Added solution to assignments

machine-learning-ex3/ex3/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

machine-learning-ex3/ex3/ex3.m

+%% Machine Learning Online Class - Exercise 3 | Part 1: One-vs-all
+
+%  Instructions
+%  ------------
+%
+%  This file contains code that helps you get started on the
+%  linear exercise. You will need to complete the following functions
+%  in this exericse:
+%
+%     lrCostFunction.m (logistic regression cost function)
+%     oneVsAll.m
+%     predictOneVsAll.m
+%     predict.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
+
+%% Setup the parameters you will use for this part of the exercise
+input_layer_size  = 400;  % 20x20 Input Images of Digits
+num_labels = 10;          % 10 labels, from 1 to 10
+                          % (note that we have mapped "0" to label 10)
+
+%% =========== Part 1: Loading and Visualizing Data =============
+%  We start the exercise by first loading and visualizing the dataset.
+%  You will be working with a dataset that contains handwritten digits.
+%
+
+% Load Training Data
+fprintf('Loading and Visualizing Data ...\n')
+
+load('ex3data1.mat'); % training data stored in arrays X, y
+m = size(X, 1);
+
+% Randomly select 100 data points to display
+rand_indices = randperm(m);
+sel = X(rand_indices(1:100), :);
+
+displayData(sel);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% ============ Part 2a: Vectorize Logistic Regression ============
+%  In this part of the exercise, you will reuse your logistic regression
+%  code from the last exercise. You task here is to make sure that your
+%  regularized logistic regression implementation is vectorized. After
+%  that, you will implement one-vs-all classification for the handwritten
+%  digit dataset.
+%
+
+% Test case for lrCostFunction
+fprintf('\nTesting lrCostFunction() with regularization');
+
+theta_t = [-2; -1; 1; 2];
+X_t = [ones(5,1) reshape(1:15,5,3)/10];
+y_t = ([1;0;1;0;1] >= 0.5);
+lambda_t = 3;
+[J grad] = lrCostFunction(theta_t, X_t, y_t, lambda_t);
+
+fprintf('\nCost: %f\n', J);
+fprintf('Expected cost: 2.534819\n');
+fprintf('Gradients:\n');
+fprintf(' %f \n', grad);
+fprintf('Expected gradients:\n');
+fprintf(' 0.146561\n -0.548558\n 0.724722\n 1.398003\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+%% ============ Part 2b: One-vs-All Training ============
+fprintf('\nTraining One-vs-All Logistic Regression...\n')
+
+lambda = 0.1;
+[all_theta] = oneVsAll(X, y, num_labels, lambda);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================ Part 3: Predict for One-Vs-All ================
+
+pred = predictOneVsAll(all_theta, X);
+
+fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);
+

machine-learning-ex3/ex3/ex3_nn.m

+%% Machine Learning Online Class - Exercise 3 | Part 2: Neural Networks
+
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the
+%  linear exercise. You will need to complete the following functions 
+%  in this exericse:
+%
+%     lrCostFunction.m (logistic regression cost function)
+%     oneVsAll.m
+%     predictOneVsAll.m
+%     predict.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
+
+%% Setup the parameters you will use for this exercise
+input_layer_size  = 400;  % 20x20 Input Images of Digits
+hidden_layer_size = 25;   % 25 hidden units
+num_labels = 10;          % 10 labels, from 1 to 10   
+                          % (note that we have mapped "0" to label 10)
+
+%% =========== Part 1: Loading and Visualizing Data =============
+%  We start the exercise by first loading and visualizing the dataset. 
+%  You will be working with a dataset that contains handwritten digits.
+%
+
+% Load Training Data
+fprintf('Loading and Visualizing Data ...\n')
+
+load('ex3data1.mat');
+m = size(X, 1);
+
+% Randomly select 100 data points to display
+sel = randperm(size(X, 1));
+sel = sel(1:100);
+
+displayData(X(sel, :));
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%% ================ Part 2: Loading Pameters ================
+% In this part of the exercise, we load some pre-initialized 
+% neural network parameters.
+
+fprintf('\nLoading Saved Neural Network Parameters ...\n')
+
+% Load the weights into variables Theta1 and Theta2
+load('ex3weights.mat');
+
+%% ================= Part 3: Implement Predict =================
+%  After training the neural network, we would like to use it to predict
+%  the labels. You will now implement the "predict" function to use the
+%  neural network to predict the labels of the training set. This lets
+%  you compute the training set accuracy.
+
+pred = predict(Theta1, Theta2, X);
+
+fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+%  To give you an idea of the network's output, you can also run
+%  through the examples one at the a time to see what it is predicting.
+
+%  Randomly permute examples
+rp = randperm(m);
+
+for i = 1:m
+    % Display 
+    fprintf('\nDisplaying Example Image\n');
+    displayData(X(rp(i), :));
+
+    pred = predict(Theta1, Theta2, X(rp(i),:));
+    fprintf('\nNeural Network Prediction: %d (digit %d)\n', pred, mod(pred, 10));
+    
+    % Pause with quit option
+    s = input('Paused - press enter to continue, q to exit:','s');
+    if s == 'q'
+      break
+    end
+end
+

