First Commit

computeCentroids.m

+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.
+%
+count = zeros(K,1);
+for i = 1:m,
+   centroids(idx(i,1),:) = centroids(idx(i,1),:) + X(i,:);
+   count(idx(i,1),1)++;
+end;
+
+for i = 1:K,
+   centroids(i,:) = centroids(i,:)/count(i,1);
+end;
+   
+
+
+
+
+
+% =============================================================
+
+
+end
+

displayData.m

+function [h, display_array] = displayData(X, example_width)
+%DISPLAYDATA Display 2D data in a nice grid
+%   [h, display_array] = DISPLAYDATA(X, example_width) displays 2D data
+%   stored in X in a nice grid. It returns the figure handle h and the 
+%   displayed array if requested.
+
+% Set example_width automatically if not passed in
+if ~exist('example_width', 'var') || isempty(example_width) 
+	example_width = round(sqrt(size(X, 2)));
+end
+
+% Gray Image
+colormap(gray);
+
+% Compute rows, cols
+[m n] = size(X);
+example_height = (n / example_width);
+
+% Compute number of items to display
+display_rows = floor(sqrt(m));
+display_cols = ceil(m / display_rows);
+
+% Between images padding
+pad = 1;
+
+% Setup blank display
+display_array = - ones(pad + display_rows * (example_height + pad), ...
+                       pad + display_cols * (example_width + pad));
+
+% Copy each example into a patch on the display array
+curr_ex = 1;
+for j = 1:display_rows
+	for i = 1:display_cols
+		if curr_ex > m, 
+			break; 
+		end
+		% Copy the patch
+		
+		% Get the max value of the patch
+		max_val = max(abs(X(curr_ex, :)));
+		display_array(pad + (j - 1) * (example_height + pad) + (1:example_height), ...
+		              pad + (i - 1) * (example_width + pad) + (1:example_width)) = ...
+						reshape(X(curr_ex, :), example_height, example_width) / max_val;
+		curr_ex = curr_ex + 1;
+	end
+	if curr_ex > m, 
+		break; 
+	end
+end
+
+% Display Image
+h = imagesc(display_array, [-1 1]);
+
+% Do not show axis
+axis image off
+
+drawnow;
+
+end

drawLine.m

+function drawLine(p1, p2, varargin)
+%DRAWLINE Draws a line from point p1 to point p2
+%   DRAWLINE(p1, p2) Draws a line from point p1 to point p2 and holds the
+%   current figure
+
+plot([p1(1) p2(1)], [p1(2) p2(2)], varargin{:});
+
+end
\ No newline at end of file

