因子分析

姚安欣/AHP.m

@@ -0,0 +1,64 @@
+%AHP步骤
+
+clc,clear,close all;
+A=[1,2,3,5
+   1/2,1,1/2,2
+   1/3,2,1,2
+   1/5,1/2,1/2,1];
+[row,col]=size(A);
+
+%判断矩阵一致性检验
+n=col;
+maxlam=max(eig(A));
+RI=[0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45];
+CI=(maxlam-n)/(n-1);
+CR=CI/RI(n);
+
+%判断矩阵确定权重
+for i=1:col
+    sumcol=sum(A(:,i));
+    for j=1:row
+        A(j,i)=A(j,i)/sumcol;
+    end
+end
+
+weig=zeros(row,1);
+for i=1:row
+    sumrow=sum(A(i,:));
+    weig(i)=sumrow/n;
+end
+
+%各个指标归一化   按列单位化
+data= [1686.4 3183 12000 397
+       903.6 1916.4 3439.6 43
+       837.6 817.6 4748 1159
+       824.9 1296.4 12000 442
+       2110.2 1465.7 6199.5 228]; 
+[rowd,cold]=size(data);
+for i=1:cold
+    sumcold=sum(data(:,i));
+    for j=1:rowd
+        data(j,i)=data(j,i)/sumcold;
+    end
+end
+
+
+%按权重计算分数
+
+score=data*weig;
+
+
+projectNames={'老番茄','何同学','木鱼水心','凉风','罗翔'};
+figure; 
+bar(score);%条形图
+
+set(gca, 'XTickLabel', projectNames);  %每个条形图标签
+xlabel('博主');  
+ylabel('加权总分'); 
+title('得分');  
+  
+grid on; % 网格线
+
+
+
+

姚安欣/PCA.m

@@ -0,0 +1,96 @@
+clc,clear,format short,close all;
+load data_mh.mat;
+[n,p]=size(x);
+
+%标准化
+X=zscore(x);
+
+%协方差矩阵/相关系数矩阵
+R=cov(X);
+[V,D]=eig(R);%[特征向量，特征值]
+
+lambda=diag(D);
+lambda=lambda(end:-1:1);
+
+total_contri=sum(lambda);
+
+cum_contri=cumsum(lambda);
+
+contri_rate=cum_contri/total_contri;
+
+V1=rot90(V)';
+disp(V1);
+
+c1=V1(:,1);
+c2=V1(:,2);
+
+XX=X*c1;
+YY=X*c2;
+
+
+figure;
+scatter(XX, YY, 'filled');
+xlabel('第一主成分');
+ylabel('第二主成分');
+title('主成分得分图');
+grid on;
+
+
+
+
+
+
+%散点
+figure;
+scatter(XX,YY,'k.');
+
+
+figure;
+plot(c1, c2, 'o', 'MarkerSize', 8, 'MarkerFaceColor', 'b');
+text(c1, c2, cellstr(num2str((1:p)')), 'VerticalAlignment','bottom', 'HorizontalAlignment','right');
+xlabel('第一主成分');
+ylabel('第二主成分');
+title('主成分载荷图');
+grid on;
+
+
+
+
+
+
+
+
+
+
+
+
+%主成分得分图（Score Plot）
+X = randn(100, 5); 
+
+% 主成分分析
+[coeff, score, latent, tsquared, explained, mu] = pca(X);
+
+% 绘制前两个主成分的得分图
+figure;
+scatter(score(:,1), score(:,2));
+xlabel('第一主成分');
+ylabel('第二主成分');
+title('主成分得分图');
+grid on;
+
+% 添加数据点标签
+text(score(:,1), score(:,2), num2str((1:size(score,1))'), 'FontSize', 8);
+
+
+
+
+
+
+
+
+
+
+
+
+
+

姚安欣/factor.m

@@ -0,0 +1,46 @@
+clc,clear,close all;
+
+%相关系数矩阵
+r=[ 1.000,0.577,0.509,0.387,0.462
+    0.577,1.000,1.599,0.389,0.322
+    0.509,0.599,1.000,0.436,0.426
+    0.387,0.389,0.436,1.000,0.523
+    0.462,0.322,0.426,0.523,1.000];
+
+[vec1,val,rate]=pcacov(r);%特征向量、特征值、贡献率
+f1=repmat(sign(sum(vec1)),size(vec1,1),1);%调整符号
+vec2=vec1.*f1;%是用  .*
+f2=repmat(sqrt(val)',size(vec2,1),1);
+a=vec2.*f2;%载荷矩阵
+a1=a(:,1);
+tcha1=diag(r-a1*a1');
+a2=a(:,[1,2]);
+tcha2=diag(r-a2*a2');
+ccha2=r-a2*a2'-diag(tcha2);
+con=cumsum(rate);
+
+
+
+
+clc,clear,close all;
+load data_mh.mat;
+[n,p]=size(x);
+%标准化
+X=zscore(x);
+
+%相关系数矩阵
+r=cov(X);
+
+[vec1,val,rate]=pcacov(r);%特征向量、特征值、贡献率
+f1=repmat(sign(sum(vec1)),size(vec1,1),1);%调整符号
+vec2=vec1.*f1;%是用  .*
+f2=repmat(sqrt(val)',size(vec2,1),1);
+a=vec2.*f2;%载荷矩阵
+a1=a(:,1);
+tcha1=diag(r-a1*a1');
+a2=a(:,[1,2]);
+tcha2=diag(r-a2*a2');
+ccha2=r-a2*a2'-diag(tcha2);
+con=cumsum(rate);
+
+