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Image_Compression
Commit 1732d4ef authored by SHASHIJ GUPTA's avatar SHASHIJ GUPTA
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bird_small.mat 0 → 100644
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computeCentroids.m 0 → 100644
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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 0 → 100644
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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 0 → 100644
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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
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ex7.m 0 → 100644
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%% 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 0 → 100644
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%% 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;
ex7data1.mat 0 → 100644
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ex7data2.mat 0 → 100644
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ex7faces.mat 0 → 100644
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featureNormalize.m 0 → 100644
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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 0 → 100644
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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 0 → 100644
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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 0 → 100644
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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 0 → 100644
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============================================================================
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 0 → 100644
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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
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