ICA-face-recognition.rar_ICA_ICA face recognition_face matlab_ic

%%%%%%%%%%%%%%%%%%%%%%%%%% 初始化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc;clear all;close all; %%%%%%%%%%%%%% 读入原始图像，混合，并输出混合图像 %%%%%%%%%%%%%%%%%% % 读入混合前的原始图片并显示 t=0:1/100:9; I1=sin(t); I2=randn(1,901); I3=square(4*t); subplot(4,3,1),plot(I1),title('输入信号1'), subplot(4,3,2),plot(I2),title('输入信号2'), subplot(4,3,3),plot(I3),title('输入信号3'), % 将其组成矩阵 S=[I1;I2;I3]; % 图片个数即为变量数，图片的像素数即为采样数 % 因此S_all是一个变量个数＊采样个数的矩阵 Sweight=randn(size(S,1)); % 取一随机矩阵，作为信号混合的权矩阵 MixedS=Sweight*S; % 得到三个混合信号矩阵 % 将混合矩阵重新排列并输出 subplot(4,3,4),plot(MixedS(1,:)),title('混合信号1'), subplot(4,3,5),plot(MixedS(2,:)),title('混合信号2'), subplot(4,3,6),plot(MixedS(3,:)),title('混合信号3'), MixedS_bak=MixedS; % 将混合后的数据备份，以便在恢复时直接调用 %%%%%%%%%%%%%%%%%%%%%%%%%% 标准化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MixedS_mean=zeros(3,1); for i=1:3 MixedS_mean(i)=mean(MixedS(i,:)); end % 计算MixedS的均值 for i=1:3 for j=1:size(MixedS,2) MixedS(i,j)=MixedS(i,j)-MixedS_mean(i); end end %%%%%%%%%%%%%%%%%%%%%%%%%%% 白化 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MixedS_cov=cov(MixedS'); % cov为求协方差的函数 [E,D]=eig(MixedS_cov); % 对图片矩阵的协方差函数进行特征值分解 Q=inv(sqrt(D))*(E)'; % Q为白化矩阵 MixedS_white=Q*MixedS; % MixedS_white为白化后的图片矩阵 IsI=cov(MixedS_white'); % IsI应为单位阵 %%%%%%%%%%%%%%%%%%%%%%%%　FASTICA算法 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% X=MixedS_white; % 以下算法将对X进行操作 [VariableNum,SampleNum]=size(X); numofIC=VariableNum; % 在此应用中，独立元个数等于变量个数 B=zeros(numofIC,VariableNum); % 初始化列向量w的寄存矩阵,B=[b1 b2 ... bd] for r=1:numofIC % 迭代求取每一个独立元 i=1;maxIterationsNum=100; % 设置最大迭代次数（即对于每个独立分量而言迭代均不超过此次数） IterationsNum=0; b=rand(numofIC,1)-.5; % 随机设置b初值 b=b/norm(b); % 对b标准化 while i<=maxIterationsNum+1 if i == maxIterationsNum % 循环结束处理 fprintf('\n第%d分量在%d次迭代内并不收敛。', r,maxIterationsNum); break; end bOld=b; a2=1; u=1; t=X'*b; g=(exp(2.*t)-1)./(exp(2.*t)+1); dg=4*exp(2.*t)./(exp(2.*t)+1).^2; b=((1-u)*t'*g*b+u*X*g)/SampleNum-mean(dg)*b; % 核心公式，参见理论部分公式2.52 b=b-B*B'*b; % 对b正交化 b=b/norm(b); if abs(abs(b'*bOld)-1)<1e-9 % 如果收敛，则保存b B(:,r)=b; break; end i=i+1; end end %%%%%%%%%%%%%%%%%%%%%%%%% 数据复原并构图 %%%%%%%%%%%%%%%%%%%%%%%% ICAedS=B'*Q*MixedS_bak; % 参见理论部分公式2.55 % 将混合矩阵重新排列并输出 subplot(4,3,7),plot(ICAedS(1,:)),title('ICA输出信号1'), subplot(4,3,8),plot(ICAedS(2,:)),title('ICA输出信号2'), subplot(4,3,9),plot(ICAedS(3,:)),title('ICA输出信号3'), %%%%%%%%%%%%%%%%%%%%%%%%% PCA计算并构图 %%%%%%%%%%%%%%%%%%%%%%%% [V,D]=eig(MixedS_cov); Vtmp=zeros(size(V,1),1); for j=1:2 for i=1:2 if D(i,i)