二維數據的白化處理

這篇博客實現起來比較簡單，首先先去下載pca_2d.zip，然后打開pca_2d.m改代碼，具體代碼見下面 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.
%從txt文件里面加載數據，并畫出原始數據散點圖
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 --------------------?
%計算出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，去除第二維向量
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白化處理,使用epsilon是為了正則化
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處理，使得結果更接近原始數據
% -------------------- 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. :)
最終你會看到6張圖片

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