机器学习(Andrew Ng)作业代码

Programming Exercise 1: Linear Regression

单变量线性回归

warmUpExercise

要求：输出5阶单位阵
直接使用eye(5,5)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(5,5);

% ===========================================
end

plotData

要求：读入若干组数据(x,y)，将它们绘制成散点图

使用MATLAB的plot()命令即可

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.

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

    figure; % open a new figure window

    data=load('ex1data1.txt');
    [n,m]=size(data);
    xdata=data(:,1);
    ydata=data(:,2);
    for i=1:n
        plot(xdata,ydata,'rx');
    end
    xlabel('X Axis');
    ylabel('Y Axis');
% ============================================================
end

输出结果：

computeCost

要求：读入\(m\)组数据(X,y)，计算用\(y=\theta^T X(\theta=(\theta_0,\theta_1)^T,X=(1,x^{(i)})^T)\)拟合这组数据的均方误差\(J(\theta)\)

\[J(\theta)=\frac 1 {2m}\sum_{i=1}^m(\theta^T X^{(i)}-y^{(i)})^2\]

function J = computeCost(X, y, theta)
%传入:X,y为m维行向量，theta为二维列向量
%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.

    for i=1:m
        J=J+(theta'*[1,X(i)]'-y(i))^2;
    end

    J=J/(2*m);

% =========================================================================
end