complete ex4

machine learning/machine-learning-ex4/ex4/checkNNGradients.m

@@ -1,52 +1,52 @@
-function checkNNGradients(lambda)
-%CHECKNNGRADIENTS Creates a small neural network to check the
-%backpropagation gradients
-%   CHECKNNGRADIENTS(lambda) Creates a small neural network to check the
-%   backpropagation gradients, it will output the analytical gradients
-%   produced by your backprop code and the numerical gradients (computed
-%   using computeNumericalGradient). These two gradient computations should
-%   result in very similar values.
-%
-
-if ~exist('lambda', 'var') || isempty(lambda)
-    lambda = 0;
-end
-
-input_layer_size = 3;
-hidden_layer_size = 5;
-num_labels = 3;
-m = 5;
-
-% We generate some 'random' test data
-Theta1 = debugInitializeWeights(hidden_layer_size, input_layer_size);
-Theta2 = debugInitializeWeights(num_labels, hidden_layer_size);
-% Reusing debugInitializeWeights to generate X
-X  = debugInitializeWeights(m, input_layer_size - 1);
-y  = 1 + mod(1:m, num_labels)';
-
-% Unroll parameters
-nn_params = [Theta1(:) ; Theta2(:)];
-
-% Short hand for cost function
-costFunc = @(p) nnCostFunction(p, input_layer_size, hidden_layer_size, ...
-                               num_labels, X, y, lambda);
-
-[cost, grad] = costFunc(nn_params);
-numgrad = computeNumericalGradient(costFunc, nn_params);
-
-% Visually examine the two gradient computations.  The two columns
-% you get should be very similar. 
-disp([numgrad grad]);
-fprintf(['The above two columns you get should be very similar.\n' ...
-         '(Left-Your Numerical Gradient, Right-Analytical Gradient)\n\n']);
-
-% Evaluate the norm of the difference between two solutions.  
-% If you have a correct implementation, and assuming you used EPSILON = 0.0001 
-% in computeNumericalGradient.m, then diff below should be less than 1e-9
-diff = norm(numgrad-grad)/norm(numgrad+grad);
-
-fprintf(['If your backpropagation implementation is correct, then \n' ...
-         'the relative difference will be small (less than 1e-9). \n' ...
-         '\nRelative Difference: %g\n'], diff);
-
-end
+function checkNNGradients(lambda)
+%CHECKNNGRADIENTS Creates a small neural network to check the
+%backpropagation gradients
+%   CHECKNNGRADIENTS(lambda) Creates a small neural network to check the
+%   backpropagation gradients, it will output the analytical gradients
+%   produced by your backprop code and the numerical gradients (computed
+%   using computeNumericalGradient). These two gradient computations should
+%   result in very similar values.
+%
+
+if ~exist('lambda', 'var') || isempty(lambda)
+    lambda = 0;
+end
+
+input_layer_size = 3;
+hidden_layer_size = 5;
+num_labels = 3;
+m = 5;
+
+% We generate some 'random' test data
+Theta1 = debugInitializeWeights(hidden_layer_size, input_layer_size);
+Theta2 = debugInitializeWeights(num_labels, hidden_layer_size);
+% Reusing debugInitializeWeights to generate X
+X  = debugInitializeWeights(m, input_layer_size - 1);
+y  = 1 + mod(1:m, num_labels)';
+
+% Unroll parameters
+nn_params = [Theta1(:) ; Theta2(:)];
+
+% Short hand for cost function
+costFunc = @(p) nnCostFunction(p, input_layer_size, hidden_layer_size, ...
+                               num_labels, X, y, lambda);
+
+[cost, grad] = costFunc(nn_params);
+numgrad = computeNumericalGradient(costFunc, nn_params);
+
+% Visually examine the two gradient computations.  The two columns
+% you get should be very similar. 
+disp([numgrad grad]);
+fprintf(['The above two columns you get should be very similar.\n' ...
+         '(Left-Your Numerical Gradient, Right-Analytical Gradient)\n\n']);
+
+% Evaluate the norm of the difference between two solutions.  
+% If you have a correct implementation, and assuming you used EPSILON = 0.0001 
+% in computeNumericalGradient.m, then diff below should be less than 1e-9
+diff = norm(numgrad-grad)/norm(numgrad+grad);
+
+fprintf(['If your backpropagation implementation is correct, then \n' ...
+         'the relative difference will be small (less than 1e-9). \n' ...
+         '\nRelative Difference: %g\n'], diff);
+
+end

