octave 通用线性回归模型计算 机器学习

00 [机器学习: octave 通用线性回归模型计算].md

octave 通用线性回归模型计算

generalCompute.m

function [result] =  generalCompute(X, y, alpha, num_iters,targetX)

    X_original = X; % 留一个副本

    m = length(y);

    % 选择参数
    theta = zeros(size(X,2) + 1, 1); % 参数

    % 数据收缩, 下面的mu和sigma可以在最后预测时用上，对targetX进行收缩
    [X mu sigma] = featureGeneralNormalize(X); 

    % Add intercept term to X | 在第一列加上1
    X = [ones(m, 1) X];


    % 执行梯度算法
    [theta, J_history] = gradientGeneral(X, y, theta, alpha, num_iters, targetX);


    % 绘制点图 
    figure;
    plot(X_original, y, 'rx', 'MarkerSize', 10); %% 绘制点图的时候取原始数据
    xlabel('x');
    ylabel('y ');
    

    % Plot the linear fit
    hold on; % keep previous plot visible
    %% 这里有问题 ??? 为何是X * theta 而不是X_original * theta 
    plot(X_original, X * theta , '-b'); %% 绘制直线图的时候取原始数据
    legend('Training data', 'Linear regression')
    hold off % don't overlay any more plots on this figure

    % Plot the convergence graph | 绘制趋势图
    figure;
    plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);
    xlabel('Number of iterations');
    ylabel('Cost J');


    % Grid over which we will calculate J
    %theta0_vals = linspace(-10, 10, 100);
    %theta1_vals = linspace(-1, 4, 100);
    %theta2_vals = linspace(-1, 4, 100);


    % Surface plot  | 曲面图
    %figure;
    %surf(theta, J_history);
    %xlabel('\theta_0'); ylabel('\theta_1');

    % Contour plot | 轮廓图 等高线图
    %figure;
    % Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100
    %contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
    %xlabel('\theta_0'); ylabel('\theta_1');
    %hold on;
    %plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);


    % 显示预测结果

    %% 这里有问题 ？？？ 结果和直线直觉不符合
    
    
    %targetX = featureGeneralNormalize(targetX);
    targetX = (targetX - mu)./sigma;
    targetX = [1 targetX ];  %% 前面加一列 1
    price =  targetX * theta; 
    disp('the result is: '),disp(price);

    result = price;

end

% ============================================================

%% 梯度下降
function [theta, J_history] = gradientGeneral(X, y, theta_p, alpha, num_iters)

    % Initialize some useful values
    m = length(y); % number of training examples
    J_history = zeros(num_iters, 1);

    theta = theta_p;

    for iter = 1:num_iters

        %vectorized version 
        % below two are equal 
        %delta = ((theta' * X' - y')*X)'; 
        delta = X' * (X * theta - y);
       
        %fprintf('Delta : %f', delta);
        theta = theta - alpha / m * delta;

        % Save the cost J in every iteration    
        J_history(iter) = computeCostGeneral(X, y, theta);

    end

end

% ============================================================

% cost function 
function J = computeCostGeneral(X, y, theta)

    % Initialize some useful values
    m = length(y); % number of training examples

    % 预测函数
    predictions = X * theta ;

    % the squared errors should be as usual
    sqrErrors = (predictions - y) .^ 2;

    % the result of the function is as it is defined regularly.
    %J = (1/(2*m)) * sum(sqrErrors);

    %fprintf('J : %f', J);

    % 向量化的版本
    J = 1/(2 * m) * (X * theta - y)' * (X * theta - y);



end

% ============================================================

%% 维度缩放
function [X_norm, mu, sigma] = featureGeneralNormalize(X)

    % You need to set these values correctly
    X_norm = X;
    %mu = zeros(1, size(X, 2));
    %sigma = zeros(1, size(X, 2));


    mu    = mean(X);
    sigma = std(X);

    indicies = 1:size(X, 2);



    %for i = indicies,
    %  XminusMu  = X(:, i) - mu(i);
    %  X_norm(:, i) = XminusMu / sigma(i);
      %X_norm(:, i) = (X(:,i) - mu(1,i))/sigma(1,i);  %% see the blog ,don't understand 
    %end

    X_norm = (X - mu) ./ sigma;


    % ============================================================

end




% ============================================================