ex7.m

+%% Machine Learning Online Class
+%  Exercise 7 | Principle Component Analysis and K-Means Clustering
+%
+%  Instructions
+%  ------------
+%
+%  This file contains code that helps you get started on the
+%  exercise. You will need to complete the following functions:
+%
+%     pca.m
+%     projectData.m
+%     recoverData.m
+%     computeCentroids.m
+%     findClosestCentroids.m
+%     kMeansInitCentroids.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% ================= Part 1: Find Closest Centroids ====================
+%  To help you implement K-Means, we have divided the learning algorithm 
+%  into two functions -- findClosestCentroids and computeCentroids. In this
+%  part, you should complete the code in the findClosestCentroids function. 
+%
+fprintf('Finding closest centroids.\n\n');
+
+% Load an example dataset that we will be using
+load('ex7data2.mat');
+
+% Select an initial set of centroids
+K = 3; % 3 Centroids
+initial_centroids = [3 3; 6 2; 8 5];
+
+% Find the closest centroids for the examples using the
+% initial_centroids
+idx = findClosestCentroids(X, initial_centroids);
+
+fprintf('Closest centroids for the first 3 examples: \n')
+fprintf(' %d', idx(1:3));
+fprintf('\n(the closest centroids should be 1, 3, 2 respectively)\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% ===================== Part 2: Compute Means =========================
+%  After implementing the closest centroids function, you should now
+%  complete the computeCentroids function.
+%
+fprintf('\nComputing centroids means.\n\n');
+
+%  Compute means based on the closest centroids found in the previous part.
+centroids = computeCentroids(X, idx, K);
+
+fprintf('Centroids computed after initial finding of closest centroids: \n')
+fprintf(' %f %f \n' , centroids');
+fprintf('\n(the centroids should be\n');
+fprintf('   [ 2.428301 3.157924 ]\n');
+fprintf('   [ 5.813503 2.633656 ]\n');
+fprintf('   [ 7.119387 3.616684 ]\n\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% =================== Part 3: K-Means Clustering ======================
+%  After you have completed the two functions computeCentroids and
+%  findClosestCentroids, you have all the necessary pieces to run the
+%  kMeans algorithm. In this part, you will run the K-Means algorithm on
+%  the example dataset we have provided. 
+%
+fprintf('\nRunning K-Means clustering on example dataset.\n\n');
+
+% Load an example dataset
+load('ex7data2.mat');
+
+% Settings for running K-Means
+K = 3;
+max_iters = 10;
+
+% For consistency, here we set centroids to specific values
+% but in practice you want to generate them automatically, such as by
+% settings them to be random examples (as can be seen in
+% kMeansInitCentroids).
+initial_centroids = [3 3; 6 2; 8 5];
+
+% Run K-Means algorithm. The 'true' at the end tells our function to plot
+% the progress of K-Means
+[centroids, idx] = runkMeans(X, initial_centroids, max_iters, true);
+fprintf('\nK-Means Done.\n\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% ============= Part 4: K-Means Clustering on Pixels ===============
+%  In this exercise, you will use K-Means to compress an image. To do this,
+%  you will first run K-Means on the colors of the pixels in the image and
+%  then you will map each pixel onto its closest centroid.
+%  
+%  You should now complete the code in kMeansInitCentroids.m
+%
+
+fprintf('\nRunning K-Means clustering on pixels from an image.\n\n');
+
+%  Load an image of a bird
+A = double(imread('bird_small.png'));
+
+% If imread does not work for you, you can try instead
+%   load ('bird_small.mat');
+
+A = A / 255; % Divide by 255 so that all values are in the range 0 - 1
+
+% Size of the image
+img_size = size(A);
+
+% Reshape the image into an Nx3 matrix where N = number of pixels.
+% Each row will contain the Red, Green and Blue pixel values
+% This gives us our dataset matrix X that we will use K-Means on.
+X = reshape(A, img_size(1) * img_size(2), 3);
+
+% Run your K-Means algorithm on this data
+% You should try different values of K and max_iters here
+K = 16; 
+max_iters = 10;
+
+% When using K-Means, it is important the initialize the centroids
+% randomly. 
+% You should complete the code in kMeansInitCentroids.m before proceeding
+initial_centroids = kMeansInitCentroids(X, K);
+
+% Run K-Means
+[centroids, idx] = runkMeans(X, initial_centroids, max_iters);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================= Part 5: Image Compression ======================
+%  In this part of the exercise, you will use the clusters of K-Means to
+%  compress an image. To do this, we first find the closest clusters for
+%  each example. After that, we 
+
+fprintf('\nApplying K-Means to compress an image.\n\n');
+
+% Find closest cluster members
+idx = findClosestCentroids(X, centroids);
+
+% Essentially, now we have represented the image X as in terms of the
+% indices in idx. 
+
+% We can now recover the image from the indices (idx) by mapping each pixel
+% (specified by its index in idx) to the centroid value
+X_recovered = centroids(idx,:);
+
+% Reshape the recovered image into proper dimensions
+X_recovered = reshape(X_recovered, img_size(1), img_size(2), 3);
+
+% Display the original image 
+subplot(1, 2, 1);
+imagesc(A); 
+title('Original');
+
+% Display compressed image side by side
+subplot(1, 2, 2);
+imagesc(X_recovered)
+title(sprintf('Compressed, with %d colors.', K));
+
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+

