协方差分析.zip

% ********** 协方差矩阵的matlab理解 ********** % clc;clear all;close all; % ******一维数据的分析方法——方差 ******* sigma = 1; x = sigma .* (randn(100000,1)-1); figure(1) ksdensity(x); grid on; title('概率分布 \sigma = 1'); % ****** 一维数据的分布特性 ***** %———————————————————————————————————— % ******二维到N维数据的分析方法——方差 ******* % 构造一组二维数据： x = 5.*randn(1,1000); % 标准差为5 y = 1.*randn(1,1000); D = [x;y]; figure plot(D(1,:),D(2,:),'.'); hold on ksdensity(x); hold on ksdensity(y'); grid on; title('二维分布'); axis equal; % —————————————————————— % % ***** 多元正态分布与线性变换1 ***** N = 1000; x = 4.*randn(1,N); y = 1.*randn(1,N); D = [x;y]; new_D = rotate_2D(45)*D; %旋转角度45度 figure plot(new_D(1,:),new_D(2,:),'.'); grid on; axis equal; % ***** 多元正态分布与线性变换2 ***** N = 1000; x = 1.*randn(1,N); y = 1.*randn(1,N); D = [x;y]; T = rotate_2D(45)*[4 0;0 1]; %T=R*S new_D = T*D; figure plot(new_D(1,:),new_D(2,:),'.'); grid on; axis equal % —————————————————————— % N = 1000; x = 1.*randn(1,N); y = 1.*randn(1,N); D = [x;y]; T = rotate_2D(45)*[4 0;0 1]; new_D = T*D; Rxx = new_D*new_D'./(N-1); [V,D] = eig(Rxx); %矩阵特征值分解 figure plot(new_D(1,:),new_D(2,:),'.'); grid on; axis equal; hold on; quiver(0,0,V(1,1).*sqrt(D(1,1)),V(2,1).*sqrt(D(1,1)),'LineWidth',3) quiver(0,0,V(1,2)*sqrt(D(2,2)),V(2,2)*sqrt(D(2,2)),'LineWidth',3) legend('数据分布','特征向量1','特征向量2')