吳恩達機器學習編程作業與筆記（1）第2周：Linear Regression 線性迴歸

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這裏涉及到5個文件

warmUpExercise.m

這個是用來練手的，在代碼區生成一個單位矩陣，即A=eye(5)即可

function A = warmUpExercise()
%WARMUPEXERCISE Example function in octave
%   A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix

A = [];
% ============= YOUR CODE HERE ==============
% Instructions: Return the 5x5 identity matrix 
%               In octave, we return values by defining which variables
%               represent the return values (at the top of the file)
%               and then set them accordingly. 
  A=eye(5);
% ===========================================


end

ex1.m

這個文件是用於在練習過程中觀察變化用的，在開始的時候，在命令行中輸入

ex1()

此時，程序運行後，你會多次暫停，每次暫停，完成相應文件的編程

plotData.m

先將數據畫成圖檢查一下

function plotData(x, y)
%PLOTDATA Plots the data points x and y into a new figure 
%   PLOTDATA(x,y) plots the data points and gives the figure axes labels of
%   population and profit.

figure; % open a new figure window

% ====================== YOUR CODE HERE ======================
% Instructions: Plot the training data into a figure using the 
%               "figure" and "plot" commands. Set the axes labels using
%               the "xlabel" and "ylabel" commands. Assume the 
%               population and revenue data have been passed in
%               as the x and y arguments of this function.
%
% Hint: You can use the 'rx' option with plot to have the markers
%       appear as red crosses. Furthermore, you can make the
%       markers larger by using plot(..., 'rx', 'MarkerSize', 10);
plot(x, y, 'rx', 'MarkerSize', 10); 
ylabel('Profit in $10,000s'); 
xlabel('Population of City in 10,000s'); 
% ============================================================

end

computeCost.m

計算cost function

function J = computeCost(X, y, theta)
%COMPUTECOST Compute cost for linear regression
%   J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
%   parameter for linear regression to fit the data points in X and y

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

% You need to return the following variables correctly 
J = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
%               You should set J to the cost.
J = sum((X*theta-y).^2)/(2*m);
% =========================================================================

end

gradientDescent.m

梯度下降算法

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by 
%   taking num_iters gradient steps with learning rate alpha

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

    % ====================== YOUR CODE HERE ======================
    % Instructions: Perform a single gradient step on the parameter vector
    %               theta. 
    %
    % Hint: While debugging, it can be useful to print out the values
    %       of the cost function (computeCost) and gradient here.
    %
    theta(1) = theta(1) - alpha*sum(X*temp-y)/m;
    theta(2) = theta(2) - alpha*sum((X*temp-y).*X(:,2))/m;
    temp = theta;
    % ============================================================

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

end

end