ex7_pca.m

+%% Machine Learning Online Class
+%  Exercise 7 | Principle Component Analysis and K-Means Clustering
+%
+%  Instructions
+%  ------------
+%
+%  This file contains code that helps you get started on the
+%  exercise. You will need to complete the following functions:
+%
+%     pca.m
+%     projectData.m
+%     recoverData.m
+%     computeCentroids.m
+%     findClosestCentroids.m
+%     kMeansInitCentroids.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% ================== Part 1: Load Example Dataset  ===================
+%  We start this exercise by using a small dataset that is easily to
+%  visualize
+%
+fprintf('Visualizing example dataset for PCA.\n\n');
+
+%  The following command loads the dataset. You should now have the 
+%  variable X in your environment
+load ('ex7data1.mat');
+
+%  Visualize the example dataset
+plot(X(:, 1), X(:, 2), 'bo');
+axis([0.5 6.5 2 8]); axis square;
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% =============== Part 2: Principal Component Analysis ===============
+%  You should now implement PCA, a dimension reduction technique. You
+%  should complete the code in pca.m
+%
+fprintf('\nRunning PCA on example dataset.\n\n');
+
+%  Before running PCA, it is important to first normalize X
+[X_norm, mu, sigma] = featureNormalize(X);
+
+%  Run PCA
+[U, S] = pca(X_norm);
+
+%  Compute mu, the mean of the each feature
+
+%  Draw the eigenvectors centered at mean of data. These lines show the
+%  directions of maximum variations in the dataset.
+hold on;
+drawLine(mu, mu + 1.5 * S(1,1) * U(:,1)', '-k', 'LineWidth', 2);
+drawLine(mu, mu + 1.5 * S(2,2) * U(:,2)', '-k', 'LineWidth', 2);
+hold off;
+
+fprintf('Top eigenvector: \n');
+fprintf(' U(:,1) = %f %f \n', U(1,1), U(2,1));
+fprintf('\n(you should expect to see -0.707107 -0.707107)\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% =================== Part 3: Dimension Reduction ===================
+%  You should now implement the projection step to map the data onto the 
+%  first k eigenvectors. The code will then plot the data in this reduced 
+%  dimensional space.  This will show you what the data looks like when 
+%  using only the corresponding eigenvectors to reconstruct it.
+%
+%  You should complete the code in projectData.m
+%
+fprintf('\nDimension reduction on example dataset.\n\n');
+
+%  Plot the normalized dataset (returned from pca)
+plot(X_norm(:, 1), X_norm(:, 2), 'bo');
+axis([-4 3 -4 3]); axis square
+
+%  Project the data onto K = 1 dimension
+K = 1;
+Z = projectData(X_norm, U, K);
+fprintf('Projection of the first example: %f\n', Z(1));
+fprintf('\n(this value should be about 1.481274)\n\n');
+
+X_rec  = recoverData(Z, U, K);
+fprintf('Approximation of the first example: %f %f\n', X_rec(1, 1), X_rec(1, 2));
+fprintf('\n(this value should be about  -1.047419 -1.047419)\n\n');
+
+%  Draw lines connecting the projected points to the original points
+hold on;
+plot(X_rec(:, 1), X_rec(:, 2), 'ro');
+for i = 1:size(X_norm, 1)
+    drawLine(X_norm(i,:), X_rec(i,:), '--k', 'LineWidth', 1);
+end
+hold off
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% =============== Part 4: Loading and Visualizing Face Data =============
+%  We start the exercise by first loading and visualizing the dataset.
+%  The following code will load the dataset into your environment
+%
+fprintf('\nLoading face dataset.\n\n');
+
+%  Load Face dataset
+load ('ex7faces.mat')
+
+%  Display the first 100 faces in the dataset
+displayData(X(1:100, :));
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% =========== Part 5: PCA on Face Data: Eigenfaces  ===================
+%  Run PCA and visualize the eigenvectors which are in this case eigenfaces
+%  We display the first 36 eigenfaces.
+%
+fprintf(['\nRunning PCA on face dataset.\n' ...
+         '(this might take a minute or two ...)\n\n']);
+
+%  Before running PCA, it is important to first normalize X by subtracting 
+%  the mean value from each feature
+[X_norm, mu, sigma] = featureNormalize(X);
+
+%  Run PCA
+[U, S] = pca(X_norm);
+
+%  Visualize the top 36 eigenvectors found
+displayData(U(:, 1:36)');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ============= Part 6: Dimension Reduction for Faces =================
+%  Project images to the eigen space using the top k eigenvectors 
+%  If you are applying a machine learning algorithm 
+fprintf('\nDimension reduction for face dataset.\n\n');
+
+K = 100;
+Z = projectData(X_norm, U, K);
+
+fprintf('The projected data Z has a size of: ')
+fprintf('%d ', size(Z));
+
+fprintf('\n\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ==== Part 7: Visualization of Faces after PCA Dimension Reduction ====
+%  Project images to the eigen space using the top K eigen vectors and 
+%  visualize only using those K dimensions
+%  Compare to the original input, which is also displayed
+
+fprintf('\nVisualizing the projected (reduced dimension) faces.\n\n');
+
+K = 100;
+X_rec  = recoverData(Z, U, K);
+
+% Display normalized data
+subplot(1, 2, 1);
+displayData(X_norm(1:100,:));
+title('Original faces');
+axis square;
+
+% Display reconstructed data from only k eigenfaces
+subplot(1, 2, 2);
+displayData(X_rec(1:100,:));
+title('Recovered faces');
+axis square;
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% === Part 8(a): Optional (ungraded) Exercise: PCA for Visualization ===
+%  One useful application of PCA is to use it to visualize high-dimensional
+%  data. In the last K-Means exercise you ran K-Means on 3-dimensional 
+%  pixel colors of an image. We first visualize this output in 3D, and then
+%  apply PCA to obtain a visualization in 2D.
+
+close all; close all; clc
+
+% Reload the image from the previous exercise and run K-Means on it
+% For this to work, you need to complete the K-Means assignment first
+A = double(imread('bird_small.png'));
+
+% If imread does not work for you, you can try instead
+%   load ('bird_small.mat');
+
+A = A / 255;
+img_size = size(A);
+X = reshape(A, img_size(1) * img_size(2), 3);
+K = 16; 
+max_iters = 10;
+initial_centroids = kMeansInitCentroids(X, K);
+[centroids, idx] = runkMeans(X, initial_centroids, max_iters);
+
+%  Sample 1000 random indexes (since working with all the data is
+%  too expensive. If you have a fast computer, you may increase this.
+sel = floor(rand(1000, 1) * size(X, 1)) + 1;
+
+%  Setup Color Palette
+palette = hsv(K);
+colors = palette(idx(sel), :);
+
+%  Visualize the data and centroid memberships in 3D
+figure;
+scatter3(X(sel, 1), X(sel, 2), X(sel, 3), 10, colors);
+title('Pixel dataset plotted in 3D. Color shows centroid memberships');
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% === Part 8(b): Optional (ungraded) Exercise: PCA for Visualization ===
+% Use PCA to project this cloud to 2D for visualization
+
+% Subtract the mean to use PCA
+[X_norm, mu, sigma] = featureNormalize(X);
+
+% PCA and project the data to 2D
+[U, S] = pca(X_norm);
+Z = projectData(X_norm, U, 2);
+
+% Plot in 2D
+figure;
+plotDataPoints(Z(sel, :), idx(sel), K);
+title('Pixel dataset plotted in 2D, using PCA for dimensionality reduction');
+fprintf('Program paused. Press enter to continue.\n');
+pause;

