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toydecisiontree.py
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toydecisiontree.py
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#!/usr/bin/python2.7
import numpy as np
from abstractclassifier import AbstractClassifier
# Test data from Toby Segaran's book
raw_data=[['slashdot', 'USA', 'yes', 18, 'None'], ['google', 'France', 'yes', 23, 'Premium'], ['digg', 'USA', 'yes', 24, 'Basic'], ['kiwitobes', 'France', 'yes', 23, 'Basic'], ['google', 'UK', 'no', 21, 'Premium'], ['(direct)', 'New Zealand', 'no', 12, 'None'], ['(direct)', 'UK', 'no', 21, 'Basic'], ['google', 'USA', 'no', 24, 'Premium'], ['slashdot', 'France', 'yes', 19, 'None'], ['digg', 'USA', 'no', 18, 'None'], ['google', 'UK', 'no', 18, 'None'], ['kiwitobes', 'UK', 'no', 19, 'None'], ['digg', 'New Zealand', 'yes', 12, 'Basic'], ['slashdot', 'UK', 'no', 21, 'None'], ['google', 'UK', 'yes', 18, 'Basic'], ['kiwitobes', 'France', 'yes', 19, 'Basic']]
train_data=[r[:-1] for r in raw_data]
train_labels=[r[-1] for r in raw_data]
"""
Steps to construct decision tree
1) Compute score (default: entropy) for each possible split on all attributes for all available rows
2) Select the split with the highest information gain
3) Add new node with data evaluating to true in split
4) Add new node with data evaluating to false in split
5) Goto 1 using true branch
6) Goto 1 using false branch
7) Return node
"""
class DTNode():
"""
DTNode : Decision tree node
Attributes
----------
true_branch : DTNode or None which handles the data for which the current node evaluated to true
false_branch: DTNode or None which handles the data for which the current node evaluated to false
attr_idx : The index of the attribute used for comparison in this node
val : The value to compare to
results: None or, if this is a leaf of the decision tree the result class
"""
def __init__(self, tb_node=None, fb_node=None, attr_idx=-1, val=None, results=None):
self.true_branch=tb_node
self.false_branch=fb_node
self.attr_idx=attr_idx
self.val=val
self.results=results
def __repr__(self):
print self.true_branch==None, self.false_branch==None, self.attr_idx, self,val, self.results
class ToyDecisionTree(AbstractClassifier):
"""
ToyDecisionTree
Documentation used for implementation:
- Book: Toby Segaran: Collective Intelligence
Note: Categorial variables/attributes must be encoded as literals
else they will treated as continuous i.e. their numerical order will be of importance
Attributes
----------
tree : DTNode based structure representing the decision tree
Examples
--------
>>> import numpy as np
>>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
>>> Y = np.array([1, 1, 1, 2, 2, 2])
>>> from toydecisiontree import ToyDecisionTree
>>> clf = ToyDecisionTree()
>>> clf.fit(X, Y)
>>> print(clf.predict([[-0.8, -1]]))
([1],[])
TODOs
-----
- Improve documentation
- Pruning
- Min split criteria
- Other scores which allow e.g. regression (tyically: variance)
- Feature importance
- Investigate reason for the much higher performance of sklearn decision tree
"""
def __init__(self):
self.tree=None
def fit(self, train_data, train_labels, score=None):
""" create decision tree using train_data """
train_data=np.array(train_data)
train_labels=np.array(train_labels)
self.tree=self.generatetree(train_data, train_labels)
def predict(self, test_data):
test_data=np.array(test_data)
# stay compatible with return value of DT
return [self.predict_instance(r, self.tree) for r in test_data],[]
def predict_instance(self, instance, node):
if node.results!=None:
return node.results[0][0] #,node.results[1]
# if attr is numerical
try:
if instance[node.attr_idx] >= float(node.val):
r=self.predict_instance( instance, node.true_branch )
else:
r=self.predict_instance( instance, node.false_branch )
# if attr is a string attribute
except:
if instance[node.attr_idx] == node.val:
r=self.predict_instance( instance, node.true_branch )
else:
r=self.predict_instance( instance, node.false_branch )
return r
def entropy(self, train_labels):
""" lower bound of bits necessary to encode each class based on its probability """
unique_vals, unique_counts=np.unique(train_labels, return_counts=True)
p=unique_counts/float(len(train_labels))
intermediate=-p*np.log2(p)
return(np.sum(intermediate))
def split_data(self, train_data, train_labels, attr_idx, val):
""" split data by comparing attribute keyed by attribute index to value """
# if attr is numerical
try:
train_attr=np.array(train_data[:, attr_idx], dtype=float)
selector=(train_attr>=float(val))
# if attr is a string attribute
except:
selector=(train_data[:,attr_idx] == val)
tb_labels=train_labels[selector]
tb_data=train_data[selector,:]
fb_labels=train_labels[-selector]
fb_data=train_data[-selector,:]
return(tb_data, tb_labels, fb_data, fb_labels)
def generatetree(self, train_data, train_labels, score=None):
""" recursively generate decision tree """
if score==None:
score=self.entropy
if train_data.shape[0]==0:
return DTNode()
current_score=score(train_labels)
best_gain=0.0
best_attr_idx=None
best_val=None
# find best split accross all attributes and values
for attr_idx in range(train_data.shape[1]):
# unique values of this attribute in training data
attrib_vals=np.unique(train_data[:,attr_idx])
for val in attrib_vals:
(tb_data, tb_labels, fb_data, fb_labels)=self.split_data(train_data, train_labels, attr_idx, val)
# compute information gain
p=float(tb_labels.shape[0])/train_data.shape[0]
gain=current_score - p* score(tb_labels) - (1-p)*score(fb_labels)
if gain>best_gain and tb_labels.shape[0]>0 and fb_labels.shape[0]>0:
best_gain=gain
best_attr_idx=attr_idx
best_val=val
best_tb=(tb_data, tb_labels)
best_fb=(fb_data, fb_labels)
if best_gain>0.0:
tb_node=self.generatetree(best_tb[0], best_tb[1])
fb_node=self.generatetree(best_fb[0], best_fb[1])
return DTNode(tb_node=tb_node, fb_node=fb_node, attr_idx=best_attr_idx, val=best_val)
else:
ra,rb=np.unique(train_labels, return_counts=True)
res= np.vstack((ra,rb)).tolist()
return DTNode(results=res)
def printtree(self,tree,indent):
#print tree
if tree.results!=None:
print str(tree.results)
else:
print tree.attr_idx, ":", tree.val , "?"
indent+=3
print " "*indent+'T:',
self.printtree(tree.true_branch,indent)
print " "*indent+'F:',
self.printtree(tree.false_branch,indent)
def __repr__(self):
self.printtree(self.tree, 0)
return ""
if __name__=="__main__":
x=ToyDecisionTree()
x.fit(train_data, train_labels)
print x
print x.predict(train_data)