Coursera machine learning week 8 assignment answers – Andrew Ng

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