featureNormalize.m

+function [X_norm, mu, sigma] = featureNormalize(X)
+%FEATURENORMALIZE Normalizes the features in X 
+%   FEATURENORMALIZE(X) returns a normalized version of X where
+%   the mean value of each feature is 0 and the standard deviation
+%   is 1. This is often a good preprocessing step to do when
+%   working with learning algorithms.
+
+mu = mean(X);
+X_norm = bsxfun(@minus, X, mu);
+
+sigma = std(X_norm);
+X_norm = bsxfun(@rdivide, X_norm, sigma);
+
+
+% ============================================================
+
+end

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.
+%
+
+for i = 1:size(X,1),
+   [a idx(i)] = min(sum(((X(i,:) - centroids).*(X(i,:) - centroids)),2));
+end;   
+
+
+
+
+
+% =============================================================
+
+end
+

kMeansInitCentroids.m

+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
+%
+
+randidx = randperm(size(X, 1));
+% Take the first K examples as centroids
+centroids = X(randidx(1:K), :);
+
+
+
+
+
+
+% =============================================================
+
+end
+

lib/jsonlab/AUTHORS.txt

+The author of "jsonlab" toolbox is Qianqian Fang. Qianqian
+is currently an Assistant Professor at Massachusetts General Hospital, 
+Harvard Medical School.
+
+Address: Martinos Center for Biomedical Imaging, 
+         Massachusetts General Hospital, 
+         Harvard Medical School
+         Bldg 149, 13th St, Charlestown, MA 02129, USA
+URL: http://nmr.mgh.harvard.edu/~fangq/
+Email: <fangq at nmr.mgh.harvard.edu> or <fangqq at gmail.com>
+
+
+The script loadjson.m was built upon previous works by
+
+- Nedialko Krouchev: http://www.mathworks.com/matlabcentral/fileexchange/25713
+       date: 2009/11/02
+- François Glineur: http://www.mathworks.com/matlabcentral/fileexchange/23393
+       date: 2009/03/22
+- Joel Feenstra: http://www.mathworks.com/matlabcentral/fileexchange/20565
+       date: 2008/07/03
+
+
+This toolbox contains patches submitted by the following contributors:
+
+- Blake Johnson <bjohnso at bbn.com>
+  part of revision 341
+
+- Niclas Borlin <Niclas.Borlin at cs.umu.se>
+  various fixes in revision 394, including
+  - loadjson crashes for all-zero sparse matrix.
+  - loadjson crashes for empty sparse matrix.
+  - Non-zero size of 0-by-N and N-by-0 empty matrices is lost after savejson/loadjson.
+  - loadjson crashes for sparse real column vector.
+  - loadjson crashes for sparse complex column vector.
+  - Data is corrupted by savejson for sparse real row vector.
+  - savejson crashes for sparse complex row vector. 
+
+- Yul Kang <yul.kang.on at gmail.com>
+  patches for svn revision 415.
+  - savejson saves an empty cell array as [] instead of null
+  - loadjson differentiates an empty struct from an empty array

