matlab的判别分析.docx

广西某锰矿床已知两种不同锰矿石各项评价指标如下表所列。现新发现湖润锰矿床，初步定为氧化锰矿石，试用两类判别定其属性。类别序号氧化锰矿石12341.1934.9935.6211.869.8410.560.1820.1780.26136.2227.8221.02碳酸锰矿石12323.2125.0519.235.466.846.610.110.1340.13721.1727.326.61湖润锰石(待判)123426.9325.4727.3828.9812.6610.2510.3810.980.1520.1320.1200.11130.2033.4631.2031.21Matlab执行代码:g1=[41.19 11.86 0.182 36.22;34.99 9.84 0.178 27.82;35.62 10.56 0.261 21.02];g2=[23.21 5.46 0.11 21.17;25.05 6.84 0.134 27.3;19.23 6.61 0.137 26.61];fprintf(做距离判别分析:\n)fprintf(在两个总体的协方差矩阵相等的假设下进行判别分析:\n)fprintf(两个样本的协方差矩阵s1,s2分别为\n)s1=cov(g1)s2=cov(g2)fprintf(因为两个总体的协方差矩阵相等,所以协方差的联合估计s为:\n)[m1,n2]=size(g1);[m2,n2]=size(g2);s=((m1-1)*s1+(m2-1)*s2)/(m1+m2-2)fprintf(两个总体的马氏平方距离为:\n)sn=inv(s);u1=mean(g1);u2=mean(g2);ucz=(u1-u2);dmj=(u1-u2)*sn*uczfprintf(该值反映了两个总体的分离程度,线性函数的判别函数为:\n)syms x1;syms x2;syms x3;syms x4;x=[x1;x2;x3;x4];u1z=u1;u2z=u2;a1=(sn*u1z);b1=(u1*sn*u1z)/2;a2=(sn*u2z);b2=(u2*sn*u2z)/2;w1=vpa((a1*x-b1),4)w2=vpa((a2*x-b2),4)fprintf(用回代法作出误判率p1为:\n)fprintf(比较gwh1和gwh2大小\n)g=[g1;g2];[m,n]=size(g);for i=1:mghdw1(i,:)=a1.*g(i,:);ghdw2(i,:)=a2.*g(i,:); gwh1(i)=sum(ghdw1(i,:))-b1;gwh2(i)=sum(ghdw2(i,:))-b2;endgwh1gwh2fprintf(经比较得g1中1,2,3号判入g1;g2中1,2,3号判入g2,则误判率的回带估计为:\n)p1=0fprintf(用交叉估计法确认距离判别的误判率：\n)fprintf(依次剔除g1总体中1，2，3号样本是的判别函数值x1w1，x1w2为：)for I=1:3 xg1=g1;xg1(I,:)=[]; xs1=cov(xg1); x1s=(xs1+2*s2)/3;x1sn=x1s; xu1=mean(xg1);x1w1(I)=sum((x1sn*xu1).*g1(I,:))-0.5*xu1*x1sn*xu1;x1w2(I)=sum((x1sn*u2).*g1(I,:))-0.5*u2*x1sn*u2;endx1w1x1w2for I1=1:3if(x1w1(I1)=x1w2(I1))zp1(I1)=1;endendzg1=sum(zp1);fprintf(依次剔除g2总体中1，2，3号样本的判别函数值x2w1,x2w2为:)for J=1:3 xg2=g2;xg2(J,:)=[]; xs2=cov(xg2); x2s=(2*s1+xs2)/3;x2sn=x2s; xu2=mean(xg2);x2w1(J)=sum((x2sn*xu2).*g2(J,:))-0.5*u1*x2sn*u1;x2w2(J)=sum((x2sn*xu2).*g2(J,:))-0.5*xu2*x2sn*xu2;endx2w1x2w2for J1=1:3if(x2w1(J1)x2w2(J1))zp2(J1)=1;endendzg2=sum(zp2);fprintf(由上比较得，交叉法所得的误判率为：\n)zp=zg1+zg2;jwpl=(6-zp)/6fprintf(判别新样品:\n)yp=[26.93 12.66 0.152 30.20;25.47 10.25 0.132 33.46;27.38 10.38 0.120 31.20;28.98 10.98 0.111 31.21]