machine learning/machine-learning-ex4/ex4/computeNumericalGradient.m

@@ -1,29 +1,29 @@
-function numgrad = computeNumericalGradient(J, theta)
-%COMPUTENUMERICALGRADIENT Computes the gradient using "finite differences"
-%and gives us a numerical estimate of the gradient.
-%   numgrad = COMPUTENUMERICALGRADIENT(J, theta) computes the numerical
-%   gradient of the function J around theta. Calling y = J(theta) should
-%   return the function value at theta.
-
-% Notes: The following code implements numerical gradient checking, and 
-%        returns the numerical gradient.It sets numgrad(i) to (a numerical 
-%        approximation of) the partial derivative of J with respect to the 
-%        i-th input argument, evaluated at theta. (i.e., numgrad(i) should 
-%        be the (approximately) the partial derivative of J with respect 
-%        to theta(i).)
-%                
-
-numgrad = zeros(size(theta));
-perturb = zeros(size(theta));
-e = 1e-4;
-for p = 1:numel(theta)
-    % Set perturbation vector
-    perturb(p) = e;
-    loss1 = J(theta - perturb);
-    loss2 = J(theta + perturb);
-    % Compute Numerical Gradient
-    numgrad(p) = (loss2 - loss1) / (2*e);
-    perturb(p) = 0;
-end
-
-end
+function numgrad = computeNumericalGradient(J, theta)
+%COMPUTENUMERICALGRADIENT Computes the gradient using "finite differences"
+%and gives us a numerical estimate of the gradient.
+%   numgrad = COMPUTENUMERICALGRADIENT(J, theta) computes the numerical
+%   gradient of the function J around theta. Calling y = J(theta) should
+%   return the function value at theta.
+
+% Notes: The following code implements numerical gradient checking, and 
+%        returns the numerical gradient.It sets numgrad(i) to (a numerical 
+%        approximation of) the partial derivative of J with respect to the 
+%        i-th input argument, evaluated at theta. (i.e., numgrad(i) should 
+%        be the (approximately) the partial derivative of J with respect 
+%        to theta(i).)
+%                
+
+numgrad = zeros(size(theta));
+perturb = zeros(size(theta));
+e = 1e-4;
+for p = 1:numel(theta)
+    % Set perturbation vector
+    perturb(p) = e;
+    loss1 = J(theta - perturb);
+    loss2 = J(theta + perturb);
+    % Compute Numerical Gradient
+    numgrad(p) = (loss2 - loss1) / (2*e);
+    perturb(p) = 0;
+end
+
+end

machine learning/machine-learning-ex4/ex4/debugInitializeWeights.m

@@ -1,22 +1,22 @@
-function W = debugInitializeWeights(fan_out, fan_in)
-%DEBUGINITIALIZEWEIGHTS Initialize the weights of a layer with fan_in
-%incoming connections and fan_out outgoing connections using a fixed
-%strategy, this will help you later in debugging
-%   W = DEBUGINITIALIZEWEIGHTS(fan_in, fan_out) initializes the weights 
-%   of a layer with fan_in incoming connections and fan_out outgoing 
-%   connections using a fix set of values
-%
-%   Note that W should be set to a matrix of size(1 + fan_in, fan_out) as
-%   the first row of W handles the "bias" terms
-%
-
-% Set W to zeros
-W = zeros(fan_out, 1 + fan_in);
-
-% Initialize W using "sin", this ensures that W is always of the same
-% values and will be useful for debugging
-W = reshape(sin(1:numel(W)), size(W)) / 10;
-
-% =========================================================================
-
-end
+function W = debugInitializeWeights(fan_out, fan_in)
+%DEBUGINITIALIZEWEIGHTS Initialize the weights of a layer with fan_in
+%incoming connections and fan_out outgoing connections using a fixed
+%strategy, this will help you later in debugging
+%   W = DEBUGINITIALIZEWEIGHTS(fan_in, fan_out) initializes the weights 
+%   of a layer with fan_in incoming connections and fan_out outgoing 
+%   connections using a fix set of values
+%
+%   Note that W should be set to a matrix of size(1 + fan_in, fan_out) as
+%   the first row of W handles the "bias" terms
+%
+
+% Set W to zeros
+W = zeros(fan_out, 1 + fan_in);
+
+% Initialize W using "sin", this ensures that W is always of the same
+% values and will be useful for debugging
+W = reshape(sin(1:numel(W)), size(W)) / 10;
+
+% =========================================================================
+
+end

machine learning/machine-learning-ex4/ex4/displayData.m

@@ -1,59 +1,59 @@
-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
+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/machine-learning-ex4/ex4/ex4.m

