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.

%

for i=1:size(X,1),

  for j=1:K,

    dis(j)=sum( (centroids(j,:)-X(i,:)).^2, 2 );

  endfor

  [t,idx(i)]=min(dis);

endfor

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

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.

%

for i=1:K,

  ALL=0;

  cnt=sum(idx==i);

  temp=find(idx==i);

  for j=1:numel(temp),

    ALL=ALL+X(temp(j),:);

  endfor

  centroids(i,:)=ALL/cnt;

endfor

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

end

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,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);

%

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.

%

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

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

end