二维数据的白化处理

这篇博客实现起来比较简单，首先先去下载pca_2d.zip，然后打开pca_2d.m改代码，具体代码见下面

close all


%%================================================================
%% Step 0: Load data
%  We have provided the code to load data from pcaData.txt into x.
%  x is a 2 * 45 matrix, where the kth column x(:,k) corresponds to
%  the kth data point.Here we provide the code to load natural image data into x.
%  You do not need to change the code below.
%从txt文件里面加载数据，并画出原始数据散点图
x = load('pcaData.txt','-ascii');
figure(1);
scatter(x(1, :), x(2, :));
title('Raw data');




%%================================================================
%% Step 1a: Implement PCA to obtain U 
%  Implement PCA to obtain the rotation matrix U, which is the eigenbasis
%  sigma. 


% -------------------- YOUR CODE HERE -------------------- 
%得到特征向量,u是特征向量,s是特征值,v是u'
u = zeros(size(x, 1)); % You need to compute this
[u,s,v]=svd(x);


% -------------------------------------------------------- 
hold on
plot([0 u(1,1)], [0 u(2,1)]);
plot([0 u(1,2)], [0 u(2,2)]);
scatter(x(1, :), x(2, :));
hold off


%%================================================================
%% Step 1b: Compute xRot, the projection on to the eigenbasis
%  Now, compute xRot by projecting the data on to the basis defined
%  by U. Visualize the points by performing a scatter plot.


% -------------------- YOUR CODE HERE -------------------- 
%计算出xRot
xRot = zeros(size(x)); % You need to compute this
xRot=u'*x;




% -------------------------------------------------------- 


% Visualise the covariance matrix. You should see a line across the
% diagonal against a blue background.
figure(2);
scatter(xRot(1, :), xRot(2, :));
title('xRot');


%%================================================================
%% Step 2: Reduce the number of dimensions from 2 to 1. 
%  Compute xRot again (this time projecting to 1 dimension).
%  Then, compute xHat by projecting the xRot back onto the original axes 
%  to see the effect of dimension reduction


% -------------------- YOUR CODE HERE -------------------- 
%得到xHat，去除第二维向量
k = 1; % Use k = 1 and project the data onto the first eigenbasis
xHat = zeros(size(x)); % You need to compute this
xHat(1:k,:)=xRot(1:k,:);
xHat=u*xHat;




% -------------------------------------------------------- 
figure(3);
scatter(xHat(1, :), xHat(2, :));
title('xHat');




%%================================================================
%% Step 3: PCA Whitening
%  Complute xPCAWhite and plot the results.
%PCA白化处理,使用epsilon是为了正则化
epsilon = 1e-5;
% -------------------- YOUR CODE HERE -------------------- 
xPCAWhite = zeros(size(x)); % You need to compute this
xPCAWhite = diag(1./sqrt(diag(s)+epsilon))*xRot;






% -------------------------------------------------------- 
figure(4);
scatter(xPCAWhite(1, :), xPCAWhite(2, :));
title('xPCAWhite');


%%================================================================
%% Step 3: ZCA Whitening
%  Complute xZCAWhite and plot the results.
%ZCA处理，使得结果更接近原始数据
% -------------------- YOUR CODE HERE -------------------- 
xZCAWhite = zeros(size(x)); % You need to compute this
xZCAWhite = u*xPCAWhite;


% -------------------------------------------------------- 
figure(5);
scatter(xZCAWhite(1, :), xZCAWhite(2, :));
title('xZCAWhite');


%% Congratulations! When you have reached this point, you are done!
%  You can now move onto the next PCA exercise. :)

最终你会看到6张图片