Programming Exercise 7: K-means Clustering and Principal Component Analysis Machine Learning
2016-12-27 22:19
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大家好,今天总结Coursera网课上Andrew Ng MachineLearning 第七次作业
(1)findClosestCentroids.m
(2) computeCentroids.m
(3) pca.m
(4) projectData.m
(5)recoverData.m
(1)findClosestCentroids.m
function idx = findClosestCentroids(X, centroids) %FINDCLOSESTCENTROIDS computes the centroid memberships for every example % idx = FINDCLOSESTCENTROIDS (X, centroids) returns the closest centroids % in idx for a dataset X where each row is a single example. idx = m x 1 % vector of centroid assignments (i.e. each entry in range [1..K]) % % Set K K = size(centroids, 1); % You need to return the following variables correctly. idx = zeros(size(X,1), 1); % ====================== YOUR CODE HERE ====================== % Instructions: Go over every example, find its closest centroid, and store % the index inside idx at the appropriate location. % Concretely, idx(i) should contain the index of the centroid % closest to example i. Hence, it should be a value in the % range 1..K % % Note: You can use a for-loop over the examples to compute this. % m=size(X,1); for i=1:m idx_K=zeros(K,1); for j=1:K idx_K(j)=sqrt(sum(( X(i,:)-centroids(j,:)).^2))^2; end [value index]=min(idx_K); idx(i,1)=index; end % ============================================================= end
(2) computeCentroids.m
function centroids = computeCentroids(X, idx, K) %COMPUTECENTROIDS returs the new centroids by computing the means of the %data points assigned to each centroid. % centroids = COMPUTECENTROIDS(X, idx, K) returns the new centroids by % computing the means of the data points assigned to each centroid. It is % given a dataset X where each row is a single data point, a vector % idx of centroid assignments (i.e. each entry in range [1..K]) for each % example, and K, the number of centroids. You should return a matrix % centroids, where each row of centroids is the mean of the data points % assigned to it. % % Useful variables [m n] = size(X); % You need to return the following variables correctly. centroids = zeros(K, n); % ====================== YOUR CODE HERE ====================== % Instructions: Go over every centroid and compute mean of all points that % belong to it. Concretely, the row vector centroids(i, :) % should contain the mean of the data points assigned to % centroid i. % % Note: You can use a for-loop over the centroids to compute this. % for i=1:K centroids(i,:)=((idx==i)'*X)/sum(idx==i); end % ============================================================= end
(3) 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=1/m*X'*X; [U, S, V] = svd(Sigma); % ========================================================================= end
(4) 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 c a7b2 olumns). % 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); % Ureduce=U(:,1:K); Z=X*Ureduce; % ============================================================= end
(5)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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