http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=MachineLearning&doc=exercises/ex2/ex2.html
练习1 的作业 ：
我使用的 Octave ，
Understanding
We'd like to understand better what gradient descent has done, and visualize the relationship between the parameters and
. In this problem, we'll plot
as a 3D surface plot. (When applying learning algorithms, we don't usually try to plot
since usually
is very high-dimensional so that we don't have any simple way to plot or visualize
. But because the example here uses a very low dimensional
, we'll plot
to gain more intuition about linear regression.) Recall that the formula for
is
程序如下：
x = load('C:/Users/samsung/Desktop/ex2Data/ex2x.dat');
y = load('C:/Users/samsung/Desktop/ex2Data/ex2y.dat');
m= length(y);
x = [ones(m,1),x];
J_vals = zeros(100,100);
theta0_vals = linspace(-3,3,100);
theta1_vals = linspace(-1,1,100);
for i =1:length(theta0_vals)
for j = 1:length(theta1_vals)
t=[theta0_vals(i);theta1_vals(j)];
J_vals(i,j) = (x*t - y)'*(x*t-y)/(2*m);
end
end
J_vals = J_vals';
figure;
surf(theta0_vals, theta1_vals, J_vals);
xlabel('\theta_0'); ylabel('\theta_1');
练习 2 ：
x = load('C:/Users/samsung/Desktop/ex2Data/ex2x.dat');
y = load('C:/Users/samsung/Desktop/ex2Data/ex2y.dat');
figure % open a new figure window
plot(x, y, 'o');
ylabel('Height in meters');
xlabel('Age in years');
theta = [0;0];
alfa = 0.07;
m = length(y);
x = [ones(m,1),x];
##temp = x(:,2)' *(x*theta -y)/m * alfa;
#for i = 1:1500
#theta =theta - x' *(x*theta -y)/ m * alfa;
#end ##z这里的循环使用了 梯度下降迭代法，求出 theta
theta = inv(x'*x)*x'*y; ##是同一公式，计算速度快
hold on % Plot new data without clearing old plot
plot(x(:,2), x*theta, '-')
% remember that x is now a matrix with 2 columns
% and the second column contains the time info
legend('Training data', 'Linear regression')