machine-learning-ex3/ex3/fmincg.m

+function [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
+% Minimize a continuous differentialble multivariate function. Starting point
+% is given by "X" (D by 1), and the function named in the string "f", must
+% return a function value and a vector of partial derivatives. The Polack-
+% Ribiere flavour of conjugate gradients is used to compute search directions,
+% and a line search using quadratic and cubic polynomial approximations and the
+% Wolfe-Powell stopping criteria is used together with the slope ratio method
+% for guessing initial step sizes. Additionally a bunch of checks are made to
+% make sure that exploration is taking place and that extrapolation will not
+% be unboundedly large. The "length" gives the length of the run: if it is
+% positive, it gives the maximum number of line searches, if negative its
+% absolute gives the maximum allowed number of function evaluations. You can
+% (optionally) give "length" a second component, which will indicate the
+% reduction in function value to be expected in the first line-search (defaults
+% to 1.0). The function returns when either its length is up, or if no further
+% progress can be made (ie, we are at a minimum, or so close that due to
+% numerical problems, we cannot get any closer). If the function terminates
+% within a few iterations, it could be an indication that the function value
+% and derivatives are not consistent (ie, there may be a bug in the
+% implementation of your "f" function). The function returns the found
+% solution "X", a vector of function values "fX" indicating the progress made
+% and "i" the number of iterations (line searches or function evaluations,
+% depending on the sign of "length") used.
+%
+% Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
+%
+% See also: checkgrad 
+%
+% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
+%
+%
+% (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen
+% 
+% Permission is granted for anyone to copy, use, or modify these
+% programs and accompanying documents for purposes of research or
+% education, provided this copyright notice is retained, and note is
+% made of any changes that have been made.
+% 
+% These programs and documents are distributed without any warranty,
+% express or implied.  As the programs were written for research
+% purposes only, they have not been tested to the degree that would be
+% advisable in any important application.  All use of these programs is
+% entirely at the user's own risk.
+%
+% [ml-class] Changes Made:
+% 1) Function name and argument specifications
+% 2) Output display
+%
+
+% Read options
+if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter')
+    length = options.MaxIter;
+else
+    length = 100;
+end
+
+
+RHO = 0.01;                            % a bunch of constants for line searches
+SIG = 0.5;       % RHO and SIG are the constants in the Wolfe-Powell conditions
+INT = 0.1;    % don't reevaluate within 0.1 of the limit of the current bracket
+EXT = 3.0;                    % extrapolate maximum 3 times the current bracket
+MAX = 20;                         % max 20 function evaluations per line search
+RATIO = 100;                                      % maximum allowed slope ratio
+
+argstr = ['feval(f, X'];                      % compose string used to call function
+for i = 1:(nargin - 3)
+  argstr = [argstr, ',P', int2str(i)];
+end
+argstr = [argstr, ')'];
+
+if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
+S=['Iteration '];
+
+i = 0;                                            % zero the run length counter
+ls_failed = 0;                             % no previous line search has failed
+fX = [];
+[f1 df1] = eval(argstr);                      % get function value and gradient
+i = i + (length<0);                                            % count epochs?!
+s = -df1;                                        % search direction is steepest
+d1 = -s'*s;                                                 % this is the slope
+z1 = red/(1-d1);                                  % initial step is red/(|s|+1)
+
+while i < abs(length)                                      % while not finished
+  i = i + (length>0);                                      % count iterations?!
+
+  X0 = X; f0 = f1; df0 = df1;                   % make a copy of current values
+  X = X + z1*s;                                             % begin line search
+  [f2 df2] = eval(argstr);
+  i = i + (length<0);                                          % count epochs?!
+  d2 = df2'*s;