@@ -1,234 +1,240 @@
-%% Machine Learning Online Class - Exercise 4 Neural Network Learning
-
-%  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:
-%
-%     sigmoidGradient.m
-%     randInitializeWeights.m
-%     nnCostFunction.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('ex4data1.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 Parameters ================
-% 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('ex4weights.mat');
-
-% Unroll parameters 
-nn_params = [Theta1(:) ; Theta2(:)];
-
-%% ================ Part 3: Compute Cost (Feedforward) ================
-%  To the neural network, you should first start by implementing the
-%  feedforward part of the neural network that returns the cost only. You
-%  should complete the code in nnCostFunction.m to return cost. After
-%  implementing the feedforward to compute the cost, you can verify that
-%  your implementation is correct by verifying that you get the same cost
-%  as us for the fixed debugging parameters.
-%
-%  We suggest implementing the feedforward cost *without* regularization
-%  first so that it will be easier for you to debug. Later, in part 4, you
-%  will get to implement the regularized cost.
-%
-fprintf('\nFeedforward Using Neural Network ...\n')
-
-% Weight regularization parameter (we set this to 0 here).
-lambda = 0;
-
-J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
-                   num_labels, X, y, lambda);
-
-fprintf(['Cost at parameters (loaded from ex4weights): %f '...
-         '\n(this value should be about 0.287629)\n'], J);
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-%% =============== Part 4: Implement Regularization ===============
-%  Once your cost function implementation is correct, you should now
-%  continue to implement the regularization with the cost.
-%
-
-fprintf('\nChecking Cost Function (w/ Regularization) ... \n')
-
-% Weight regularization parameter (we set this to 1 here).
-lambda = 1;
-
-J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
-                   num_labels, X, y, lambda);
-
-fprintf(['Cost at parameters (loaded from ex4weights): %f '...
-         '\n(this value should be about 0.383770)\n'], J);
-
-fprintf('Program paused. Press enter to continue.\n');
-pause;
-
-
-%% ================ Part 5: Sigmoid Gradient  ================
-%  Before you start implementing the neural network, you will first
-%  implement the gradient for the sigmoid function. You should complete the
-%  code in the sigmoidGradient.m file.
-%
-
-fprintf('\nEvaluating sigmoid gradient...\n')
-
-g = sigmoidGradient([-1 -0.5 0 0.5 1]);
-fprintf('Sigmoid gradient evaluated at [-1 -0.5 0 0.5 1]:\n  ');
-fprintf('%f ', g);
-fprintf('\n\n');
-
-fprintf('Program paused. Press enter to continue.\n');
-pause;
-
-
-%% ================ Part 6: Initializing Pameters ================
-%  In this part of the exercise, you will be starting to implment a two
-%  layer neural network that classifies digits. You will start by
-%  implementing a function to initialize the weights of the neural network
-%  (randInitializeWeights.m)
-
-fprintf('\nInitializing Neural Network Parameters ...\n')
-
-initial_Theta1 = randInitializeWeights(input_layer_size, hidden_layer_size);
-initial_Theta2 = randInitializeWeights(hidden_layer_size, num_labels);
-
-% Unroll parameters
-initial_nn_params = [initial_Theta1(:) ; initial_Theta2(:)];
-
-
-%% =============== Part 7: Implement Backpropagation ===============
-%  Once your cost matches up with ours, you should proceed to implement the
-%  backpropagation algorithm for the neural network. You should add to the
-%  code you've written in nnCostFunction.m to return the partial
-%  derivatives of the parameters.
-%
-fprintf('\nChecking Backpropagation... \n');
-
-%  Check gradients by running checkNNGradients
-checkNNGradients;
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-
-%% =============== Part 8: Implement Regularization ===============
-%  Once your backpropagation implementation is correct, you should now
-%  continue to implement the regularization with the cost and gradient.
-%
-
-fprintf('\nChecking Backpropagation (w/ Regularization) ... \n')
-
-%  Check gradients by running checkNNGradients
-lambda = 3;
-checkNNGradients(lambda);
-
-% Also output the costFunction debugging values
-debug_J  = nnCostFunction(nn_params, input_layer_size, ...
-                          hidden_layer_size, num_labels, X, y, lambda);
-
-fprintf(['\n\nCost at (fixed) debugging parameters (w/ lambda = %f): %f ' ...
-         '\n(for lambda = 3, this value should be about 0.576051)\n\n'], lambda, debug_J);
-
-fprintf('Program paused. Press enter to continue.\n');
-pause;
-
-
-%% =================== Part 8: Training NN ===================
-%  You have now implemented all the code necessary to train a neural 
-%  network. To train your neural network, we will now use "fmincg", which
-%  is a function which works similarly to "fminunc". Recall that these
-%  advanced optimizers are able to train our cost functions efficiently as
-%  long as we provide them with the gradient computations.
-%
-fprintf('\nTraining Neural Network... \n')
-
-%  After you have completed the assignment, change the MaxIter to a larger
-%  value to see how more training helps.
-options = optimset('MaxIter', 50);
-
-%  You should also try different values of lambda
-lambda = 1;
-
-% Create "short hand" for the cost function to be minimized
-costFunction = @(p) nnCostFunction(p, ...
-                                   input_layer_size, ...
-                                   hidden_layer_size, ...
-                                   num_labels, X, y, lambda);
-
-% Now, costFunction is a function that takes in only one argument (the
-% neural network parameters)
-[nn_params, cost] = fmincg(costFunction, initial_nn_params, options);
-
-% Obtain Theta1 and Theta2 back from nn_params
-Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
-                 hidden_layer_size, (input_layer_size + 1));
-
-Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
-                 num_labels, (hidden_layer_size + 1));
-
-fprintf('Program paused. Press enter to continue.\n');
-pause;
-
-
-%% ================= Part 9: Visualize Weights =================
-%  You can now "visualize" what the neural network is learning by 
-%  displaying the hidden units to see what features they are capturing in 
-%  the data.
-
-fprintf('\nVisualizing Neural Network... \n')
-
-displayData(Theta1(:, 2:end));
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-pause;
-
-%% ================= Part 10: 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);
