题目为:使用有多个变量的线性回归来预测房屋的价格。ex1data2.txt 房屋价格的训练集. 第一列为房屋面积,第二列为房屋中的房间数量,第三列为实际的价格。
预测X_p=[1650 3];的价格
1. 首先由于x1和x2相差太多,所以需要使用feature scalling. 这里采用mean derivation. 或者是max-min
function [X_norm, mu, sigma] = featureNormalize(X)
%FEATURENORMALIZE Normalizes the features in X
% FEATURENORMALIZE(X) returns a normalized version of X where
% the mean value of each feature is 0 and the standard deviation
% is 1. This is often a good preprocessing step to do when
% working with learning algorithms.
% You need to set these values correctly
X_norm = X;
disp(size(X_norm));
m = size(X,1);
mu = zeros(1, size(X, 2));
sigma = zeros(1, size(X, 2));
mu = mean(X);
sigma = std(X);
disp('mu'),disp(mu);
disp('sigma'),disp(sigma);
for i=1:m;
X_norm(i,:) = (X(i,:)-mu )./ sigma;
end;
%disp('X_norm'),disp(X_norm);
function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
%GRADIENTDESCENTMULTI Performs gradient descent to learn theta
% theta = GRADIENTDESCENTMULTI(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);
for iter = 1:num_iters
h= zeros(m,1);
disp('computeCostMulti');
J_history(iter) = computeCostMulti(X, y, theta);%只是为了展示J的变化,计算实际的值时可以不需要
h=X*theta; %计算hypothesis function
tmp1 = zeros(size(X,2),1);
for i=1:m
tmp1= tmp1+(h(i)-y(i)).*X(i,:)'; %计算sum((hi-yi)*xi)
end;
theta = theta - (alpha/m)*tmp1;%计算Jtheta
disp(J_history(iter));
disp(theta);
end;
function J = computeCostMulti(X, y, theta)
%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
% J = COMPUTECOSTMULTI(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;
h= zeros(m,1);
h = X*theta;
J = (1/(2*m))*sum((h-y).^2);
disp('J'),disp(J);
function [theta] = normalEqn(X, y)
%NORMALEQN Computes the closed-form solution to linear regression
% NORMALEQN(X,y) computes the closed-form solution to linear
% regression using the normal equations.
theta = zeros(size(X, 2), 1);
theta = pinv(X'*X)*X'*y;
%% Machine Learning Online Class
% Exercise 1: Linear regression with multiple variables
%% Initialization
%% ================ Part 1: Feature Normalization ================
%% Clear and Close Figures
clear ; close all; clc
fprintf('Loading data ...\n');
%% Load Data
data = load('ex1data2.txt');
X = data(:, 1:2);
y = data(:, 3);
m = length(y);
% Print out some data points
fprintf('First 10 examples from the dataset: \n');
fprintf(' x = [%.0f %.0f], y = %.0f \n', [X(1:10,:) y(1:10,:)]');
% Scale features and set them to zero mean
fprintf('Normalizing Features ...\n');
[X mu sigma] = featureNormalize(X);
% Add intercept term to X
X = [ones(m, 1) X];
%% ================ Part 2: Gradient Descent ================
fprintf('Running gradient descent ...\n');
% Choose some alpha value
alpha = 0.01;
num_iters = 400;
% Init Theta and Run Gradient Descent
theta = zeros(3, 1);
[theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);
% Plot the convergence graph
figure;
plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);
xlabel('Number of iterations');
ylabel('Cost J');
% Display gradient descent's result
fprintf('Theta computed from gradient descent: \n');
fprintf(' %f \n', theta);
fprintf('\n');
% Estimate the price of a 1650 sq-ft, 3 br house
price = 0; % You should change this
X_p=[1650 3];
X_p = (X_p - mu)./sigma;
X_p = [1 X_p];
price = theta'*X_p';
% ============================================================
fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
'(using gradient descent):\n $%f\n'], price);
%% ================ Part 3: Normal Equations ================
fprintf('Solving with normal equations...\n');
%% Load Data
data = csvread('ex1data2.txt');
X = data(:, 1:2);
y = data(:, 3);
m = length(y);
% Add intercept term to X
X = [ones(m, 1) X];
% Calculate the parameters from the normal equation
theta = normalEqn(X, y);
% Display normal equation's result
fprintf('Theta computed from the normal equations: \n');
fprintf(' %f \n', theta);
fprintf('\n');
% Estimate the price of a 1650 sq-ft, 3 br house
price = 0; % You should change this
X_p=[1650 3];
X_p = [1 X_p];
disp(X_p');
price = theta'*X_p';
% ============================================================
fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
'(using normal equations):\n $%f\n'], price);
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