Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 5.760379e-19.

% Logstic Regress with Newton's Method

clear all;
close all;
clc;

% data 
x = [0.230000 0.394000;
    0.11000 0.690000;
    0.13000 0.440000;
    0.24000 0.510000;
    0.33000 0.440000;
    0.36000 0.550000;
    0.35000 0.660000;
    0.41000 0.470000;
    0.52000 0.695000;
    0.53000 0.590000;
    0.39500 0.250000;
    0.41000 0.075000;
    0.49000 0.220000;
    0.52000 0.130000;
    0.57000 0.070000;
    0.35000 0.140000;
    0.62000 0.170000;
    0.63000 0.280000;
    0.62500 0.350000;
0.780000 0.282000];

y = [0;
    0;
    0;
    0;
    0;
    0;
    0;
    0;
    0;
    0;
    1;
    1;
    1;
    1;
    1;
    1;
    1;
    1;
    1;
    1];

[m, n] = size(x);
x = [ones(m, 1), x]; 

% plot the datas
figure
pos = find(y); neg = find(y == 0);%find是找到的一个向量，其结果是find函数括号值为真时的值的编号
plot(x(pos, 2), x(pos,3), '+')
hold on
plot(x(neg, 2), x(neg, 3), 'o')
hold on
xlabel('axis X')
ylabel('axis Y')

% Initialize fitting parameters
x0 = 0;
i = 1;
theta_new = zeros(n+1, 1);
theta_old = ones(n+1, 1);
err = abs((theta_new - theta_old)'*(theta_new - theta_old)); 
e = 0.0001;
N = 100;
T = [];

% Define the sigmoid function
g = inline('1.0 ./ (1.0 + exp(-z))'); 

% Newton's method
while (i<=N && err>e)
    % Calculate the hypothesis function
    z = x * theta_new;
    h = g(z);
     
    % Calculate gradient and hessian.
    grad = x' * (h-y);
    H = x' * diag(h) * diag(1-h) * x;
    theta_new = theta_new - H\grad;
    T = [T;i theta_new'];
    i = i +1;
    theta_old = theta_new;
end
Result = array2table(T); %converts m-by-n array T
Result.Properties.VariableNames = {'Iter', 'theta_new', 'Itera', 'thet_new'}; %Variable names, specified as a cell array of character vectors or a string array whose elements are nonempty and distinct. The number of names must equal the number of variables.

plot_x = [x(:,2)];
plot_y = (-1./theta_new(3)).*(theta_new(2).*plot_x +theta_new(1));
plot(plot_x, plot_y)
legend('Label 1', 'Label 2', 'Decision Boundary')
hold off

This is where i get the warning: theta_new = theta_new - H\grad. How should i solve it? I hope someone can help me.

[Stephen23]

You should take a look at the INLINE documentation:

and consider using designed for the purpose anonymous functions, just as the documentation recommends.

Answer 1

[DGM]

Your table has 4 columns, but you only have two labels in the vector called "Variables". Depending on your intent, you can add more labels to "Variables", or you can restrict the range of labels being assigned on the LHS so that it matches the length of the RHS. For instance, if you wanted to rename the first two columns:

Result.Properties.VariableNames(1:numel(Variables)) = Variables;

or some arbitrary selection of two columns:

Result.Properties.VariableNames([1 3]) = Variables;

[Jin En Ng]

how can i restrict the range of labels on LHS so that it matches the length of RHS?

[DGM]

Both of the above are examples of doing that. It just depends on which range is desired.

If it's safe to assume that the table width is greater than or equal to the size of Variables:

Variables = {'Iter', 'theta_new', 'Itera', 'thet_new'};
Result.Properties.VariableNames(1:numel(Variables)) = Variables;

The length of the RHS is 4, so this will set the labels for the first 4 columns. If you want to pick 4 different columns instead of just the first 4, you'll have to adjust that.

[Jin En Ng]

It still doesn't print the value with each iteration in the command window.

[DGM]

I'm not sure what it's supposed to be printing. You can pick the variable of interest and display it using disp() somewhere inside the loop.

For example, you could print the most recent row of T by placing this at the end of the loop.

disp(T(end,:))