%% 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);    

sel(1:100); 1 2 3 4 5 ...100

a = X(sel, :);

X(sel, :); 
1.......
2.......
3.......
4.......
5.......
.
.
.
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(:)];

https://www.cnblogs.com/liu-wang/p/9466123.html

%% ================ 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 = 10): %f \' ...
\'\n(this value should be about 0.576051)\n\n\'], 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);