AdaBoost Python implementation of the AdaBoost (Adaptive Boosting) classification algorithm.

adaboost.py

from __future__ import division
from numpy import *

class AdaBoost:

    def __init__(self, training_set):
        self.training_set = training_set
        self.N = len(self.training_set)
        self.weights = ones(self.N)/self.N
        self.RULES = []
        self.ALPHA = []

    def set_rule(self, func, test=False):
        errors = array([t[1]!=func(t[0]) for t in self.training_set])
        e = (errors*self.weights).sum()
        if test: return e
        alpha = 0.5 * log((1-e)/e)
        print 'e=%.2f a=%.2f'%(e, alpha)
        w = zeros(self.N)
        for i in range(self.N):
            if errors[i] == 1: w[i] = self.weights[i] * exp(alpha)
            else: w[i] = self.weights[i] * exp(-alpha)
        self.weights = w / w.sum()
        self.RULES.append(func)
        self.ALPHA.append(alpha)

    def evaluate(self):
        NR = len(self.RULES)
        for (x,l) in self.training_set:
            hx = [self.ALPHA[i]*self.RULES[i](x) for i in range(NR)]
            print x, sign(l) == sign(sum(hx))
        
if __name__ == '__main__':

    examples = []
    examples.append(((1,  2  ), 1))
    examples.append(((1,  4  ), 1))
    examples.append(((2.5,5.5), 1))
    examples.append(((3.5,6.5), 1))
    examples.append(((4,  5.4), 1))
    examples.append(((2,  1  ),-1))
    examples.append(((2,  4  ),-1))
    examples.append(((3.5,3.5),-1))
    examples.append(((5,  2  ),-1))
    examples.append(((5,  5.5),-1))

    m = AdaBoost(examples)
    m.set_rule(lambda x: 2*(x[0] < 1.5)-1)
    m.set_rule(lambda x: 2*(x[0] < 4.5)-1)
    m.set_rule(lambda x: 2*(x[1] > 5)-1)
    m.evaluate()

I'm totally new to adaboosting and still haven't found a way to make much sense of it. I'm not following on what the purpose of the function "set_rule" does and attributes RULES and ALPHA, as well as what the examples themselves are representing. Are they just coordinates on a graph and the values at those locations are either 1 or -1?