明天第一节课8.55才上,还是把今天看的东西整理一下吧。
今天主要是看了NG前几章讲的单线性回归、多线性回归、逻辑回归的matlab实现,之前觉得那些东西理解还好,但是写代码好难的样子,但是今天看了大牛的代码发现真的很easy... 但是是很有技巧的用的矩阵去实现。
比如单线性回归里面的j=0和j=1这两种情况,直接把x转换成x = [ones(m, 1) x] , 第一列全是1了,刚好可以把j=0时x=1代入去运算,这样子梯度 grad = (1/m).* x‘ * ((x * theta) - y) , theta = theta - alpha .* grad ,外面加个循环就可以求出theta0 和 theta 1 (其实都在theta矩阵里)。
clear all; close all; clc x = load(‘ex2x.dat‘); y = load(‘ex2y.dat‘); m = length(y); % number of training examples % Plot the training data figure; % open a new figure window plot(x, y, ‘o‘); ylabel(‘Height in meters‘) xlabel(‘Age in years‘) % Gradient descent x = [ones(m, 1) x]; % Add a column of ones to x theta = zeros(size(x(1,:)))‘; % initialize fitting parameters MAX_ITR = 1500; alpha = 0.07; for num_iterations = 1:MAX_ITR % This is a vectorized version of the % gradient descent update formula % It‘s also fine to use the summation formula from the videos % Here is the gradient %代价函数的导数:刚好把j=0和j=1的情况巧妙的用矩阵的方法归为一个式子 %grad = 1/m * (h-y) 或 1/m * (h-y)*x grad = (1/m).* x‘ * ((x * theta) - y); % Here is the actual update theta = theta - alpha .* grad; % Sequential update: The wrong way to do gradient descent % grad1 = (1/m).* x(:,1)‘ * ((x * theta) - y); % theta(1) = theta(1) + alpha*grad1; % grad2 = (1/m).* x(:,2)‘ * ((x * theta) - y); % theta(2) = theta(2) + alpha*grad2; end % print theta to screen theta % Plot the linear fit hold on; % keep previous plot visible plot(x(:,2), x*theta, ‘-‘) legend(‘Training data‘, ‘Linear regression‘)%标出图像中各曲线标志所代表的意义 hold off % don‘t overlay any more plots on this figure,指关掉前面的那幅图
还有就是牛顿法直接求解参数,一句w=inv(x‘*x)*x‘*y 就直接求出了theta0 和 theta 1 ,看来还需看看最优化这方面的东西啊。
%%方法一 x = load(‘ex2x.dat‘); y = load(‘ex2y.dat‘); plot(x,y,‘*‘) xlabel(‘height‘) ylabel(‘age‘) x = [ones(size(x,1),1),x]; w=inv(x‘*x)*x‘*y hold on %plot(x,0.0639*x+0.7502) plot(x(:,2),0.0639*x(:,2)+0.7502)%更正后的代码
后面就是画代价函数的三维图,一个surf函数直接可以画出三维图像。
可参考:http://huzhyi21.blog.163.com/blog/static/1007396201061052214302/
% Calculate J matrix % Grid over which we will calculate J theta0_vals = linspace(-3, 3, 100); theta1_vals = linspace(-1, 1, 100); % initialize J_vals to a matrix of 0‘s J_vals = zeros(length(theta0_vals), length(theta1_vals)); for i = 1:length(theta0_vals) for j = 1:length(theta1_vals) t = [theta0_vals(i); theta1_vals(j)]; J_vals(i,j) = (1/2*m) .* (x * t - y)‘ * (x * t - y); %J_vals就是代价函数: 1/2m * (h-y)^2 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‘; % Surface plot figure; surf(theta0_vals, theta1_vals, J_vals) xlabel(‘\theta_0‘); ylabel(‘\theta_1‘);
时间: 2024-10-05 21:10:09