lib/jsonlab/ChangeLog.txt

+============================================================================
+
+   JSONlab - a toolbox to encode/decode JSON/UBJSON files in MATLAB/Octave
+
+----------------------------------------------------------------------------
+
+JSONlab ChangeLog (key features marked by *):
+
+== JSONlab 1.0 (codename: Optimus - Final), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2015/01/02 polish help info for all major functions, update examples, finalize 1.0
+ 2014/12/19 fix a bug to strictly respect NoRowBracket in savejson
+
+== JSONlab 1.0.0-RC2 (codename: Optimus - RC2), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2014/11/22 show progress bar in loadjson ('ShowProgress') 
+ 2014/11/17 add Compact option in savejson to output compact JSON format ('Compact')
+ 2014/11/17 add FastArrayParser in loadjson to specify fast parser applicable levels
+ 2014/09/18 start official github mirror: https://github.com/fangq/jsonlab
+
+== JSONlab 1.0.0-RC1 (codename: Optimus - RC1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2014/09/17  fix several compatibility issues when running on octave versions 3.2-3.8
+ 2014/09/17  support 2D cell and struct arrays in both savejson and saveubjson
+ 2014/08/04  escape special characters in a JSON string
+ 2014/02/16  fix a bug when saving ubjson files
+
+== JSONlab 0.9.9 (codename: Optimus - beta), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2014/01/22  use binary read and write in saveubjson and loadubjson
+
+== JSONlab 0.9.8-1 (codename: Optimus - alpha update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2013/10/07 better round-trip conservation for empty arrays and structs (patch submitted by Yul Kang)
+
+== JSONlab 0.9.8 (codename: Optimus - alpha), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+ 2013/08/23 *universal Binary JSON (UBJSON) support, including both saveubjson and loadubjson
+
+== JSONlab 0.9.1 (codename: Rodimus, update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+ 2012/12/18 *handling of various empty and sparse matrices (fixes submitted by Niclas Borlin)
+
+== JSONlab 0.9.0 (codename: Rodimus), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2012/06/17 *new format for an invalid leading char, unpacking hex code in savejson
+ 2012/06/01  support JSONP in savejson
+ 2012/05/25  fix the empty cell bug (reported by Cyril Davin)
+ 2012/04/05  savejson can save to a file (suggested by Patrick Rapin)
+
+== JSONlab 0.8.1 (codename: Sentiel, Update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2012/02/28  loadjson quotation mark escape bug, see http://bit.ly/yyk1nS
+ 2012/01/25  patch to handle root-less objects, contributed by Blake Johnson
+
+== JSONlab 0.8.0 (codename: Sentiel), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2012/01/13 *speed up loadjson by 20 fold when parsing large data arrays in matlab
+ 2012/01/11  remove row bracket if an array has 1 element, suggested by Mykel Kochenderfer
+ 2011/12/22 *accept sequence of 'param',value input in savejson and loadjson
+ 2011/11/18  fix struct array bug reported by Mykel Kochenderfer
+
+== JSONlab 0.5.1 (codename: Nexus Update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2011/10/21  fix a bug in loadjson, previous code does not use any of the acceleration
+ 2011/10/20  loadjson supports JSON collections - concatenated JSON objects
+
+== JSONlab 0.5.0 (codename: Nexus), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2011/10/16  package and release jsonlab 0.5.0
+ 2011/10/15 *add json demo and regression test, support cpx numbers, fix double quote bug
+ 2011/10/11 *speed up readjson dramatically, interpret _Array* tags, show data in root level
+ 2011/10/10  create jsonlab project, start jsonlab website, add online documentation
+ 2011/10/07 *speed up savejson by 25x using sprintf instead of mat2str, add options support
+ 2011/10/06 *savejson works for structs, cells and arrays
+ 2011/09/09  derive loadjson from JSON parser from MATLAB Central, draft savejson.m

lib/jsonlab/LICENSE_BSD.txt

+Copyright 2011-2015 Qianqian Fang <fangq at nmr.mgh.harvard.edu>. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification, are
+permitted provided that the following conditions are met:
+
+   1. Redistributions of source code must retain the above copyright notice, this list of
+      conditions and the following disclaimer.
+
+   2. Redistributions in binary form must reproduce the above copyright notice, this list
+      of conditions and the following disclaimer in the documentation and/or other materials
+      provided with the distribution.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ''AS IS'' AND ANY EXPRESS OR IMPLIED
+WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS 
+OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+The views and conclusions contained in the software and documentation are those of the
+authors and should not be interpreted as representing official policies, either expressed
+or implied, of the copyright holders.

lib/jsonlab/jsonopt.m

+function val=jsonopt(key,default,varargin)
+%
+% val=jsonopt(key,default,optstruct)
+%
+% setting options based on a struct. The struct can be produced
+% by varargin2struct from a list of 'param','value' pairs
+%
+% authors:Qianqian Fang (fangq<at> nmr.mgh.harvard.edu)
+%
+% $Id: loadjson.m 371 2012-06-20 12:43:06Z fangq $
+%
+% input:
+%      key: a string with which one look up a value from a struct
+%      default: if the key does not exist, return default
+%      optstruct: a struct where each sub-field is a key 
+%
+% output:
+%      val: if key exists, val=optstruct.key; otherwise val=default
+%
+% license:
+%     BSD, see LICENSE_BSD.txt files for details
+%
+% -- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
+% 
+
+val=default;
+if(nargin<=2) return; end
+opt=varargin{1};
+if(isstruct(opt) && isfield(opt,key))
+    val=getfield(opt,key);
+end
+

lib/jsonlab/mergestruct.m

+function s=mergestruct(s1,s2)
+%
+% s=mergestruct(s1,s2)
+%
+% merge two struct objects into one
+%
+% authors:Qianqian Fang (fangq<at> nmr.mgh.harvard.edu)
+% date: 2012/12/22
+%
+% input:
+%      s1,s2: a struct object, s1 and s2 can not be arrays
+%
+% output:
+%      s: the merged struct object. fields in s1 and s2 will be combined in s.
+%
+% license:
+%     BSD, see LICENSE_BSD.txt files for details 
+%
+% -- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
+%
+
+if(~isstruct(s1) || ~isstruct(s2))
+    error('input parameters contain non-struct');
+end
+if(length(s1)>1 || length(s2)>1)
+    error('can not merge struct arrays');
+end
+fn=fieldnames(s2);
+s=s1;
+for i=1:length(fn)              
+    s=setfield(s,fn{i},getfield(s2,fn{i}));
+end
+

