数学建模竞赛蠓虫分类.doc

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=[ ; ];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('UsingBayesprincipalis:')Apf=find(pwx1>pwx2)+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('Usingfisherprincipalis:')Apf=find(dpyb>y0)+n1+n2,figure(2);t=::;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([,,,]);感知器准则及梯度下降算法:样本的增广化:样本的规增广化:(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=;a=1-2*rand(3,1);k=0;whilek<100000k=k+1;y=x1(:,rem(k,n1+n2)+1);ifa'*y<epsla=a+y;endendy1=a'*x1(:,1:n1+n2);ind=find(y1<=0);display('thesamplesforfirstclassusingpeceptronprincipalis:')Apf=find(a'*x1(:,n1+n2+1:end)>0)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%MSEb=ones(n1+n2,1);