吴恩达机器学习第七次作业Part2： PCA主成分分析与K-means聚类算法
这是习题和答案的下载地址，全网最便宜，只要一积分哦~~~
https://download.csdn.net/download/wukongakk/10602657
0.综述
pac
1.Load Example Dataset
% We start this exercise by using a small dataset that is easily to
% visualize
%
fprintf('Visualizing example dataset for PCA.\n\n');
% The following command loads the dataset. You should now have the
% variable X in your environment
load ('ex7data1.mat');
% Visualize the example dataset
plot(X(:, 1), X(:, 2), 'bo');
axis([0.5 6.5 2 8]); axis square;
fprintf('Program paused. Press enter to continue.\n');
pause;
2.Principal Component Analysis
% You should now implement PCA, a dimension reduction technique. You
% should complete the code in pca.m
%
fprintf('\nRunning PCA on example dataset.\n\n');
% Before running PCA, it is important to first normalize X
[X_norm, mu, sigma] = featureNormalize(X);
% Run PCA
[U, S] = pca(X_norm);
% Compute mu, the mean of the each feature
% Draw the eigenvectors centered at mean of data. These lines show the
% directions of maximum variations in the dataset.
hold on;
drawLine(mu, mu + 1.5 * S(1,1) * U(:,1)', '-k', 'LineWidth', 2);
drawLine(mu, mu + 1.5 * S(2,2) * U(:,2)', '-k', 'LineWidth', 2);
hold off;
fprintf('Top eigenvector: \n');
fprintf(' U(:,1) = %f %f \n', U(1,1), U(2,1));
fprintf('\n(you should expect to see -0.707107 -0.707107)\n');
fprintf('Program paused. Press enter to continue.\n');
pause;
function [U, S] = pca(X)
%PCA Run principal component analysis on the dataset X
% [U, S, X] = pca(X) computes eigenvectors of the covariance matrix of X
% Returns the eigenvectors U, the eigenvalues (on diagonal) in S
%
% Useful values
[m, n] = size(X);
% You need to return the following variables correctly.
U = zeros(n);
S = zeros(n);
% ====================== YOUR CODE HERE ======================
% Instructions: You should first compute the covariance matrix. Then, you
% should use the "svd" function to compute the eigenvectors
% and eigenvalues of the covariance matrix.
%
% Note: When computing the covariance matrix, remember to divide by m (the
% number of examples).
%
Sigma = 1/m * X'* X;
[U, S, V] = svd(Sigma);
% =========================================================================
end
function [X_norm, mu, sigma] = featureNormalize(X)
%FEATURENORMALIZE Normalizes the features in X
% FEATURENORMALIZE(X) returns a normalized version of X where
% the mean value of each feature is 0 and the standard deviation
% is 1. This is often a good preprocessing step to do when
% working with learning algorithms.
mu = mean(X);
X_norm = bsxfun(@minus, X, mu);
sigma = std(X_norm);
%std为求标准偏差
X_norm = bsxfun(@rdivide, X_norm, sigma);
% ============================================================
end3.Dimension Reduction
在这个实例中，我们把二维数据变为一维。
% You should now implement the projection step to map the data onto the
% first k eigenvectors. The code will then plot the data in this reduced
% dimensional space. This will show you what the data looks like when
% using only the corresponding eigenvectors to reconstruct it.
%
% You should complete the code in projectData.m
%
fprintf('\nDimension reduction on example dataset.\n\n');
% Plot the normalized dataset (returned from pca)
plot(X_norm(:, 1), X_norm(:, 2), 'bo');
axis([-4 3 -4 3]); axis square
% Project the data onto K = 1 dimension
K = 1;
Z = projectData(X_norm, U, K);
fprintf('Projection of the first example: %f\n', Z(1));
fprintf('\n(this value should be about 1.481274)\n\n');
X_rec = recoverData(Z, U, K);
fprintf('Approximation of the first example: %f %f\n', X_rec(1, 1), X_rec(1, 2));
fprintf('\n(this value should be about -1.047419 -1.047419)\n\n');
% Draw lines connecting the projected points to the original points
hold on;
plot(X_rec(:, 1), X_rec(:, 2), 'ro');
for i = 1:size(X_norm, 1)
drawLine(X_norm(i,:), X_rec(i,:), '--k', 'LineWidth', 1);
end
hold off
fprintf('Program paused. Press enter to continue.\n');
pause;function Z = projectData(X, U, K)
%PROJECTDATA Computes the reduced data representation when projecting only
%on to the top k eigenvectors
% Z = projectData(X, U, K) computes the projection of
% the normalized inputs X into the reduced dimensional space spanned by
% the first K columns of U. It returns the projected examples in Z.