+  f3 = f1; d3 = d1; z3 = -z1;             % initialize point 3 equal to point 1
+  if length>0, M = MAX; else M = min(MAX, -length-i); end
+  success = 0; limit = -1;                     % initialize quanteties
+  while 1
+    while ((f2 > f1+z1*RHO*d1) || (d2 > -SIG*d1)) && (M > 0) 
+      limit = z1;                                         % tighten the bracket
+      if f2 > f1
+        z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3);                 % quadratic fit
+      else
+        A = 6*(f2-f3)/z3+3*(d2+d3);                                 % cubic fit
+        B = 3*(f3-f2)-z3*(d3+2*d2);
+        z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A;       % numerical error possible - ok!
+      end
+      if isnan(z2) || isinf(z2)
+        z2 = z3/2;                  % if we had a numerical problem then bisect
+      end
+      z2 = max(min(z2, INT*z3),(1-INT)*z3);  % don't accept too close to limits
+      z1 = z1 + z2;                                           % update the step
+      X = X + z2*s;
+      [f2 df2] = eval(argstr);
+      M = M - 1; i = i + (length<0);                           % count epochs?!
+      d2 = df2'*s;
+      z3 = z3-z2;                    % z3 is now relative to the location of z2
+    end
+    if f2 > f1+z1*RHO*d1 || d2 > -SIG*d1
+      break;                                                % this is a failure
+    elseif d2 > SIG*d1
+      success = 1; break;                                             % success
+    elseif M == 0
+      break;                                                          % failure
+    end
+    A = 6*(f2-f3)/z3+3*(d2+d3);                      % make cubic extrapolation
+    B = 3*(f3-f2)-z3*(d3+2*d2);
+    z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3));        % num. error possible - ok!
+    if ~isreal(z2) || isnan(z2) || isinf(z2) || z2 < 0 % num prob or wrong sign?
+      if limit < -0.5                               % if we have no upper limit
+        z2 = z1 * (EXT-1);                 % the extrapolate the maximum amount
+      else
+        z2 = (limit-z1)/2;                                   % otherwise bisect
+      end
+    elseif (limit > -0.5) && (z2+z1 > limit)         % extraplation beyond max?
+      z2 = (limit-z1)/2;                                               % bisect
+    elseif (limit < -0.5) && (z2+z1 > z1*EXT)       % extrapolation beyond limit
+      z2 = z1*(EXT-1.0);                           % set to extrapolation limit
+    elseif z2 < -z3*INT
+      z2 = -z3*INT;
+    elseif (limit > -0.5) && (z2 < (limit-z1)*(1.0-INT))  % too close to limit?
+      z2 = (limit-z1)*(1.0-INT);
+    end
+    f3 = f2; d3 = d2; z3 = -z2;                  % set point 3 equal to point 2
+    z1 = z1 + z2; X = X + z2*s;                      % update current estimates
+    [f2 df2] = eval(argstr);
+    M = M - 1; i = i + (length<0);                             % count epochs?!
+    d2 = df2'*s;
+  end                                                      % end of line search
+
+  if success                                         % if line search succeeded
+    f1 = f2; fX = [fX' f1]';
+    fprintf('%s %4i | Cost: %4.6e\r', S, i, f1);
+    s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2;      % Polack-Ribiere direction
+    tmp = df1; df1 = df2; df2 = tmp;                         % swap derivatives
+    d2 = df1'*s;
+    if d2 > 0                                      % new slope must be negative
+      s = -df1;                              % otherwise use steepest direction
+      d2 = -s'*s;    
+    end
+    z1 = z1 * min(RATIO, d1/(d2-realmin));          % slope ratio but max RATIO
+    d1 = d2;
+    ls_failed = 0;                              % this line search did not fail
+  else
+    X = X0; f1 = f0; df1 = df0;  % restore point from before failed line search
+    if ls_failed || i > abs(length)          % line search failed twice in a row
+      break;                             % or we ran out of time, so we give up
+    end
+    tmp = df1; df1 = df2; df2 = tmp;                         % swap derivatives
+    s = -df1;                                                    % try steepest
+    d1 = -s'*s;
+    z1 = 1/(1-d1);                     
+    ls_failed = 1;                                    % this line search failed
+  end
+  if exist('OCTAVE_VERSION')
+    fflush(stdout);
+  end
+end
+fprintf('\n');

machine-learning-ex3/ex3/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

machine-learning-ex3/ex3/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

machine-learning-ex3/ex3/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.

