Machine Learning by Andrew Ng --- Logistic Regression with two classes

this is a example to build a logistic regression model to predict whether a student gets admitted into a university.

As usual,loading and plotting your data:

and the plotData.m file is :

the hypothesis function and the Cost function are both different from Linear Regression ,which like:

Fora matrix, your function should perform the sigmoid function on every element.

Then we have derivatied J and grad,with these two formulas ,we can then use an Octave
built-in function called fminunc. To derivaty theta.

input these commands:

%  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
initial_theta = zeros(n + 1, 1);


% Compute and display initial cost and gradient
[cost, grad] = costFunction(initial_theta, X, y);

%  Set options for fminunc
options = optimset('GradObj', 'on', 'MaxIter', 400);


%  Run fminunc to obtain the optimal theta
%  This function will return theta and the cost 
[theta, cost] = ...
fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);

Then U got theta

plotDecisionBoundary(theta, X, y);

Finally,U can predict your own data .

Note: This example is with no Regularization.