%
% You need to return the following variables correctly.
Z = zeros(size(X, 1), K);
% ====================== YOUR CODE HERE ======================
% Instructions: Compute the projection of the data using only the top K
% eigenvectors in U (first K columns).
% For the i-th example X(i,:), the projection on to the k-th
% eigenvector is given as follows:
% x = X(i, :)';
% projection_k = x' * U(:, k);
%
U_reduce = U(:, 1:K);
Z =X * U_reduce;
% =============================================================
end
function X_rec = recoverData(Z, U, K)
%RECOVERDATA Recovers an approximation of the original data when using the
%projected data
% X_rec = RECOVERDATA(Z, U, K) recovers an approximation the
% original data that has been reduced to K dimensions. It returns the
% approximate reconstruction in X_rec.
%
% You need to return the following variables correctly.
X_rec = zeros(size(Z, 1), size(U, 1));
% ====================== YOUR CODE HERE ======================
% Instructions: Compute the approximation of the data by projecting back
% onto the original space using the top K eigenvectors in U.
%
% For the i-th example Z(i,:), the (approximate)
% recovered data for dimension j is given as follows:
% v = Z(i, :)';
% recovered_j = v' * U(j, 1:K)';
%
% Notice that U(j, 1:K) is a row vector.
%
U_reduce = U(:, 1:K);
X_rec = Z * U_reduce';
% =============================================================
end
4.Loading and Visualizing Face Data
% We start the exercise by first loading and visualizing the dataset.
% The following code will load the dataset into your environment
%
fprintf('\nLoading face dataset.\n\n');
% Load Face dataset
load ('ex7faces.mat')
% Display the first 100 faces in the dataset
displayData(X(1:100, :));
fprintf('Program paused. Press enter to continue.\n');
pause;
5.PCA on Face Data: Eigenfaces
% Run PCA and visualize the eigenvectors which are in this case eigenfaces
% We display the first 36 eigenfaces.
%
fprintf(['\nRunning PCA on face dataset.\n' ...
'(this mght take a minute or two ...)\n\n']);
% Before running PCA, it is important to first normalize X by subtracting
% the mean value from each feature
[X_norm, mu, sigma] = featureNormalize(X);
% Run PCA
[U, S] = pca(X_norm);
% Visualize the top 36 eigenvectors found
displayData(U(:, 1:36)');
fprintf('Program paused. Press enter to continue.\n');
pause;
6.Dimension Reduction for Faces
% Project images to the eigen space using the top k eigenvectors
% If you are applying a machine learning algorithm
fprintf('\nDimension reduction for face dataset.\n\n');
K = 100;
Z = projectData(X_norm, U, K);
fprintf('The projected data Z has a size of: ')
fprintf('%d ', size(Z));
fprintf('\n\nProgram paused. Press enter to continue.\n');
pause;
7.Visualization of Faces after PCA Dimension Reduction
% Project images to the eigen space using the top K eigen vectors and
% visualize only using those K dimensions
% Compare to the original input, which is also displayed
fprintf('\nVisualizing the projected (reduced dimension) faces.\n\n');
K = 100;
X_rec = recoverData(Z, U, K);
% Display normalized data
subplot(1, 2, 1);
displayData(X_norm(1:100,:));
title('Original faces');
axis square;
% Display reconstructed data from only k eigenfaces
subplot(1, 2, 2);
displayData(X_rec(1:100,:));
title('Recovered faces');
axis square;
fprintf('Program paused. Press enter to continue.\n');
pause;