一、ex4.m

%% 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 %400 input units
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)); %置乱
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 = 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);

二、nnCostFunction.m

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); % m% You need to return the following variables correctly
J = 0; % 1*1
Theta1_grad = zeros(size(Theta1)); % hidden_layer_size*1
Theta2_grad = zeros(size(Theta2)); % num_labels*1% ====================== 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.
%X = [ones(m, 1), X]; % add ones m*(n+1)
a1 = X;
z2 = Theta1 * X' ;
a2 = sigmoid(z2);a2 = [ones(m, 1), a2'];
z3 = Theta2 * a2';
a3 = sigmoid(z3);h = a3; % m*k
y_temp = zeros(num_labels, m); for i = 1:m
y_temp(y(i), i) = 1;
endpart1 = y_temp .* log(h);
part2 = (1-y_temp) .* log((1-h));
sum1 = sum(sum(-part1 - part2));
J_ori = sum1 / m;% regularized cost function
punish_Theta1 = sum(sum(Theta1(:, 2:end).^2));
punish_Theta2 = sum(sum(Theta2(:, 2:end).^2));J = J_ori + lambda/2/m*(punish_Theta1 + punish_Theta2);%BP
for t = 1:m
a1 = X(t, :);
z2 = Theta1 * a1';
a2 = sigmoid(z2);
a2 = [1; a2];z3 = Theta2 * a2;
a3 = sigmoid(z3);z2 = [1;  z2];delta3 = a3 - y_temp(:, t);
delta2 = (Theta2' * delta3) .* sigmoidGradient(z2);
delta2 = delta2(2:end);Theta2_grad = Theta2_grad + delta3 * a2';
Theta1_grad = Theta1_grad + delta2 * a1;
end
Theta2_grad = Theta2_grad / m;
Theta1_grad = Theta1_grad / m;% Regularized
reg_theta1 = Theta1(:, 2:end) * lambda/m;
reg_theta2 = Theta2(:, 2:end) * lambda/m;Theta1_grad(:, 2:end) = Theta1_grad(:, 2:end) + reg_theta1;
Theta2_grad(:, 2:end) = Theta2_grad(:, 2:end) + reg_theta2;% -------------------------------------------------------------% =========================================================================% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];end

三、sigmoidGradient.m

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)); % the same size with 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).h = sigmoid(z);
g = h .* (1-h);% =============================================================end

四、submit results

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Machine Learning week 5 quiz: programming assignment-Multi-Neural Network Learning

一、ex4.m

二、nnCostFunction.m

三、sigmoidGradient.m

四、submit results

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