新增域名网站建设方案,网站底部备案代码,万网网站加速,2018做网站还赚钱吗二维数据的白化处理 这篇博客实现起来比较简单#xff0c;首先先去下载pca_2d.zip#xff0c;然后打开pca_2d.m改代码#xff0c;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 matri…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 xRotu*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,:); xHatu*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