二维数据的白化处理
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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. :)
%%================================================================
%% 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
1 0
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