machine-learning-ex3/ex3/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
+

machine-learning-ex3/ex3/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
+

machine-learning-ex3/ex3/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
+

machine-learning-ex3/ex3/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

machine-learning-ex3/ex3/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

machine-learning-ex3/ex3/lrCostFunction.m

+function [J, grad] = lrCostFunction(theta, X, y, lambda)
+%LRCOSTFUNCTION Compute cost and gradient for logistic regression with
+%regularization
+%   J = LRCOSTFUNCTION(theta, X, y, lambda) computes the cost of using
+%   theta as the parameter for regularized logistic regression and the
+%   gradient of the cost w.r.t. to the parameters.
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly
+J = 0;
+grad = zeros(size(theta));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+%
+% Hint: The computation of the cost function and gradients can be
+%       efficiently vectorized. For example, consider the computation
+%
+%           sigmoid(X * theta)
+%
+%       Each row of the resulting matrix will contain the value of the
+%       prediction for that example. You can make use of this to vectorize
+%       the cost function and gradient computations.
+%
+% Hint: When computing the gradient of the regularized cost function,
+%       there're many possible vectorized solutions, but one solution
+%       looks like:
+%           grad = (unregularized gradient for logistic regression)
+%           temp = theta;
+%           temp(1) = 0;   % because we don't add anything for j = 0
+%           grad = grad + YOUR_CODE_HERE (using the temp variable)
+%
+
+sigmo = sigmoid(X * theta);
+
+Jreg = lambda / (2 * m) * (theta' * theta - theta(1) .^2);
+
+J = 1 / m * (-y' * log(sigmo) - (1 - y)' * log(1 - sigmo)) + Jreg;
+
+temp = theta;
+temp(1) = 0;
+gradreg = lambda / m * temp;
+
+grad = 1 / m * X' * (sigmo - y) + gradreg;
+
+% =============================================================
+
+grad = grad(:);
+
+end
\ No newline at end of file

machine-learning-ex3/ex3/oneVsAll.m

+function [all_theta] = oneVsAll(X, y, num_labels, lambda)
+%ONEVSALL trains multiple logistic regression classifiers and returns all
+%the classifiers in a matrix all_theta, where the i-th row of all_theta 
+%corresponds to the classifier for label i
+%   [all_theta] = ONEVSALL(X, y, num_labels, lambda) trains num_labels
+%   logisitc regression classifiers and returns each of these classifiers
+%   in a matrix all_theta, where the i-th row of all_theta corresponds 
+%   to the classifier for label i
+
+% Some useful variables
+m = size(X, 1);
+n = size(X, 2);
+
+% You need to return the following variables correctly 
+all_theta = zeros(num_labels, n + 1);
+
+% Add ones to the X data matrix
+X = [ones(m, 1) X];
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: You should complete the following code to train num_labels
+%               logistic regression classifiers with regularization
+%               parameter lambda. 
+%
+% Hint: theta(:) will return a column vector.
+%
+% Hint: You can use y == c to obtain a vector of 1's and 0's that tell use 
+%       whether the ground truth is true/false for this class.
+%
+% Note: For this assignment, we recommend using fmincg to optimize the cost
+%       function. It is okay to use a for-loop (for c = 1:num_labels) to
+%       loop over the different classes.
+%
+%       fmincg works similarly to fminunc, but is more efficient when we
+%       are dealing with large number of parameters.
+%
+% Example Code for fmincg:
+%
+%     % Set Initial theta
+%     initial_theta = zeros(n + 1, 1);
+%     
+%     % Set options for fminunc
+%     options = optimset('GradObj', 'on', 'MaxIter', 50);
+% 
+%     % Run fmincg to obtain the optimal theta
+%     % This function will return theta and the cost 
+%     [theta] = ...
+%         fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), ...
+%                 initial_theta, options);
+%
+
+options = optimset('GradObj', 'on', 'MaxIter', 50);
+for c=1:num_labels
+    initial_theta = zeros(n + 1, 1);
+    [theta] = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)),initial_theta, options);
+    all_theta(c,:)=theta';
+end
+
+
+
+
+
+
+
+
+
+
+% =========================================================================
+
+
+end
\ No newline at end of file

machine-learning-ex3/ex3/predict.m

+function p = predict(Theta1, Theta2, X)
+%PREDICT Predict the label of an input given a trained neural network
+%   p = PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the
+%   trained weights of a neural network (Theta1, Theta2)
+
+% Useful values
+m = size(X, 1);
+num_labels = size(Theta2, 1);
+
+% You need to return the following variables correctly 
+p = zeros(size(X, 1), 1);
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Complete the following code to make predictions using
+%               your learned neural network. You should set p to a 
+%               vector containing labels between 1 to num_labels.
+%
+% Hint: The max function might come in useful. In particular, the max
+%       function can also return the index of the max element, for more
+%       information see 'help max'. If your examples are in rows, then, you
+%       can use max(A, [], 2) to obtain the max for each row.
+%
+X = [ones(size(X,1),1), X];
+temp = [ones(size(X,1),1), sigmoid(X*(Theta1'))]*(Theta2');
+[~, p] = max(temp, [], 2);
+% =========================================================================
+
+
+end