-
-
+%% Machine Learning Online Class - Exercise 4 Neural Network Learning
+
+%  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:
+%
+%     sigmoidGradient.m
+%     randInitializeWeights.m
+%     nnCostFunction.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('ex4data1.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 Parameters ================
+% 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('ex4weights.mat');
+
+% Unroll parameters 
+nn_params = [Theta1(:) ; Theta2(:)];
+
+%% ================ Part 3: Compute Cost (Feedforward) ================
+%  To the neural network, you should first start by implementing the
+%  feedforward part of the neural network that returns the cost only. You
+%  should complete the code in nnCostFunction.m to return cost. After
+%  implementing the feedforward to compute the cost, you can verify that
+%  your implementation is correct by verifying that you get the same cost
+%  as us for the fixed debugging parameters.
+%
+%  We suggest implementing the feedforward cost *without* regularization
+%  first so that it will be easier for you to debug. Later, in part 4, you
+%  will get to implement the regularized cost.
+%
+fprintf('\nFeedforward Using Neural Network ...\n')
+
+% Weight regularization parameter (we set this to 0 here).
+lambda = 0;
+
+J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
+                   num_labels, X, y, lambda);
+
+fprintf(['Cost at parameters (loaded from ex4weights): %f '...
+         '\n(this value should be about 0.287629)\n'], J);
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% =============== Part 4: Implement Regularization ===============
+%  Once your cost function implementation is correct, you should now
+%  continue to implement the regularization with the cost.
+%
+
+fprintf('\nChecking Cost Function (w/ Regularization) ... \n')
+
+% Weight regularization parameter (we set this to 1 here).
+lambda = 1;
+
+J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
+                   num_labels, X, y, lambda);
+
+fprintf(['Cost at parameters (loaded from ex4weights): %f '...
+         '\n(this value should be about 0.383770)\n'], J);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================ Part 5: Sigmoid Gradient  ================
+%  Before you start implementing the neural network, you will first
+%  implement the gradient for the sigmoid function. You should complete the
+%  code in the sigmoidGradient.m file.
+%
+
+fprintf('\nEvaluating sigmoid gradient...\n')
+
+g = sigmoidGradient([-1 -0.5 0 0.5 1]);
+fprintf('Sigmoid gradient evaluated at [-1 -0.5 0 0.5 1]:\n  ');
+fprintf('%f ', g);
+fprintf('\n\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================ Part 6: Initializing Pameters ================
+%  In this part of the exercise, you will be starting to implment a two
+%  layer neural network that classifies digits. You will start by
+%  implementing a function to initialize the weights of the neural network
+%  (randInitializeWeights.m)
+
+fprintf('\nInitializing Neural Network Parameters ...\n')
+
+initial_Theta1 = randInitializeWeights(input_layer_size, hidden_layer_size);
+initial_Theta2 = randInitializeWeights(hidden_layer_size, num_labels);
+
+% Unroll parameters
+initial_nn_params = [initial_Theta1(:) ; initial_Theta2(:)];
+
+
+%% =============== Part 7: Implement Backpropagation ===============
+%  Once your cost matches up with ours, you should proceed to implement the
+%  backpropagation algorithm for the neural network. You should add to the
+%  code you've written in nnCostFunction.m to return the partial
+%  derivatives of the parameters.
+%
+fprintf('\nChecking Backpropagation... \n');
+
+%  Check gradients by running checkNNGradients
+checkNNGradients;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% =============== Part 8: Implement Regularization ===============
+%  Once your backpropagation implementation is correct, you should now
+%  continue to implement the regularization with the cost and gradient.
+%
+
+fprintf('\nChecking Backpropagation (w/ Regularization) ... \n')
+
+%  Check gradients by running checkNNGradients
+lambda = 3;
+checkNNGradients(lambda);
+
+% Also output the costFunction debugging values
+debug_J  = nnCostFunction(nn_params, input_layer_size, ...
+                          hidden_layer_size, num_labels, X, y, lambda);
+
+fprintf(['\n\nCost at (fixed) debugging parameters (w/ lambda = %f): %f ' ...
+         '\n(for lambda = 3, this value should be about 0.576051)\n\n'], lambda, debug_J);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% =================== Part 8: Training NN ===================
+%  You have now implemented all the code necessary to train a neural 
+%  network. To train your neural network, we will now use "fmincg", which
+%  is a function which works similarly to "fminunc". Recall that these
+%  advanced optimizers are able to train our cost functions efficiently as
+%  long as we provide them with the gradient computations.
+%
+fprintf('\nTraining Neural Network... \n')
+
+t=cputime;
+
+
+%  After you have completed the assignment, change the MaxIter to a larger
+%  value to see how more training helps.
+options = optimset('MaxIter', 50);
+
+%  You should also try different values of lambda
+lambda = 1;
+
+% Create "short hand" for the cost function to be minimized
+costFunction = @(p) nnCostFunction(p, ...
+                                   input_layer_size, ...
+                                   hidden_layer_size, ...
+                                   num_labels, X, y, lambda);
+
+% Now, costFunction is a function that takes in only one argument (the
+% neural network parameters)
+[nn_params, cost] = fmincg(costFunction, initial_nn_params, options);
+
+printf('Total cpu time: %f seconds\n', cputime-t);
+
+
+% Obtain Theta1 and Theta2 back from nn_params
+Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
+                 hidden_layer_size, (input_layer_size + 1));
+
+Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
+                 num_labels, (hidden_layer_size + 1));
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================= Part 9: Visualize Weights =================
+%  You can now "visualize" what the neural network is learning by 
+%  displaying the hidden units to see what features they are capturing in 
+%  the data.
+
+fprintf('\nVisualizing Neural Network... \n')
+
+displayData(Theta1(:, 2:end));
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ================= Part 10: 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);
+
+