lib/jsonlab/varargin2struct.m

+function opt=varargin2struct(varargin)
+%
+% opt=varargin2struct('param1',value1,'param2',value2,...)
+%   or
+% opt=varargin2struct(...,optstruct,...)
+%
+% convert a series of input parameters into a structure
+%
+% authors:Qianqian Fang (fangq<at> nmr.mgh.harvard.edu)
+% date: 2012/12/22
+%
+% input:
+%      'param', value: the input parameters should be pairs of a string and a value
+%       optstruct: if a parameter is a struct, the fields will be merged to the output struct
+%
+% output:
+%      opt: a struct where opt.param1=value1, opt.param2=value2 ...
+%
+% license:
+%     BSD, see LICENSE_BSD.txt files for details 
+%
+% -- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
+%
+
+len=length(varargin);
+opt=struct;
+if(len==0) return; end
+i=1;
+while(i<=len)
+    if(isstruct(varargin{i}))
+        opt=mergestruct(opt,varargin{i});
+    elseif(ischar(varargin{i}) && i<len)
+        opt=setfield(opt,varargin{i},varargin{i+1});
+        i=i+1;
+    else
+        error('input must be in the form of ...,''name'',value,... pairs or structs');
+    end
+    i=i+1;
+end
+

lib/makeValidFieldName.m

+function str = makeValidFieldName(str)
+% From MATLAB doc: field names must begin with a letter, which may be
+% followed by any combination of letters, digits, and underscores.
+% Invalid characters will be converted to underscores, and the prefix
+% "x0x[Hex code]_" will be added if the first character is not a letter.
+    isoct=exist('OCTAVE_VERSION','builtin');
+    pos=regexp(str,'^[^A-Za-z]','once');
+    if(~isempty(pos))
+        if(~isoct)
+            str=regexprep(str,'^([^A-Za-z])','x0x${sprintf(''%X'',unicode2native($1))}_','once');
+        else
+            str=sprintf('x0x%X_%s',char(str(1)),str(2:end));
+        end
+    end
+    if(isempty(regexp(str,'[^0-9A-Za-z_]', 'once' ))) return;  end
+    if(~isoct)
+        str=regexprep(str,'([^0-9A-Za-z_])','_0x${sprintf(''%X'',unicode2native($1))}_');
+    else
+        pos=regexp(str,'[^0-9A-Za-z_]');
+        if(isempty(pos)) return; end
+        str0=str;
+        pos0=[0 pos(:)' length(str)];
+        str='';
+        for i=1:length(pos)
+            str=[str str0(pos0(i)+1:pos(i)-1) sprintf('_0x%X_',str0(pos(i)))];
+        end
+        if(pos(end)~=length(str))
+            str=[str str0(pos0(end-1)+1:pos0(end))];
+        end
+    end

