Plotting decision boundary of logistic regression in MATLAB

Question

Ryan Rizzo 2019-4-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/456866-plotting-decision-boundary-of-logistic-regression-in-matlab

I am running logistic regression on a small dataset which looks like this:

After implementing gradient descent and the cost function, I am getting a 100% accuracy in the prediction stage, However I want to be sure that everything is in order so I am trying to plot the decision boundary line which separates the two datasets.

Below I present plots showing the cost function and theta parameters. As can be seen, currently I am printing the decision boundary line incorrectly.

**Extracting data**

 clear all; close all; clc;
    
    alpha = 0.01;
    num_iters = 1000;
    
    %% Plotting data
    x1 = linspace(0,3,50);
    mqtrue = 5;
    cqtrue = 30;
    dat1 = mqtrue*x1+5*randn(1,50);
    
    x2 = linspace(7,10,50);
    dat2 = mqtrue*x2 + (cqtrue + 5*randn(1,50));
    
    x = [x1 x2]'; % X
    
    subplot(2,2,1);
    dat = [dat1 dat2]'; % Y
    
    scatter(x1, dat1); hold on;
    scatter(x2, dat2, '*'); hold on;
    classdata = (dat>40);

**Computing Cost, Gradient and plotting**

 %  Setup the data matrix appropriately, and add ones for the intercept term
    [m, n] = size(x);
    
    % Add intercept term to x and X_test
    x = [ones(m, 1) x];
    
    % Initialize fitting parameters
    theta = zeros(n + 1, 1);
    %initial_theta = [0.2; 0.2];
    
    J_history = zeros(num_iters, 1); 
    
    plot_x = [min(x(:,2))-2,  max(x(:,2))+2]
    
    for iter = 1:num_iters 
    % Compute and display initial cost and gradient
        [cost, grad] = logistic_costFunction(theta, x, classdata);
        theta = theta - alpha * grad;
        J_history(iter) = cost;
    
        fprintf('Iteration #%d - Cost = %d... \r\n',iter, cost);
        
        
        subplot(2,2,2);
        hold on; grid on;
        plot(iter, J_history(iter), '.r');  title(sprintf('Plot of cost against number of iterations. Cost is %g',J_history(iter)));
        xlabel('Iterations')
        ylabel('MSE')
        drawnow
        
        subplot(2,2,3);
        grid on;
        plot3(theta(1), theta(2), J_history(iter),'o')
        title(sprintf('Tita0 = %g, Tita1=%g', theta(1), theta(2)))
        xlabel('Tita0')
        ylabel('Tita1')
        zlabel('Cost')
        hold on;
        drawnow
        
        subplot(2,2,1);
        grid on;    
        % Calculate the decision boundary line
        plot_y = theta(2).*plot_x + theta(1);  % <--- Boundary line 
        % Plot, and adjust axes for better viewing
        plot(plot_x, plot_y)
        hold on;
        drawnow
        
    end
    
    fprintf('Cost at initial theta (zeros): %f\n', cost);
    fprintf('Gradient at initial theta (zeros): \n');
    fprintf(' %f \n', grad);

The above code is implementing gradient descent correctly (I think) but I am still unable to show the boundary line plot. Any suggestions would be appreciated.