machine learning/machine-learning-ex4/ex4/fmincg.m

@@ -1,175 +1,175 @@
-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');
+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/machine-learning-ex4/ex4/myex4.m

@@ -1,54 +1,90 @@
-%% 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('ex4data1.mat');
-m = size(X, 1);
-
-% Randomly select 100 data points to display
-sel = randperm(size(X, 1));
-sel = sel(1:100);
-
-% Load the weights into variables Theta1 and Theta2
-load('ex4weights.mat');
-
-% Unroll parameters 
-nn_params = [Theta1(:) ; Theta2(:)];
-
-
-fprintf('\nFeedforward Using Neural Network ...\n')
-
-% Weight regularization parameter (we set this to 0 here).
-lambda = 0;
-
-J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
-                   num_labels, X, y, lambda);
-
-fprintf(['Cost at parameters (loaded from ex4weights): %f '...
-         '\n(this value should be about 0.287629)\n'], J);
-
-fprintf('\nProgram paused. Press enter to continue.\n');
-fprintf('\nEvaluating sigmoid gradient...\n')
-
-g = sigmoidGradient([-1 -0.5 0 0.5 1]);
-fprintf('Sigmoid gradient evaluated at [-1 -0.5 0 0.5 1]:\n  ');
-fprintf('%f ', g);
-fprintf('\n\n');
-
-fprintf('Program paused. Press enter to continue.\n');
-pause;
-
+%% 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('ex4data1.mat');
+m = size(X, 1);
+
+% Randomly select 100 data points to display
+sel = randperm(size(X, 1));
+sel = sel(1:100);
+
+% Load the weights into variables Theta1 and Theta2
+load('ex4weights.mat');
+
+% Unroll parameters 
+nn_params = [Theta1(:) ; Theta2(:)];
+
+
+fprintf('\nFeedforward Using Neural Network ...\n')
+
+% Weight regularization parameter (we set this to 0 here).
+lambda = 0;
+
+J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
+                   num_labels, X, y, lambda);
+
+fprintf(['Cost at parameters (loaded from ex4weights): %f '...
+         '\n(this value should be about 0.287629)\n'], J);
+
+lambda = 1;
+J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
+                   num_labels, X, y, lambda);         
+fprintf(['Cost at parameters (loaded from ex4weights)=> lambda = 1: %f '...
+         '\n(this value should be about 0.383770)\n'], J);
+         
+fprintf('\nProgram paused. Press enter to continue.\n');
+fprintf('\nEvaluating sigmoid gradient...\n')
+
+g = sigmoidGradient([-1 -0.5 0 0.5 1]);
+fprintf('Sigmoid gradient evaluated at [-1 -0.5 0 0.5 1]:\n  ');
+fprintf('%f ', g);
+fprintf('\n\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+
+%% ================ Part 6: Initializing Pameters ================
+%  In this part of the exercise, you will be starting to implment a two
+%  layer neural network that classifies digits. You will start by
+%  implementing a function to initialize the weights of the neural network
+%  (randInitializeWeights.m)
+
+fprintf('\nInitializing Neural Network Parameters ...\n')
+
+initial_Theta1 = randInitializeWeights(input_layer_size, hidden_layer_size);
+initial_Theta2 = randInitializeWeights(hidden_layer_size, num_labels);
+
+% Unroll parameters
+initial_nn_params = [initial_Theta1(:) ; initial_Theta2(:)];
+
+
+%% =============== Part 7: Implement Backpropagation ===============
+%  Once your cost matches up with ours, you should proceed to implement the
+%  backpropagation algorithm for the neural network. You should add to the
+%  code you've written in nnCostFunction.m to return the partial
+%  derivatives of the parameters.
+%
+fprintf('\nChecking Backpropagation... \n');
+
+%  Check gradients by running checkNNGradients
+checkNNGradients;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+
 %%%%%%https://github.com/rieder91/MachineLearning/blob/master/Exercise%204/ex4/nnCostFunction.m

