(x)(sin(x)./x).^2; xtrain=-4*pi:0.07*pi:4*pi; dtrain=f(xtrain); xtest=xtrain+0.5*(xtrain(2)-xtrain(1)); dtest=f(xtest); case 4 f=@(x)exp(-x.^2).*sin(x.^2); xtrain=-4*pi:0.07*pi:4*pi; dtrain=f(xtrain); xtest=xtrain+0.5*(xtrain(2)-xtrain(1)); dtest=f(xtest); % figure(1), % plot(XTrain,DTrain); end tic %取样 xnum=length(xtrain); Y=[]; X=[]; D=[]; D = ones(1,xnum); ji = 1:2:xnum; D(ji) = -1; Y = dtrain+dev*D; X=[xtrain;Y]; K=[]; H=[]; dis=[]; epsilon=1e-5; tic switch kernel case 'polynomial' for x_index=1:1:xnum; x_temp=X(:,x_index)*ones(1,xnum); x_temp=x_temp.*X; dis=sum(x_temp); K(x_index,:)=(1+dis).*(1+dis).*(1+dis); end case 'gaussian' for x_index=1:1:xnum; x_temp=X(:,x_index)*ones(1,xnum); x_temp=x_temp-X; x_temp=x_temp.*x_temp; dis=sum(x_temp); K(x_index,:)=exp(-dis./(2*sigma^2)); end case 'sigmoid' % sigmoid for x_index=1:1:xnum; x_temp=X(:,x_index)*ones(1,xnum); x_temp=x_temp-X; x_temp=x_temp.*x_temp; dis=sum(x_temp); K(x_index,:)=1./(1+exp(-dis)); end end C=inf; D_T=D'*D; H=D_T.*K; H = H+1e-10*eye(size(H)); f=-ones(xnum,1); vlb = zeros(xnum,1); vub = C*ones(xnum,1); xx0 = zeros(xnum,1); A = D; bb =0; b=1; A=[]; bb=[]; Alpha= quadprog(H,f,[],[],A,bb,vlb,vub,xx0); sv=find(Alpha>epsilon); max_sv=length(sv); for sv1_index=1:1:max_sv temp_b=0; for sv2_index=1:1:max_sv temp=Alpha(sv(sv2_index))*D(sv(sv2_index))*K(sv(sv2_index),sv(sv1_index)); temp_b=temp_b+temp; end temp_b=1/D(sv(sv1_index))-temp_b; b=[b,temp_b]; end b0=sum(b)/max_sv; b0=(b0>epsilon).*b0; switch kernel case 'polynomial' %多项式 syms m n x_temp=[m;n]*ones(1,xnum); x_temp=x_temp.*X; dis=sum(x_temp); Kc=(1+dis).*(1+dis).*(1+dis); testc1=sum(Alpha'.*D.*Kc); z=testc1+b0; case 'gaussian' %高斯 syms m n x_temp=[m;n]*ones(1,xnum); x_temp=x_temp-X; x_temp=x_temp.*x_temp; dis=sum(x_temp); Kc=exp(-dis./(2*sigma^2)); testc1=sum(Alpha'.*D.*Kc); z=testc1+b0; case 'sigmoid' %sigmoid syms m n x_temp=[m;n]*ones(1,xnum); x_temp=x_temp.*X; dis=sum(x_temp); Kc =tanh(7*dis-0.5); testc1=sum(Alpha'.*D.*Kc); z=testc1+b0; end switch qid case 1 h=ezplot(z,[1 100 -0.5 1.5]);hold on; % set(h,'color','r') case 2 h=ezplot(z,[0 4*pi -1 1]);hold on; case 3 h=ezplot(z,[-4*pi 4*pi 1.5196e-33 0.9997]);hold on; case 4 h=ezplot(z,[-4*pi 4*pi -0.0138 0.3218] );hold on; end set(h,'color','k'); toc time=toc plot(X(1,:),X(2,:),'r*');hold on; plot(xtest,dtest,'bo');hold on; legend('测试结果','样本','原函数'); title('拟合结果'); xlabel('x'); ylabel('y');