lib/submitWithConfiguration.m

+function submitWithConfiguration(conf)
+  addpath('./lib/jsonlab');
+
+  parts = parts(conf);
+
+  fprintf('== Submitting solutions | %s...\n', conf.itemName);
+
+  tokenFile = 'token.mat';
+  if exist(tokenFile, 'file')
+    load(tokenFile);
+    [email token] = promptToken(email, token, tokenFile);
+  else
+    [email token] = promptToken('', '', tokenFile);
+  end
+
+  if isempty(token)
+    fprintf('!! Submission Cancelled\n');
+    return
+  end
+
+  try
+    response = submitParts(conf, email, token, parts);
+  catch
+    e = lasterror();
+    fprintf('\n!! Submission failed: %s\n', e.message);
+    fprintf('\n\nFunction: %s\nFileName: %s\nLineNumber: %d\n', ...
+      e.stack(1,1).name, e.stack(1,1).file, e.stack(1,1).line);
+    fprintf('\nPlease correct your code and resubmit.\n');
+    return
+  end
+
+  if isfield(response, 'errorMessage')
+    fprintf('!! Submission failed: %s\n', response.errorMessage);
+  elseif isfield(response, 'errorCode')
+    fprintf('!! Submission failed: %s\n', response.message);
+  else
+    showFeedback(parts, response);
+    save(tokenFile, 'email', 'token');
+  end
+end
+
+function [email token] = promptToken(email, existingToken, tokenFile)
+  if (~isempty(email) && ~isempty(existingToken))
+    prompt = sprintf( ...
+      'Use token from last successful submission (%s)? (Y/n): ', ...
+      email);
+    reenter = input(prompt, 's');
+
+    if (isempty(reenter) || reenter(1) == 'Y' || reenter(1) == 'y')
+      token = existingToken;
+      return;
+    else
+      delete(tokenFile);
+    end
+  end
+  email = input('Login (email address): ', 's');
+  token = input('Token: ', 's');
+end
+
+function isValid = isValidPartOptionIndex(partOptions, i)
+  isValid = (~isempty(i)) && (1 <= i) && (i <= numel(partOptions));
+end
+
+function response = submitParts(conf, email, token, parts)
+  body = makePostBody(conf, email, token, parts);
+  submissionUrl = submissionUrl();
+
+  responseBody = getResponse(submissionUrl, body);
+  jsonResponse = validateResponse(responseBody);
+  response = loadjson(jsonResponse);
+end
+
+function body = makePostBody(conf, email, token, parts)
+  bodyStruct.assignmentSlug = conf.assignmentSlug;
+  bodyStruct.submitterEmail = email;
+  bodyStruct.secret = token;
+  bodyStruct.parts = makePartsStruct(conf, parts);
+
+  opt.Compact = 1;
+  body = savejson('', bodyStruct, opt);
+end
+
+function partsStruct = makePartsStruct(conf, parts)
+  for part = parts
+    partId = part{:}.id;
+    fieldName = makeValidFieldName(partId);
+    outputStruct.output = conf.output(partId);
+    partsStruct.(fieldName) = outputStruct;
+  end
+end
+
+function [parts] = parts(conf)
+  parts = {};
+  for partArray = conf.partArrays
+    part.id = partArray{:}{1};
+    part.sourceFiles = partArray{:}{2};
+    part.name = partArray{:}{3};
+    parts{end + 1} = part;
+  end
+end
+
+function showFeedback(parts, response)
+  fprintf('== \n');
+  fprintf('== %43s | %9s | %-s\n', 'Part Name', 'Score', 'Feedback');
+  fprintf('== %43s | %9s | %-s\n', '---------', '-----', '--------');
+  for part = parts
+    score = '';
+    partFeedback = '';
+    partFeedback = response.partFeedbacks.(makeValidFieldName(part{:}.id));
+    partEvaluation = response.partEvaluations.(makeValidFieldName(part{:}.id));
+    score = sprintf('%d / %3d', partEvaluation.score, partEvaluation.maxScore);
+    fprintf('== %43s | %9s | %-s\n', part{:}.name, score, partFeedback);
+  end
+  evaluation = response.evaluation;
+  totalScore = sprintf('%d / %d', evaluation.score, evaluation.maxScore);
+  fprintf('==                                   --------------------------------\n');
+  fprintf('== %43s | %9s | %-s\n', '', totalScore, '');
+  fprintf('== \n');
+end
+
+% use urlread or curl to send submit results to the grader and get a response
+function response = getResponse(url, body)
+% try using urlread() and a secure connection
+  params = {'jsonBody', body};
+  [response, success] = urlread(url, 'post', params);
+
+  if (success == 0)
+    % urlread didn't work, try curl & the peer certificate patch
+    if ispc
+      % testing note: use 'jsonBody =' for a test case
+      json_command = sprintf('echo jsonBody=%s | curl -k -X POST -d @- %s', body, url);
+    else
+      % it's linux/OS X, so use the other form
+      json_command = sprintf('echo ''jsonBody=%s'' | curl -k -X POST -d @- %s', body, url);
+    end
+    % get the response body for the peer certificate patch method
+    [code, response] = system(json_command);
+    % test the success code
+    if (code ~= 0)
+      fprintf('[error] submission with curl() was not successful\n');
+    end
+  end
+end
+
+% validate the grader's response
+function response = validateResponse(resp)
+  % test if the response is json or an HTML page
+  isJson = length(resp) > 0 && resp(1) == '{';
+  isHtml = findstr(lower(resp), '<html');
+
+  if (isJson)
+    response = resp;
+  elseif (isHtml)
+    % the response is html, so it's probably an error message
+    printHTMLContents(resp);
+    error('Grader response is an HTML message');
+  else
+    error('Grader sent no response');
+  end
+end
+
+% parse a HTML response and print it's contents
+function printHTMLContents(response)
+  strippedResponse = regexprep(response, '<[^>]+>', ' ');
+  strippedResponse = regexprep(strippedResponse, '[\t ]+', ' ');
+  fprintf(strippedResponse);
+end
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% Service configuration
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function submissionUrl = submissionUrl()
+  submissionUrl = 'https://www-origin.coursera.org/api/onDemandProgrammingImmediateFormSubmissions.v1';
+end

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

plotDataPoints.m

+function plotDataPoints(X, idx, K)
+%PLOTDATAPOINTS plots data points in X, coloring them so that those with the same
+%index assignments in idx have the same color
+%   PLOTDATAPOINTS(X, idx, K) plots data points in X, coloring them so that those 
+%   with the same index assignments in idx have the same color
+
+% Create palette
+palette = hsv(K + 1);
+colors = palette(idx, :);
+
+% Plot the data
+scatter(X(:,1), X(:,2), 15, colors);
+
+end

plotProgresskMeans.m

+function plotProgresskMeans(X, centroids, previous, idx, K, i)
+%PLOTPROGRESSKMEANS is a helper function that displays the progress of 
+%k-Means as it is running. It is intended for use only with 2D data.
+%   PLOTPROGRESSKMEANS(X, centroids, previous, idx, K, i) plots the data
+%   points with colors assigned to each centroid. With the previous
+%   centroids, it also plots a line between the previous locations and
+%   current locations of the centroids.
+%
+
+% Plot the examples
+plotDataPoints(X, idx, K);
+
+% Plot the centroids as black x's
+plot(centroids(:,1), centroids(:,2), 'x', ...
+     'MarkerEdgeColor','k', ...
+     'MarkerSize', 10, 'LineWidth', 3);
+
+% Plot the history of the centroids with lines
+for j=1:size(centroids,1)
+    drawLine(centroids(j, :), previous(j, :));
+end
+
+% Title
+title(sprintf('Iteration number %d', i))
+
+end
+