machine learning/machine-learning-ex4/ex4/nnCostFunction.bak

@@ -0,0 +1,123 @@
+function [J grad] = nnCostFunction(nn_params, ...
+                                   input_layer_size, ...
+                                   hidden_layer_size, ...
+                                   num_labels, ...
+                                   X, y, lambda)
+%NNCOSTFUNCTION Implements the neural network cost function for a two layer
+%neural network which performs classification
+%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
+%   X, y, lambda) computes the cost and gradient of the neural network. The
+%   parameters for the neural network are "unrolled" into the vector
+%   nn_params and need to be converted back into the weight matrices. 
+% 
+%   The returned parameter grad should be a "unrolled" vector of the
+%   partial derivatives of the neural network.
+%
+
+% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
+% for our 2 layer neural network
+Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
+                 hidden_layer_size, (input_layer_size + 1));
+
+Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
+                 num_labels, (hidden_layer_size + 1));
+
+% Setup some useful variables
+m = size(X, 1);
+         
+% You need to return the following variables correctly 
+J = 0;
+Theta1_grad = zeros(size(Theta1));
+Theta2_grad = zeros(size(Theta2));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: You should complete the code by working through the
+%               following parts.
+%
+% Part 1: Feedforward the neural network and return the cost in the
+%         variable J. After implementing Part 1, you can verify that your
+%         cost function computation is correct by verifying the cost
+%         computed in ex4.m
+%
+% Part 2: Implement the backpropagation algorithm to compute the gradients
+%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
+%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
+%         Theta2_grad, respectively. After implementing Part 2, you can check
+%         that your implementation is correct by running checkNNGradients
+%
+%         Note: The vector y passed into the function is a vector of labels
+%               containing values from 1..K. You need to map this vector into a 
+%               binary vector of 1's and 0's to be used with the neural network
+%               cost function.
+%
+%         Hint: We recommend implementing backpropagation using a for-loop
+%               over the training examples if you are implementing it for the 
+%               first time.
+%
+% Part 3: Implement regularization with the cost function and gradients.
+%
+%         Hint: You can implement this around the code for
+%               backpropagation. That is, you can compute the gradients for
+%               the regularization separately and then add them to Theta1_grad
+%               and Theta2_grad from Part 2.
+%
+
+% part 1
+
+X1 = [ones(m, 1) X];
+z2 = X1 * Theta1';
+a2 = sigmoid(z2);
+a2_1 = [ones(m, 1) a2];
+z3 = a2_1 * Theta2';
+a3 = sigmoid(z3);
+%sel = randperm(size(a3, 1));
+%sel = sel(1:20);
+%out = a3(sel,:)
+
+
+% This method uses an indexing trick to vectorize the creation of 'y_matrix', 
+% where each element of 'y' is mapped to a single-value row vector copied from an eye matrix.
+% check the notes in machine learning / resources /programming exercise 4 
+
+Theta1_no_bias = Theta1(:, 2:end);
+Theta2_no_bias = Theta2(:, 2:end);
+%sum(sum(Theta1_no_bias .^ 2))
+%sum(sum(Theta2_no_bias .^ 2))
+J_reg = lambda / (2 * m) * ...
+        (sum(sum(Theta1_no_bias .^ 2)) + sum(sum(Theta2_no_bias .^ 2)));
+
+
+y_matrix = eye(num_labels)(y,:);
+J = 1/m * sum(sum(-y_matrix .* log(a3) .- (1 .- y_matrix) .* log(1 - a3))) ...
+    + J_reg;
+
+
+% part 2
+%fprintf ('-> size a3=%f y=%f mask=%f \n', size(a3), size(y), size(mask));
+for t = 1: m
+endfor
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+% -------------------------------------------------------------
+
+% =========================================================================
+
+% Unroll gradients
+grad = [Theta1_grad(:) ; Theta2_grad(:)];
+
+
+end

machine learning/machine-learning-ex4/ex4/nnCostFunction.m

@@ -64,10 +64,10 @@ Theta2_grad = zeros(size(Theta2));
 
 % part 1
 
-X1 = [ones(rows(X), 1) X];
-z2 = X1 * Theta1';
+X1_1 = [ones(m, 1) X];
+z2 = X1_1 * Theta1';
 a2 = sigmoid(z2);
-a2_1 = [ones(rows(a2), 1) a2];
+a2_1 = [ones(m, 1) a2];
 z3 = a2_1 * Theta2';
 a3 = sigmoid(z3);
 %sel = randperm(size(a3, 1));
@@ -78,31 +78,61 @@ a3 = sigmoid(z3);
 % This method uses an indexing trick to vectorize the creation of 'y_matrix', 
 % where each element of 'y' is mapped to a single-value row vector copied from an eye matrix.
 % check the notes in machine learning / resources /programming exercise 4 
-%sel = randperm(size(X, 1));
-%sel = sel(1:20);
-%y = y(sel,:)
+
+Theta1_no_bias = Theta1(:, 2:end);
+Theta2_no_bias = Theta2(:, 2:end);
+%sum(sum(Theta1_no_bias .^ 2))
+%sum(sum(Theta2_no_bias .^ 2))
+J_reg = lambda / (2 * m) * ...
+        (sum(sum(Theta1_no_bias .^ 2)) + sum(sum(Theta2_no_bias .^ 2)));
+
 
 y_matrix = eye(num_labels)(y,:);
-J = 1/m * sum(sum(-y_matrix .* log(a3) .- (1 .- y_matrix) .* log(1 - a3)));
+J = 1/m * sum(sum(-y_matrix .* log(a3) .- (1 .- y_matrix) .* log(1 - a3))) ...
+    + J_reg;
 
 
 % part 2
-e3 = zeros(rows(y),1);
+delta2 = zeros(num_labels, hidden_layer_size + 1);
+delta1 = zeros(hidden_layer_size, input_layer_size + 1);
+Theta2T = Theta2(:, 2:end)';
 for t = 1: m
-  e3(t) = a3(t) .* y_matrix .- y_matrix;  
+  X1_1t = X1_1(t,:);
+  z2_t = X1_1t * Theta1';
+  % the next line is commented out because a2_t has
+  % already been computed above
+  %a2_t = sigmoid(z2_t);
   
-endfor
-
-
-
-
-
-
-
+  
+  a2_t = a2(t,:);
+  a2_1t = [1 a2_t];
+  % the next two lines are commented out because the values 
+  % are available from previous computations
+  %z3_t = a2_1t * Theta2';
+  %a3_t = sigmoid(z3_t);
+  
+  a3_t = a3(t,:);
 
