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  • 第三次作业

    function [J, grad] = lrCostFunction(theta, X, y, lambda)
    %LRCOSTFUNCTION Compute cost and gradient for logistic regression with 
    %regularization
    %   J = LRCOSTFUNCTION(theta, X, y, lambda) computes the cost of using
    %   theta as the parameter for regularized logistic regression and the
    %   gradient of the cost w.r.t. to the parameters. 
    
    % Initialize some useful values
    m = length(y); % number of training examples
    
    % You need to return the following variables correctly 
    J = 0;
    grad = zeros(size(theta));%grad 和theta 的维度一致
    
    % ====================== YOUR CODE HERE ======================
    % Instructions: Compute the cost of a particular choice of theta.
    %               You should set J to the cost.
    %               Compute the partial derivatives and set grad to the partial
    %               derivatives of the cost w.r.t. each parameter in theta
    %
    % Hint: The computation of the cost function and gradients can be
    %       efficiently vectorized. For example, consider the computation
    %
    %           sigmoid(X * theta)
    %
    %       Each row of the resulting matrix will contain the value of the
    %       prediction for that example. You can make use of this to vectorize
    %       the cost function and gradient computations. 
    %
    % Hint: When computing the gradient of the regularized cost function, 
    %       there're many possible vectorized solutions, but one solution
    %       looks like:
    %           grad = (unregularized gradient for logistic regression)
    %           temp = theta; 
    %           temp(1) = 0;   % because we don't add anything for j = 0  
    %           grad = grad + YOUR_CODE_HERE (using the temp variable)
    %
    
    
    
    h_theta = sigmoid(X * theta);    
    J = (-y' * log(h_theta) - (1 - y)' * log(1 - h_theta)) / m +  lambda * (sum(theta(2:end).^2 )) / (2 * m); %同样这里不需要计算theta(1)
    %grad = (X' * (h_theta - y) + theta * lambda) / m;
    %grad(1)=grad(1)-theta(1)*lambda/m;
    
    grad = (X' * (h_theta - y) + ([0;theta(2:end)])* lambda) / m;%theta(1)=0,
    %0;theta(2:end) 0后面是;
    
    
    % =============================================================
    
    %grad = grad(:);吧grad转化为向量,这句代码加不加都可以
    
    end
    function [all_theta] = oneVsAll(X, y, num_labels, lambda)
    %ONEVSALL trains multiple logistic regression classifiers and returns all
    %the classifiers in a matrix all_theta, where the i-th row of all_theta 
    %corresponds to the classifier for label i
    %   [all_theta] = ONEVSALL(X, y, num_labels, lambda) trains num_labels
    %   logistic regression classifiers and returns each of these classifiers
    %   in a matrix all_theta, where the i-th row of all_theta corresponds 
    %   to the classifier for label i
    
    % Some useful variables
    m = size(X, 1);
    n = size(X, 2);
    
    % You need to return the following variables correctly 
    all_theta = zeros(num_labels, n + 1);
    
    % Add ones to the X data matrix
    X = [ones(m, 1) X];
    
    % ====================== YOUR CODE HERE ======================
    % Instructions: You should complete the following code to train num_labels
    %               logistic regression classifiers with regularization
    %               parameter lambda. 
    %
    % Hint: theta(:) will return a column vector.
    %
    % Hint: You can use y == c to obtain a vector of 1's and 0's that tell you
    %       whether the ground truth is true/false for this class.
    %
    % Note: For this assignment, we recommend using fmincg to optimize the cost
    %       function. It is okay to use a for-loop (for c = 1:num_labels) to
    %       loop over the different classes.
    %
    %       fmincg works similarly to fminunc, but is more efficient when we
    %       are dealing with large number of parameters.
    %
    % Example Code for fmincg:
    %
    %     % Set Initial theta
    %     initial_theta = zeros(n + 1, 1);
    %     
    %     % Set options for fminunc
    %     options = optimset('GradObj', 'on', 'MaxIter', 50);
    % 
    %     % Run fmincg to obtain the optimal theta
    %     % This function will return theta and the cost 
    %     [theta] = ...
    %         fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), ...
    %                 initial_theta, options);
    %
    
    
    for c=1:num_labels,
        % 传入 lrCostFunction() 里的 theta 是列向量,所以 all_theta(c,:)'
        all_theta(c,:)=fmincg(@(t)(lrCostFunction(t, X, (y==c), lambda)), all_theta(c,:)', options)';%2个转置
    end
    
    % =========================================================================
    
    
    end
    function p = predictOneVsAll(all_theta, X)
    %PREDICT Predict the label for a trained one-vs-all classifier. The labels 
    %are in the range 1..K, where K = size(all_theta, 1). 
    %  p = PREDICTONEVSALL(all_theta, X) will return a vector of predictions
    %  for each example in the matrix X. Note that X contains the examples in
    %  rows. all_theta is a matrix where the i-th row is a trained logistic
    %  regression theta vector for the i-th class. You should set p to a vector
    %  of values from 1..K (e.g., p = [1; 3; 1; 2] predicts classes 1, 3, 1, 2
    %  for 4 examples) 
    
    m = size(X, 1);
    num_labels = size(all_theta, 1);
    
    % You need to return the following variables correctly 
    p = zeros(size(X, 1), 1);
    
    % Add ones to the X data matrix
    X = [ones(m, 1) X];
    
    % ====================== YOUR CODE HERE ======================
    % Instructions: Complete the following code to make predictions using
    %               your learned logistic regression parameters (one-vs-all).
    %               You should set p to a vector of predictions (from 1 to
    %               num_labels).
    %
    % Hint: This code can be done all vectorized using the max function.
    %       In particular, the max function can also return the index of the 
    %       max element, for more information see 'help max'. If your examples 
    %       are in rows, then, you can use max(A, [], 2) to obtain the max 
    %       for each row.
    %       
    
    index=0;
    pre=zeros(num_labels,1);
    for i=1:m,
        for d=1:num_labels,
            pre(d)=sigmoid(X(i,:)*(all_theta(d,:)'));
        end
        [maxnum index]=max(pre);%index=pre里的最大值
        p(i)=index;
    end
    % =========================================================================
    
    
    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);
    %为a1 添加为1的偏置,不然a2=sigmoid(Theta1*X(i,:)')维度不匹配
    X=[ones(m,1) X]; 
    
    % You need to return the following variables correctly 
    p = zeros(size(X, 1), 1);
    
    % ====================== YOUR CODE HERE ======================
    % Instructions: Complete the following code to make predictions using
    %               your learned neural network. You should set p to a 
    %               vector containing labels between 1 to num_labels.
    %
    % Hint: The max function might come in useful. In particular, the max
    %       function can also return the index of the max element, for more
    %       information see 'help max'. If your examples are in rows, then, you
    %       can use max(A, [], 2) to obtain the max for each row.
    %
    index=0;
    for i=1:m,
        a2=sigmoid(Theta1*X(i,:)');
        a2=[1;a2];%加1的偏置
        a3=sigmoid(Theta2*a2);
        [maxnum index]=max(a3);
        p(i)=index;
    end
    
    
    % =========================================================================
    
    
    end
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  • 原文地址:https://www.cnblogs.com/tingtin/p/12112274.html
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