吳恩達機器學習配套第一次編程練習（代碼+學習記錄）（Octave/Matlab）

吳恩達機器學習配套編程練習第一週（Octave/Matlab）

本文僅供個人學習記錄，儘量寫的詳細，可供參考

（注：吳恩達課程的練習只需要再他所給的一個個函數文件中增添代碼，最後運行‘主函數（ex.m）’文件即可

%% Machine Learning Online Class - Exercise 1: Linear Regression

%  Instructions
%  ------------
% 
%  This file contains code that helps you get started on the
%  linear exercise. You will need to complete the following functions 
%  in this exericse:
%
%     warmUpExercise.m
%     plotData.m
%     gradientDescent.m
%     computeCost.m
%     gradientDescentMulti.m
%     computeCostMulti.m
%     featureNormalize.m
%     normalEqn.m
%
%  For this exercise, you will not need to change any code in this file,
%  or any other files other than those mentioned above.
%
% x refers to the population size in 10,000s
% y refers to the profit in $10,000s
%

註釋介紹如圖，大概就包括了上面幾個Octave函數文件，本次分爲兩個任務，第一個是單變量的線性線性迴歸和多變量線性迴歸，其主文件對應作業包中的ex1.m和ex1_multi.m

首先第一步利用他所提供的數據文件，進行圖片繪製

%% ======================= Part 2: Plotting =======================
fprintf('Plotting Data ...\n')
data = load('ex1data1.txt');
X = data(:, 1); y = data(:, 2);
m = length(y); % number of training examples

% Plot Data
% Note: You have to complete the code in plotData.m
plotData(X, y);

讀取文件用X存第一列數據，y存第二列，m爲訓練集的個數，最後調用plotData函數，如圖

function plotData(x, y)

    figure; % open a new figure window
    plot(x, y, 'rx', 'MarkerSize', 10); % Plot the data
    ylabel('Profit in $10,000s'); % Set the y   axis label
    xlabel('Population of City in 10,000s'); % Set the x   axis label

end

其中可能不明白意思我解釋一下plot中 ‘rx’表示用紅色的叉叉來描點，然後markersize標記大小爲10

畫出來大概這樣

接着我們要運行梯度下降算法來找出一條直線擬合這些數據，來看主函數體中的第二步要求我們做什麼

%% =================== Part 3: Gradient descent ===================
fprintf('Running Gradient Descent ...\n')

X = [ones(m, 1), data(:,1)]; % Add a column of ones to x
theta = zeros(2, 1); % initialize fitting parameters

% Some gradient descent settings
iterations = 1500;
alpha = 0.01;

% compute and display initial cost
computeCost(X, y, theta)

% run gradient descent
theta = gradientDescent(X, y, theta, alpha, iterations);

% print theta to screen
fprintf('Theta found by gradient descent: ');
fprintf('%f %f \n', theta(1), theta(2));

其中我們只需要修改computeCost和gradientDescent函數即可

function J = computeCost(X, y, theta)

    J = 0;

    J = sum((X * theta - y).^2) / (2*m);     % X(79,2)  theta(2,1)

end

對應公式應該不難寫出

再看gradientDescent函數

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)

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


for iter = 1:num_iters
    theta(1) = theta(1) - alpha / m * sum(X * theta_s - y);       
    theta(2) = theta(2) - alpha / m * sum((X * theta_s - y) .* X(:,2));	

 
    J_history(iter) = computeCost(X, y, theta);

end
J_history %打印顯示

end

同樣根據課上所講的梯度下降公式，對應公式直接寫出來，進行num_iters次的迭代不斷更新theta並且再J_history中記錄下每次迭代的Cost。接着我們開始繪圖

% Plot the linear fit
hold on; % keep previous plot visible
plot(X(:,2), X*theta, 'g-')
legend('Training data', 'Linear regression')
hold off % don't overlay any more plots on this figure

成功擬合訓練集數據的直線大概長這樣

接着我們就需要用兩個新數據來預測下

% Predict values for population sizes of 35,000 and 70,000
predict1 = [1, 3.5] *theta;
fprintf('For population = 35,000, we predict a profit of %f\n',
    predict1*10000);
predict2 = [1, 7] * theta;
fprintf('For population = 70,000, we predict a profit of %f\n',
    predict2*10000);

fprintf('Program paused. Press enter to continue.\n');
pause;

運行之後得到結果

預測數據成功

最後我們用三維圖像和等高線來可視化J函數（數學意義上的函數）看看，注意函數的參數應該是theta0和theta1

%% ============= Part 4: Visualizing J(theta_0, theta_1) =============
fprintf('Visualizing J(theta_0, theta_1) ...\n')

% Grid over which we will calculate J
theta0_vals = linspace(-10, 10, 100);%linespace講-10到10分成100等分，也就是一個1X100的行向量
theta1_vals = linspace(-1, 4, 100);%類似

% initialize J_vals to a matrix of 0's
J_vals = zeros(length(theta0_vals), length(theta1_vals));%初始化一個空的J_vals矩陣

% Fill out J_vals
for i = 1:length(theta0_vals)
    for j = 1:length(theta1_vals)
	  t = [theta0_vals(i); theta1_vals(j)];    
	  J_vals(i,j) = computeCost(X, y, t);%對每一個theta0 theta1進行代價計算並記錄
    end
end


% Because of the way meshgrids work in the surf command, we need to 
% transpose J_vals before calling surf, or else the axes will be flipped
J_vals = J_vals';%轉置，surf函數的要求。
% Surface plot
figure;
surf(theta0_vals, theta1_vals, J_vals)
xlabel('\theta_0'); ylabel('\theta_1');

% Contour plot 等高線繪製，看看就行了，吳恩達的作業要求也只是要我們看懂就行，如果函數不懂的可以用help XXX來查閱
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', 20);

我把解釋寫在了代碼中，最後繪圖結果：

單變量的線性迴歸就這樣了，其實多變量的線性迴歸很類似