吴恩达机器学习 - PCA算法降维

原

吴恩达机器学习 - PCA算法降维

2018年06月25日 13:08:17 离殇灬孤狼 阅读数：152 更多

																				

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															吴恩达机器学习																
						
																							

版权声明：如果感觉写的不错，转载标明出处链接哦~blog.csdn.net/wyg1997 https://blog.csdn.net/wyg1997/article/details/80800514

题目链接：点击打开链接

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笔记：

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数据可视化：

求矩阵U和S（pca.m）：

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 = X'*X./m;
[U, S, ~] = svd(sigma);

% =========================================================================

end
   
   
   
   

    
    
    
    
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降维（projectData.m）：

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
   
   
   
   

    
    
    
    
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压缩重现（投影后的位置）（recoverData.m）：

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.
%               

X_rec = Z*U(:,1:K)';

% =============================================================

end
   
   
   
   

    
    
    
    
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效果图：

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然后是两个应用了

第一个是人脸数据的压缩，可以加速其它的学习算法

第二个是数据可视化，把一个3D的数据压缩到2D上看的更清楚

如图：

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