机器学习编程作业（exe4）总结

怼烎@ 2022-05-18 06:09 173阅读 0赞

%% 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;

![70][]

%% ================ 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 
    % 参数从矩阵展开成向量
    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;

前向传播算法：

![70 1][]

![70 2][]

![70 3][]

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
    X = [ones(m, 1) X];
    ylabel = zeros(num_labels, m);
    for i=1:m
        ylabel(y(i), i) = 1;
    end
    % 前向传播算法
    z2 = X*Theta1';
    z2 = [ones(m, 1) z2];
    a2 = sigmoid(X*Theta1');
    a2 = [ones(m, 1) a2];
    a3 = sigmoid(a2*Theta2');
    
    % 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.
    % 编写计算代价函数的代码
    for i=1:m
        J = J - log(a3(i, :))*ylabel(:, i) - (log(1 - a3(i, :)) * (1 - ylabel(:, i)));
    end
    J = J/m;
    
    J = J + lambda/2/m * (sum(sum(Theta1(:, 2:end).^2)) + sum(sum(Theta2(:, 2:end).^2)));
    
    % 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.
    %
    Delta1 = zeros(size(Theta1));
    Delta2 = zeros(size(Theta2));
    for t = 1:m
        delta3 = a3(t, :)' - ylabel(:, t);
        delta2 = Theta2'*delta3 .* sigmoidGradient(z2(t, :)');
    
        Delta1 = Delta1 + delta2(2:end) * X(t, :);
        Delta2 = Delta2 + delta3 * a2(t, :);
    end
    
    Theta1_grad = Delta1 / m;
    Theta1_grad(:, 2:end) = Theta1_grad(:, 2:end) + lambda/m*Theta1(:, 2:end);
    Theta2_grad = Delta2 / m;
    Theta2_grad(:, 2:end) = Theta2_grad(:, 2:end) + lambda/m*Theta2(:, 2:end);
    % -------------------------------------------------------------
    
    % =========================================================================
    
    % Unroll gradients
    grad = [Theta1_grad(:) ; Theta2_grad(:)];
    
    
    end

%% =============== 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;

![70 4][]

%% ================ 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;

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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
    % 初始参数
    % sqrt(6)/sqrt(L_out+L_in)
    epsilon = 0.12;
    W = rand(L_out, 1+L_in)*2*epsilon - epsilon;
    
    % =========================================================================
    
    end

%% ================ 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(:)];

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%% =============== 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);

Part 9:运行结果：

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[70]: /images/20220518/faa98682ed3647cdafc2b0155790b340.png
[70 1]: /images/20220518/a158013a57b3486aadda6a9d8febdffc.png
[70 2]: /images/20220518/0f28a57deaff42aebcef95ed109e4aa6.png
[70 3]: /images/20220518/8afb693b7d484cd9a05b787704bdee88.png
[70 4]: /images/20220518/a7a6d19e60fb494eb98b916366074729.png
[70 5]: /images/20220518/1356af506dc04a5bb266e485aa4865f8.png
[70 6]: /images/20220518/8d234bf0b66d4b90b9d4af2b2f810b26.png
[70 7]: /images/20220518/d4e6d47a57b1489eb51ceffb2430218d.png