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.
+
+
+% ====================== 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);
+%
+Z = X*U(:,1:K);
+
+
+
+% =============================================================
+
+end

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

runkMeans.m

+function [centroids, idx] = runkMeans(X, initial_centroids, ...
+                                      max_iters, plot_progress)
+%RUNKMEANS runs the K-Means algorithm on data matrix X, where each row of X
+%is a single example
+%   [centroids, idx] = RUNKMEANS(X, initial_centroids, max_iters, ...
+%   plot_progress) runs the K-Means algorithm on data matrix X, where each 
+%   row of X is a single example. It uses initial_centroids used as the
+%   initial centroids. max_iters specifies the total number of interactions 
+%   of K-Means to execute. plot_progress is a true/false flag that 
+%   indicates if the function should also plot its progress as the 
+%   learning happens. This is set to false by default. runkMeans returns 
+%   centroids, a Kxn matrix of the computed centroids and idx, a m x 1 
+%   vector of centroid assignments (i.e. each entry in range [1..K])
+%
+
+% Set default value for plot progress
+if ~exist('plot_progress', 'var') || isempty(plot_progress)
+    plot_progress = false;
+end
+
+% Plot the data if we are plotting progress
+if plot_progress
+    figure;
+    hold on;
+end
+
+% Initialize values
+[m n] = size(X);
+K = size(initial_centroids, 1);
+centroids = initial_centroids;
+previous_centroids = centroids;
+idx = zeros(m, 1);
+
+% Run K-Means
+for i=1:max_iters
+    
+    % Output progress
+    fprintf('K-Means iteration %d/%d...\n', i, max_iters);
+    if exist('OCTAVE_VERSION')
+        fflush(stdout);
+    end
+    
+    % For each example in X, assign it to the closest centroid
+    idx = findClosestCentroids(X, centroids);
+    
+    % Optionally, plot progress here
+    if plot_progress
+        plotProgresskMeans(X, centroids, previous_centroids, idx, K, i);
+        previous_centroids = centroids;
+        fprintf('Press enter to continue.\n');
+        pause;
+    end
+    
+    % Given the memberships, compute new centroids
+    centroids = computeCentroids(X, idx, K);
+end
+
+% Hold off if we are plotting progress
+if plot_progress
+    hold off;
+end
+
+end
+

submit.m

+function submit()
+  addpath('./lib');
+
+  conf.assignmentSlug = 'k-means-clustering-and-pca';
+  conf.itemName = 'K-Means Clustering and PCA';
+  conf.partArrays = { ...
+    { ...
+      '1', ...
+      { 'findClosestCentroids.m' }, ...
+      'Find Closest Centroids (k-Means)', ...
+    }, ...
+    { ...
+      '2', ...
+      { 'computeCentroids.m' }, ...
+      'Compute Centroid Means (k-Means)', ...
+    }, ...
+    { ...
+      '3', ...
+      { 'pca.m' }, ...
+      'PCA', ...
+    }, ...
+    { ...
+      '4', ...
+      { 'projectData.m' }, ...
+      'Project Data (PCA)', ...
+    }, ...
+    { ...
+      '5', ...
+      { 'recoverData.m' }, ...
+      'Recover Data (PCA)', ...
+    }, ...
+  };
+  conf.output = @output;
+
+  submitWithConfiguration(conf);
+end
+
+function out = output(partId, auxstring)
+  % Random Test Cases
+  X = reshape(sin(1:165), 15, 11);
+  Z = reshape(cos(1:121), 11, 11);
+  C = Z(1:5, :);
+  idx = (1 + mod(1:15, 3))';
+  if partId == '1'
+    idx = findClosestCentroids(X, C);
+    out = sprintf('%0.5f ', idx(:));
+  elseif partId == '2'
+    centroids = computeCentroids(X, idx, 3);
+    out = sprintf('%0.5f ', centroids(:));
+  elseif partId == '3'
+    [U, S] = pca(X);
+    out = sprintf('%0.5f ', abs([U(:); S(:)]));
+  elseif partId == '4'
+    X_proj = projectData(X, Z, 5);
+    out = sprintf('%0.5f ', X_proj(:));
+  elseif partId == '5'
+    X_rec = recoverData(X(:,1:5), Z, 5);
+    out = sprintf('%0.5f ', X_rec(:));
+  end 
+end

token.mat

+# Created by Octave 4.4.0, Tue May 29 17:50:35 2018 GMT <unknown@DESKTOP-IBF55GH>
+# name: email
+# type: sq_string
+# elements: 1
+# length: 24
+shashijgupta@hotmail.com
+
+
+# name: token
+# type: sq_string
+# elements: 1
+# length: 16
+aucrETHhdsX4pYNv
+
+