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### Coursera machine learning week 8 assignment answers

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). % % DIMENSIONS: % X = m x n Sigma = (1/m)*(X'*X); % n x n [U, S, V] = svd(Sigma); % ========================================================================= end

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); % % DIMENSIONS: % X = m x n % U = n x n % U_reduce = n x K % K = scalar U_reduce = U(:,[1:K]); % n x K Z = X * U_reduce; % m x k % ============================================================= 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. % % DIMENSIONS: % Z = m x K % U = n x n % U_reduce = n x k % K = scalar % X_rec = m x n U_reduce = U(:,1:K); % n x k X_rec = Z * U_reduce'; % m x n % ============================================================= end

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); % K x 1 == 3 x 1 % You need to return the following variables correctly. idx = zeros(size(X,1), 1); % m x 1 == 300 x 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. % % DIMENSIONS: % centroids = K x no. of features = 3 x 2 for i = 1:size(X,1) temp = zeros(K,1); for j = 1:K temp(j)=sqrt(sum((X(i,:)-centroids(j,:)).^2)); end [~,idx(i)] = min(temp); end % ============================================================= end

function centroids = computeCentroids(X, idx, K) %COMPUTECENTROIDS returns 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. % % DIMENSIONS: % X = m x n % centroids = K x n %% %%%%%% WORKING: SOLUTION1 %%%%%%%%% % for i = 1:K % idx_i = find(idx==i); %indexes of all the input which belongs to cluster j % centroids(i,:)=(1/length(idx_i))*sum(X(idx_i,:)); %calculating mean manually % end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %%%%%% WORKING: SOLUTION 2 %%%%%%%% for i = 1:K idx_i = find(idx==i); %indexes of all the input which belongs to cluster j centroids(i,:) = mean(X(idx_i,:)); % calculating mean using built-in function end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ============================================================= end

function centroids = kMeansInitCentroids(X, K) %KMEANSINITCENTROIDS This function initializes K centroids that are to be %used in K-Means on the dataset X % centroids = KMEANSINITCENTROIDS(X, K) returns K initial centroids to be % used with the K-Means on the dataset X % % You should return this values correctly centroids = zeros(K, size(X, 2)); % ====================== YOUR CODE HERE ====================== % Instructions: You should set centroids to randomly chosen examples from % the dataset X % % Randomly reorder the indices of examples randidx = randperm(size(X, 1)); % Take the first K examples as centroids centroids = X(randidx(1:K), :); % ============================================================= end

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