【-数学建模竞赛】蠓虫分类

蠓虫分类解：（1）Bayes判别：求条件概率假设假设两类数据均服从二维正态分布， 则条件概率为：决策规则为; 或等价地: 判决函数：类似地，Bayes最小风险判别可通过给出风险后得到。x=1.201.301.181.141.261.281.361.481.401.38 1.24 1.381.541.381.561.241.281.401.221.36;1.861.961.781.782.002.001.741.821.701.90 1.72 1.641.821.822.081.801.782.041.881.78;n1=6;n2=9;n3=5;plot(x(1,1:n1),x(2,1:n1),o,x(1,n1+1:n1+n2),x(2,n1+1:n1+n2),*,x(1,n1+n2+1:end),x(2,n1+n2+1:end),r+);mm1=sum(y(1:n1)/n1;mm2=sum(y(n1+1:n1+n2)/n2;sgm1=cov(x(:,1:n1); %=s1/(n1-1);sgm2=cov(x(:,n1+1:n1+n2);X=x(:,n1+n2+1:end);X=X;pxw1= mvnpdf(X, m1, sgm1);pxw2= mvnpdf(X, m2, sgm2);pwx1=pxw1./(pxw1+pxw2);pwx2=pxw2./(pxw1+pxw2);display(Using Bayes principal is:)Apf=find(pwx1pwx2)+n1+n2,（2）Fisher判别：求投影方向w*准则函数：其中最优解：m1=mean(x(:,1:n1),2);m2=mean(x(:,n1+1:n1+n2),2);s1=(x(:,1:n1)-repmat(m1,1,n1)*(x(:,1:n1)-repmat(m1,1,n1);s2=(x(:,n1+1:n1+n2)-repmat(m2,1,n2)*(x(:,n1+1:n1+n2)-repmat(m2,1,n2);S=s1+s2;w=inv(S)*(m1-m2);y=w*x;mm1=sum(y(1:n1)/n1;mm2=sum(y(n1+1:n1+n2)/n2;y0=(mm1+mm2)/2;%y0=(mm1*n1+mm2*n2)/(n1+n2);dpyb=y(n1+n2+1:end);display(Using fisher principal is:)Apf=find(dpyby0)+n1+n2,figure(2);t=1.1:0.01:1.6;kkk=-w(1)/w(2);ft=kkk*t+y0/w(2);plot(x(1,1:n1),x(2,1:n1),o,x(1,n1+1:n1+n2),x(2,n1+1:n1+n2),*,x(1,n1+n2+1:end),x(2,n1+n2+1:end),r+,t,ft);axis(1.1,1.6,1.6,2.1);感知器准则及梯度下降算法：样本的增广化： 样本的规范增广化：（仍记为）目标：求 使梯度下降法：批处理感知器算法固定增量单样本感知器%peceptronx1=ones(1,length(x);x;x1(:,n1+1:n1+n2)=-x1(:,n1+1:n1+n2);epsl=0.1;a=1-2*rand(3,1);k=0;while k k=k+1; y=x1(:,rem(k,n1+n2)+1); if a*yepsl a=a+y; end end y1=a*x1(:,1:n1+n2);ind=find(y10)pt=-a(2)*t/a(3)-a(1)/a(3);figure(3),plot(x(1,1:n1),x(2,1:n1),o,x(1,n1+1:n1+n2),x(2,n1+1:n1+n2),*,x(1,n1+n2+1:end),x(2,n1+n2+1:end),r+,t,pt,ft);最小平方误差准则： 设其中，目标： min 目标函数的梯度：令 %MSE b=ones(n1+n2,1);Y=x1(:,1:n1+n2);Y=Y;Yplus=(Y*Y)(-1)*Y;ahat=Yplus*b;mt=-ahat(2)*t/ahat(3)-ahat(1)/ahat(3);figure(4)plot(t,pt;ft;mt,x(1,1:n1),x(2,1:n1),o,x(1,n1+1:n1+n2),x(2,n1+1:n1+n2),*,x(1,n1+n2+1:end),x(2,n1+n2+1:end)