machine-learning-ex3/ex3/predictOneVsAll.m

+function p = predictOneVsAll(all_theta, X)
+%PREDICT Predict the label for a trained one-vs-all classifier. The labels 
+%are in the range 1..K, where K = size(all_theta, 1). 
+%  p = PREDICTONEVSALL(all_theta, X) will return a vector of predictions
+%  for each example in the matrix X. Note that X contains the examples in
+%  rows. all_theta is a matrix where the i-th row is a trained logistic
+%  regression theta vector for the i-th class. You should set p to a vector
+%  of values from 1..K (e.g., p = [1; 3; 1; 2] predicts classes 1, 3, 1, 2
+%  for 4 examples) 
+
+m = size(X, 1);
+num_labels = size(all_theta, 1);
+
+% You need to return the following variables correctly 
+p = zeros(size(X, 1), 1);
+
+% Add ones to the X data matrix
+X = [ones(m, 1) X];
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Complete the following code to make predictions using
+%               your learned logistic regression parameters (one-vs-all).
+%               You should set p to a vector of predictions (from 1 to
+%               num_labels).
+%
+% Hint: This code can be done all vectorized using the max function.
+%       In particular, the max function can also return the index of the 
+%       max element, for more information see 'help max'. If your examples 
+%       are in rows, then, you can use max(A, [], 2) to obtain the max 
+%       for each row.
+%       
+[~, p] = max(X*(all_theta'), [], 2);
+% =========================================================================
+
+
+end

machine-learning-ex3/ex3/sigmoid.m

+function g = sigmoid(z)
+%SIGMOID Compute sigmoid functoon
+%   J = SIGMOID(z) computes the sigmoid of z.
+
+g = 1.0 ./ (1.0 + exp(-z));
+end

machine-learning-ex3/ex3/submit.m

+function submit()
+  addpath('./lib');
+
+  conf.assignmentSlug = 'multi-class-classification-and-neural-networks';
+  conf.itemName = 'Multi-class Classification and Neural Networks';
+  conf.partArrays = { ...
+    { ...
+      '1', ...
+      { 'lrCostFunction.m' }, ...
+      'Regularized Logistic Regression', ...
+    }, ...
+    { ...
+      '2', ...
+      { 'oneVsAll.m' }, ...
+      'One-vs-All Classifier Training', ...
+    }, ...
+    { ...
+      '3', ...
+      { 'predictOneVsAll.m' }, ...
+      'One-vs-All Classifier Prediction', ...
+    }, ...
+    { ...
+      '4', ...
+      { 'predict.m' }, ...
+      'Neural Network Prediction Function' ...
+    }, ...
+  };
+  conf.output = @output;
+
+  submitWithConfiguration(conf);
+end
+
+function out = output(partId, auxdata)
+  % Random Test Cases
+  X = [ones(20,1) (exp(1) * sin(1:1:20))' (exp(0.5) * cos(1:1:20))'];
+  y = sin(X(:,1) + X(:,2)) > 0;
+  Xm = [ -1 -1 ; -1 -2 ; -2 -1 ; -2 -2 ; ...
+          1 1 ;  1 2 ;  2 1 ; 2 2 ; ...
+         -1 1 ;  -1 2 ;  -2 1 ; -2 2 ; ...
+          1 -1 ; 1 -2 ;  -2 -1 ; -2 -2 ];
+  ym = [ 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 ]';
+  t1 = sin(reshape(1:2:24, 4, 3));
+  t2 = cos(reshape(1:2:40, 4, 5));
+
+  if partId == '1'
+    [J, grad] = lrCostFunction([0.25 0.5 -0.5]', X, y, 0.1);
+    out = sprintf('%0.5f ', J);
+    out = [out sprintf('%0.5f ', grad)];
+  elseif partId == '2'
+    out = sprintf('%0.5f ', oneVsAll(Xm, ym, 4, 0.1));
+  elseif partId == '3'
+    out = sprintf('%0.5f ', predictOneVsAll(t1, Xm));
+  elseif partId == '4'
+    out = sprintf('%0.5f ', predict(t1, t2, Xm));
+  end 
+end

machine-learning-ex3/ex3/token.txt

+z3k5tth1vaMFXD7K
\ No newline at end of file