def ID3(Attributes, X, Y):
"""
Implementaion of the ID3 Algorithm
:param Attributes: List of attributes to test
:param X: set of training instances
:param Y: set of training labels
:return: decision tree build from the training data
"""
# Handle base cases
num_positive, num_negative = Calculate_Counts(Y)
# All labels are positive
if num_positive == len(Y):
return Node(label='e')
# All labels are negative
elif num_negative == len(Y):
return Node(label='-')
# No attributes left to test (Choose the most common label amongst the remaining examples)
if len(Attributes) == 0:
if num_positive > num_negative:
return Node(label='e')
elif num_positive < num_negative:
return Node(label='-')
else:
return Node(label=random.choice(['e','-']))
# Determine the best attribute
max_gain = None
max_attribute = 0
max_indices = []
positive_splits = []
negative_splits = []
gains = []
for i in range(len(Attributes)):
gain, positive_split, negative_split = Gain(Attributes[i], X, Y)
gains.append(gain)
positive_splits.append(positive_split)
negative_splits.append(negative_split)
# Keep track of max gain(s)
if max_gain == None:
max_gain = gain
max_indices.append(i)
elif gain > max_gain:
max_gain = gain
max_indices = [i]
elif gain == max_gain:
max_indices.append(i)
max_index = random.choice(max_indices)
max_attribute = Attributes[max_index]
max_positive_split = positive_splits[max_index]
max_negative_split = negative_splits[max_index]
# Remove the attribute from the list of attributes (Attrubutes - {A})
Attributes = Attributes[:max_index] + Attributes[max_index+1:]
# Set Attribute of the decision node to the one with the max gain
current_node = Node(attribute=max_attribute)
# Build positive child node
if len(max_positive_split[0]) > 0:
current_node.Positive_Branch = ID3(Attributes, max_positive_split[0], max_positive_split[1])
else:
if num_positive > num_negative:
current_node.Positive_Branch = Node(label='e')
elif num_positive < num_negative:
current_node.Positive_Branch = Node(label='-')
else:
current_node.Positive_Branch = Node(label=random.choice(['e','-']))
# Build negative child node
if len(max_negative_split[0]) > 0:
current_node.Negative_Branch = ID3(Attributes, max_negative_split[0], max_negative_split[1])
else:
if num_positive > num_negative:
current_node.Negative_Branch = Node(label='e')
elif num_positive < num_negative:
current_node.Negative_Branch = Node(label='-')
else:
current_node.Negative_Branch = Node(label=random.choice(['e','-']))
return current_node
