deep learning之PCA in 2D matlab 实现

PCA data

  -6.7644914e-01  -6.3089308e-01  -4.8915202e-01  -4.8005424e-01  -3.7842021e-01  -3.3788391e-01  -3.2023528e-01  -3.1108837e-01  -2.3145555e-01  -1.9623727e-01  -1.5678926e-01  -1.4900779e-01  -1.0861557e-01  -1.0506308e-01  -8.0899829e-02  -7.1157518e-02  -6.3251073e-02  -2.6007219e-02  -2.2553443e-02  -5.8489047e-03  -4.3935323e-03  -1.7309716e-03   7.8223728e-03   7.5386969e-02   8.6608396e-02   9.6406046e-02   1.0331683e-01   1.0531131e-01   1.1493296e-01   1.3052813e-01   1.6626253e-01   1.7901863e-01   1.9267343e-01   1.9414427e-01   1.9770003e-01   2.3043613e-01   3.2715844e-01   3.2737163e-01   3.2922364e-01   3.4869293e-01   3.7500704e-01   4.2830153e-01   4.5432503e-01   5.4422436e-01   6.6539963e-01
  -4.4722050e-01  -7.4778067e-01  -3.9074344e-01  -5.6036362e-01  -3.4291940e-01  -1.3832158e-01   1.2360939e-01  -3.3934986e-01  -8.2868433e-02  -2.4759514e-01  -1.0914760e-01   4.2243921e-01  -5.2329327e-02  -2.0126541e-01   1.3016657e-01   1.2293321e-01  -3.4787750e-01  -1.4584897e-01  -1.0559656e-01  -5.4200847e-02   1.6915422e-02  -1.1069762e-01   9.0859816e-02   1.5269096e-01  -9.4416463e-02   1.5116385e-01  -1.3540126e-01   2.4592698e-01   5.1087447e-02   2.4583340e-01  -5.9535372e-02   2.9704742e-01   1.0168115e-01   1.4258649e-01   1.0662592e-01   3.1698532e-01   6.1577841e-01   4.3911172e-01   2.7156501e-01   1.3572389e-01   3.1918066e-01   1.5122962e-01   3.4979047e-01   6.2316971e-01   5.2018811e-01

也可以在深度学习的官网上下载。

matlab实现代码如下:

clc;clear all;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.% MK=importdata('CNS.txt');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 -------------------- u = zeros(size(x, 1)); % You need to compute this    每一列就代表一个特征，2*45  就代表有2个特征avg=mean(x,2);x=x-repmat(avg,1,size(x,2));%均值化sigma=x*x'/size(x,2);[U,S,V]=svd(sigma);u=U;% -------------------------------------------------------- hold onplot([0 u(1,1)], [0 u(2,1)]);plot([0 u(1,2)], [0 u(2,2)]);scatter(x(1, :), x(2, :));%plot(x(1, :), x(2, :),'o');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 -------------------- xRot = zeros(size(x)); % You need to compute thisxRot=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 -------------------- k = 1; % Use k = 1 and project the data onto the first eigenbasisxHat = zeros(size(x)); % You need to compute thisxHat=U*[U(:,1:k),zeros(size(U,1),size(U,2)-k)]'*x;% xHat = u*([u(:,1),zeros(size(x,1),1)]'*x);% -------------------------------------------------------- figure(3);scatter(xHat(1, :), xHat(2, :));title('xHat');%%================================================================%% Step 3: PCA Whitening%  Complute xPCAWhite and plot the results.epsilon = 1e-5;% -------------------- YOUR CODE HERE -------------------- xPCAWhite = zeros(size(x)); % You need to compute thisxPCAWhite=diag(1./sqrt(diag(S)+epsilon))*U'*x;% -------------------------------------------------------- figure(4);scatter(xPCAWhite(1, :), xPCAWhite(2, :));title('xPCAWhite');%%================================================================%% Step 3: ZCA Whitening%  Complute xZCAWhite and plot the results.% -------------------- YOUR CODE HERE -------------------- xZCAWhite = zeros(size(x)); % You need to compute thisxZCAWhite = U*xPCAWhite;%xZCAWhite = U*diag(1./sqrt(diag(S)+epsilon))*U'*x;% -------------------------------------------------------- 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. :)