def entropy(objects, question):
'''Returns an entropy value. This algorithm for entropy is heavily modeled
on the ID3 decision tree algorithm for entropy. The difference is that here,
we want what would traditionally be a high entropy. To adjust for this,
we take the reciprocal of entropy before returning it.'''
objects = tuple(objects) # necessary for SQL IN statement to work
positives = model.get_num_positives(objects, question.id) *1.0
negatives = model.get_num_negatives(objects, question.id) *1.0
total = len(objects)
if positives != 0:
frac_positives = (-1*positives)/total * math.log(positives/total, 2)
else:
frac_positives = 0
if negatives != 0:
frac_negatives = (-1*negatives)/total * math.log(negatives/total, 2)
else:
frac_negatives = 0
entropy = frac_positives + frac_negatives
entropy *= (positives + negatives)/total # weighted average
if entropy != 0: entropy = 1/entropy # minimizes rather than maximizes
else: entropy = float('inf')
return entropy
def simple_entropy(objects,question):
'''Returns an entropy value for a question based on the weights for all the
objects. Entropy is low if for a given question, the number of yes and no
answers is about even, and the number of unsure answers is low.'''
objects = tuple(objects) # necessary for SQL IN statement to work
positives = model.get_num_positives(objects, question.id)
negatives = model.get_num_negatives(objects, question.id)
unknowns = model.get_num_unknowns(objects, question.id)
question_entropy = 0
question_entropy += positives * 1
question_entropy -= negatives * 1
question_entropy += unknowns * 5 # arbitrary weight to discourage questions with lots of unknowns
return abs(question_entropy)