Examples of matlab implementation of ICA, the program can be run directly

Just for the record, please skip it. For examples of python implementation, see the blogger’s article Portal

ICA is the deconvolution of the aliased signal

Code

clear;clc;close all;

% ts=0.005
% t=np.arange(0,1,ts)
% s1=np.sin(2*np.pi*10*t);s2=np.sin(2*np.pi*20*t);s2=np.array(20 * (5 * [2] + 5 * [-2]));a9mysubplot.mysubplot([s1,s2])
% s=0.5*s1+0.5*s2;a9myplot.myplot(s)

ts=0.005;
t=0:0.005:1;
s1=sin(2*pi*10*t);
s2=square(2*pi*20*t,50);
% plot(s2);
% figure(1);subplot(211);plot(s1);subplot(212);plot(s2);
subplot(3,2,1),plot(s1),title('输入信号1');
subplot(3,2,2),plot(s2),title('输入信号2');

S=[s1;s2]; 
% s=0.5*s1+0.5*s2;S=[s;s];
Sweight = rand(size(S,1)); 
MixedS=Sweight*S;     % 将混合矩阵重新排列并输出
subplot(3,2,3),plot(MixedS(1,:)),title('混合信号1');
subplot(3,2,4),plot(MixedS(2,:)),title('混合信号2');

MixedS_bak=MixedS;                  
%%%%%%%%%%%%%%%%%%%%%%%%%%  标准化  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MixedS_mean=zeros(2,1);
for i=1:2
    MixedS_mean(i)=mean(MixedS(i,:));
end                                        % 计算MixedS的均值

for i=1:2
    for j=1:size(MixedS,1)
        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);                      % 对信号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为白化后的信号矩阵
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
    i=1;maxIterationsNum=1000;               % 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 norm(b):向量元素平方和开根号
    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=t.*exp(-a2*t.^2/2);
        dg=(1-a2*t.^2).*exp(-a2*t.^2/2);
        b=((1-u)*t'*g*b+u*X*g)/SampleNum-mean(dg)*b;
                                           % 核心公式
        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
             B(:,r)=b;                     % 保存所得向量b
             break;
         end
        i=i+1;        
    end
end

for k=1:numofIC
    W(:,k)=B(:,k)/5^k;          % 得到解混矩阵W
end
%%%%%%%%%%%%%%%%%%%%%%%%%%  ICA计算的数据复原并构图  %%%%%%%%%%%%%%%%%%%%%%%%%
ICAedS=W'*Q*MixedS_bak;                     % 计算ICA后的矩阵

% 将混合矩阵重新排列并输出
subplot(3,2,5),plot(ICAedS(1,:)),title('ICA解混信号1');
subplot(3,2,6),plot(ICAedS(2,:)),title('ICA解混信号2');

effect

reference

Portal