Non-linear classification example

non_linear_classification.m

% my training data.
% so if x > 3 || x < 7, y = 1, otherwise y = 0.
x = 1:100;
y = [0, 0, 0, 1, 1, 1, 1, zeros(1, 93)];

% instead of theta' * x, I'm trying to create
% a non-linear decision boundary.
% So instead of y = theta_0 + theta_1 * x, I use:
function result = h(x, theta)
  result = sigmoid(theta(1) + theta(2) * x + theta(3) * ((x - theta(4))^2));
end

function result = sigmoid(z)
  result = 1 / (1 + e ^ (-z));
end

% cost function, works correctly
function distance = cost(theta)
  distance = 0;
  x = 1:100;
  y = [0, 0, 0, 1, 1, 1, 1, zeros(1, 93)];
  for i = 1:length(x) % arrays in octave are indexed starting at 1
    if (y(i) == 1)
      distance += -log(h(x(i), theta));
    else
      distance += -log(1 - h(x(i), theta));
    end
  end
  % get how far off we were on average
  distance = distance / length(x);
end

alpha = 1;
iters = 500;
m = length(x);

% initial values
theta = [0, 0, 0, 0];

% I'm not using gradient descent.
% Instead I use Octave's built-in function
% fminunc to find the optimal values of theta for me.
opt = fminunc(@cost, theta);
disp(opt);

% for each number between 1 and 10,
% print out the probability that y(i) = 1
for i = 1:100
  disp([i, h(i, opt) * 100]);
end