+  d3_t = a3_t' - y_matrix(t,:)'; 
+  % remove bias in Theta2 
+  % refer to resources| programming ex.4 Step 7
+  
+  % the theta2 transpose is taken out of the loop
+  % to prevent it from being computed over and over 
+  %d2_t = Theta2(:, 2:end)' * d3_t .* sigmoidGradient(z2_t)';
+  d2_t =  Theta2T * d3_t .* sigmoidGradient(z2_t)';
+  
+  delta2 = delta2 + d3_t * a2_1t;
+  delta1 = delta1 + d2_t * X1_1t;
+  
+endfor
 
 
 
+reg1 = lambda / m * [zeros(rows(Theta1_no_bias), 1)  Theta1_no_bias];
+reg2 = lambda / m * [zeros(rows(Theta2_no_bias), 1)  Theta2_no_bias];
+Theta1_grad = 1/m * delta1 + reg1;
+Theta2_grad = 1/m * delta2 + reg2;
 
 
 

machine learning/machine-learning-ex4/ex4/predict.m

@@ -1,20 +1,20 @@
-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);
-
-h1 = sigmoid([ones(m, 1) X] * Theta1');
-h2 = sigmoid([ones(m, 1) h1] * Theta2');
-[dummy, p] = max(h2, [], 2);
-
-% =========================================================================
-
-
-end
+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);
+
+h1 = sigmoid([ones(m, 1) X] * Theta1');
+h2 = sigmoid([ones(m, 1) h1] * Theta2');
+[dummy, p] = max(h2, [], 2);
+
+% =========================================================================
+
+
+end

machine learning/machine-learning-ex4/ex4/randInitializeWeights.m

@@ -1,32 +1,32 @@
-function W = randInitializeWeights(L_in, L_out)
-%RANDINITIALIZEWEIGHTS Randomly initialize the weights of a layer with L_in
-%incoming connections and L_out outgoing connections
-%   W = RANDINITIALIZEWEIGHTS(L_in, L_out) randomly initializes the weights 
-%   of a layer with L_in incoming connections and L_out outgoing 
-%   connections. 
-%
-%   Note that W should be set to a matrix of size(L_out, 1 + L_in) as
-%   the first column of W handles the "bias" terms
-%
-
-% You need to return the following variables correctly 
-W = zeros(L_out, 1 + L_in);
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: Initialize W randomly so that we break the symmetry while
-%               training the neural network.
-%
-% Note: The first column of W corresponds to the parameters for the bias unit
-%
-epsilon_init = 0.12;
-W = rand(L_out, 1 + L_in) * 2 * epsilon_init - epsilon_init;
-
-
-
-
-
-
-
-% =========================================================================
-
-end
+function W = randInitializeWeights(L_in, L_out)
+%RANDINITIALIZEWEIGHTS Randomly initialize the weights of a layer with L_in
+%incoming connections and L_out outgoing connections
+%   W = RANDINITIALIZEWEIGHTS(L_in, L_out) randomly initializes the weights 
+%   of a layer with L_in incoming connections and L_out outgoing 
+%   connections. 
+%
+%   Note that W should be set to a matrix of size(L_out, 1 + L_in) as
+%   the first column of W handles the "bias" terms
+%
+
+% You need to return the following variables correctly 
+W = zeros(L_out, 1 + L_in);
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Initialize W randomly so that we break the symmetry while
+%               training the neural network.
+%
+% Note: The first column of W corresponds to the parameters for the bias unit
+%
+epsilon_init = 0.12;
+W = rand(L_out, 1 + L_in) * 2 * epsilon_init - epsilon_init;
+
+
+
+
+
+
+
+% =========================================================================
+
+end

machine learning/machine-learning-ex4/ex4/sigmoid.m

@@ -1,6 +1,6 @@
-function g = sigmoid(z)
-%SIGMOID Compute sigmoid functoon
-%   J = SIGMOID(z) computes the sigmoid of z.
-
-g = 1.0 ./ (1.0 + exp(-z));
-end
+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/machine-learning-ex4/ex4/sigmoidGradient.m

@@ -1,34 +1,34 @@
-function g = sigmoidGradient(z)
-%SIGMOIDGRADIENT returns the gradient of the sigmoid function
-%evaluated at z
-%   g = SIGMOIDGRADIENT(z) computes the gradient of the sigmoid function
-%   evaluated at z. This should work regardless if z is a matrix or a
-%   vector. In particular, if z is a vector or matrix, you should return
-%   the gradient for each element.
-
-g = zeros(size(z));
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: Compute the gradient of the sigmoid function evaluated at
-%               each value of z (z can be a matrix, vector or scalar).
-
-g = gradient(z) .* ( 1 .- gradient(z))
-
-
-
-
-
-
-
-
-
-
-
-
-
-% =============================================================
-
-
-
-
-end
+function g = sigmoidGradient(z)
+%SIGMOIDGRADIENT returns the gradient of the sigmoid function
+%evaluated at z
+%   g = SIGMOIDGRADIENT(z) computes the gradient of the sigmoid function
+%   evaluated at z. This should work regardless if z is a matrix or a
+%   vector. In particular, if z is a vector or matrix, you should return
+%   the gradient for each element.
+
+g = zeros(size(z));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the gradient of the sigmoid function evaluated at
+%               each value of z (z can be a matrix, vector or scalar).
+sz = sigmoid(z); 
+g =  sz .* ( 1 .- sz);
+
+
+
+
+
+
+
+
+
+
+
+
+
+% =============================================================
+
+
+
+
+end

machine learning/machine-learning-ex4/ex4/submit.m

@@ -1,63 +1,63 @@
-function submit()
-  addpath('./lib');
-
-  conf.assignmentSlug = 'neural-network-learning';
-  conf.itemName = 'Neural Networks Learning';
-  conf.partArrays = { ...
-    { ...
-      '1', ...
-      { 'nnCostFunction.m' }, ...
-      'Feedforward and Cost Function', ...
-    }, ...
-    { ...
-      '2', ...
-      { 'nnCostFunction.m' }, ...
-      'Regularized Cost Function', ...
-    }, ...
-    { ...
-      '3', ...
-      { 'sigmoidGradient.m' }, ...
-      'Sigmoid Gradient', ...
-    }, ...
-    { ...
-      '4', ...
-      { 'nnCostFunction.m' }, ...
-      'Neural Network Gradient (Backpropagation)', ...
-    }, ...
-    { ...
-      '5', ...
-      { 'nnCostFunction.m' }, ...
-      'Regularized Gradient', ...
-    }, ...
-  };
-  conf.output = @output;
-
-  submitWithConfiguration(conf);
-end
-
-function out = output(partId, auxstring)
-  % Random Test Cases
-  X = reshape(3 * sin(1:1:30), 3, 10);
-  Xm = reshape(sin(1:32), 16, 2) / 5;
-  ym = 1 + mod(1:16,4)';
-  t1 = sin(reshape(1:2:24, 4, 3));
-  t2 = cos(reshape(1:2:40, 4, 5));
-  t  = [t1(:) ; t2(:)];
-  if partId == '1'
-    [J] = nnCostFunction(t, 2, 4, 4, Xm, ym, 0);
-    out = sprintf('%0.5f ', J);
-  elseif partId == '2'
-    [J] = nnCostFunction(t, 2, 4, 4, Xm, ym, 1.5);
-    out = sprintf('%0.5f ', J);
-  elseif partId == '3'
-    out = sprintf('%0.5f ', sigmoidGradient(X));
-  elseif partId == '4'
-    [J, grad] = nnCostFunction(t, 2, 4, 4, Xm, ym, 0);
-    out = sprintf('%0.5f ', J);
-    out = [out sprintf('%0.5f ', grad)];
-  elseif partId == '5'
-    [J, grad] = nnCostFunction(t, 2, 4, 4, Xm, ym, 1.5);
-    out = sprintf('%0.5f ', J);
-    out = [out sprintf('%0.5f ', grad)];
-  end 
-end
+function submit()
+  addpath('./lib');
+
+  conf.assignmentSlug = 'neural-network-learning';
+  conf.itemName = 'Neural Networks Learning';
+  conf.partArrays = { ...
+    { ...
+      '1', ...
+      { 'nnCostFunction.m' }, ...
+      'Feedforward and Cost Function', ...
+    }, ...
+    { ...
+      '2', ...
+      { 'nnCostFunction.m' }, ...
+      'Regularized Cost Function', ...
+    }, ...
+    { ...
+      '3', ...
+      { 'sigmoidGradient.m' }, ...
+      'Sigmoid Gradient', ...
+    }, ...
+    { ...
+      '4', ...
+      { 'nnCostFunction.m' }, ...
+      'Neural Network Gradient (Backpropagation)', ...
+    }, ...
+    { ...
+      '5', ...
+      { 'nnCostFunction.m' }, ...
+      'Regularized Gradient', ...
+    }, ...
+  };
+  conf.output = @output;
+
+  submitWithConfiguration(conf);
+end
+
+function out = output(partId, auxstring)
+  % Random Test Cases
+  X = reshape(3 * sin(1:1:30), 3, 10);
+  Xm = reshape(sin(1:32), 16, 2) / 5;
+  ym = 1 + mod(1:16,4)';
+  t1 = sin(reshape(1:2:24, 4, 3));
+  t2 = cos(reshape(1:2:40, 4, 5));
+  t  = [t1(:) ; t2(:)];
+  if partId == '1'
+    [J] = nnCostFunction(t, 2, 4, 4, Xm, ym, 0);
+    out = sprintf('%0.5f ', J);
+  elseif partId == '2'
+    [J] = nnCostFunction(t, 2, 4, 4, Xm, ym, 1.5);
+    out = sprintf('%0.5f ', J);
+  elseif partId == '3'
+    out = sprintf('%0.5f ', sigmoidGradient(X));
+  elseif partId == '4'
+    [J, grad] = nnCostFunction(t, 2, 4, 4, Xm, ym, 0);
+    out = sprintf('%0.5f ', J);
+    out = [out sprintf('%0.5f ', grad)];
+  elseif partId == '5'
+    [J, grad] = nnCostFunction(t, 2, 4, 4, Xm, ym, 1.5);
+    out = sprintf('%0.5f ', J);
+    out = [out sprintf('%0.5f ', grad)];
+  end 
+end

machine learning/machine-learning-ex4/ex4/token.mat

@@ -0,0 +1,15 @@
+# Created by Octave 4.2.2, Sun Nov 18 21:18:53 2018 HKT <astron@astron>
+# name: email
+# type: sq_string
+# elements: 1
+# length: 20
+larry1chan@gmail.com
+
+
+# name: token
+# type: sq_string
+# elements: 1
+# length: 16
+QUO3ko3qZlFGChct
+
+