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import csv
from collections import defaultdict
import pydotplus
class DecisionTree:
"""Binary tree implementation with true and false branch. """
def __init__(self, col=-1, value=None, trueBranch=None, falseBranch=None, results=None, summary=None):
self.col = col
self.value = value
self.trueBranch = trueBranch
self.falseBranch = falseBranch
self.results = results # None for nodes, not None for leaves
self.summary = summary
def divideSet(rows, column, value):
splittingFunction = None
if isinstance(value, int) or isinstance(value, float): # for int and float values
splittingFunction = lambda row : row[column] >= value
else: # for strings
splittingFunction = lambda row : row[column] == value
list1 = [row for row in rows if splittingFunction(row)]
list2 = [row for row in rows if not splittingFunction(row)]
return (list1, list2)
def uniqueCounts(rows):
results = {}
for row in rows:
#response variable is in the last column
r = row[-1]
if r not in results: results[r] = 0
results[r] += 1
return results
def entropy(rows):
from math import log
log2 = lambda x: log(x)/log(2)
results = uniqueCounts(rows)
entr = 0.0
for r in results:
p = float(results[r])/len(rows)
entr -= p*log2(p)
return entr
def gini(rows):
total = len(rows)
counts = uniqueCounts(rows)
imp = 0.0
for k1 in counts:
p1 = float(counts[k1])/total
for k2 in counts:
if k1 == k2: continue
p2 = float(counts[k2])/total
imp += p1*p2
return imp
def variance(rows):
if len(rows) == 0: return 0
data = [float(row[len(row) - 1]) for row in rows]
mean = sum(data) / len(data)
variance = sum([(d-mean)**2 for d in data]) / len(data)
return variance
def growDecisionTreeFrom(rows, evaluationFunction=entropy):
"""Grows and then returns a binary decision tree.
evaluationFunction: entropy or gini"""
if len(rows) == 0: return DecisionTree()
currentScore = evaluationFunction(rows)
bestGain = 0.0
bestAttribute = None
bestSets = None
columnCount = len(rows[0]) - 1 # last column is the result/target column
for col in range(0, columnCount):
columnValues = [row[col] for row in rows]
#unique values
lsUnique = list(set(columnValues))
for value in lsUnique:
(set1, set2) = divideSet(rows, col, value)
# Gain -- Entropy or Gini
p = float(len(set1)) / len(rows)
gain = currentScore - p*evaluationFunction(set1) - (1-p)*evaluationFunction(set2)
if gain>bestGain and len(set1)>0 and len(set2)>0:
bestGain = gain
bestAttribute = (col, value)
bestSets = (set1, set2)
dcY = {'impurity' : '%.3f' % currentScore, 'samples' : '%d' % len(rows)}
if bestGain > 0:
trueBranch = growDecisionTreeFrom(bestSets[0], evaluationFunction)
falseBranch = growDecisionTreeFrom(bestSets[1], evaluationFunction)
return DecisionTree(col=bestAttribute[0], value=bestAttribute[1], trueBranch=trueBranch,
falseBranch=falseBranch, summary=dcY)
else:
return DecisionTree(results=uniqueCounts(rows), summary=dcY)
def prune(tree, minGain, evaluationFunction=entropy, notify=False):
"""Prunes the obtained tree according to the minimal gain (entropy or Gini). """
# recursive call for each branch
if tree.trueBranch.results == None: prune(tree.trueBranch, minGain, evaluationFunction, notify)
if tree.falseBranch.results == None: prune(tree.falseBranch, minGain, evaluationFunction, notify)
# merge leaves (potentionally)
if tree.trueBranch.results != None and tree.falseBranch.results != None:
tb, fb = [], []
for v, c in tree.trueBranch.results.items(): tb += [[v]] * c
for v, c in tree.falseBranch.results.items(): fb += [[v]] * c
p = float(len(tb)) / len(tb + fb)
delta = evaluationFunction(tb+fb) - p*evaluationFunction(tb) - (1-p)*evaluationFunction(fb)
if delta < minGain:
if notify: print('A branch was pruned: gain = %f' % delta)
tree.trueBranch, tree.falseBranch = None, None
tree.results = uniqueCounts(tb + fb)
def classify(observations, tree, dataMissing=False):
"""Classifies the observationss according to the tree.
dataMissing: true or false if data are missing or not. """
def classifyWithoutMissingData(observations, tree):
if tree.results != None: # leaf
return tree.results
else:
v = observations[tree.col]
branch = None
if isinstance(v, int) or isinstance(v, float):
if v >= tree.value: branch = tree.trueBranch
else: branch = tree.falseBranch
else:
if v == tree.value: branch = tree.trueBranch
else: branch = tree.falseBranch
return classifyWithoutMissingData(observations, branch)
def classifyWithMissingData(observations, tree):
if tree.results != None: # leaf
return tree.results
else:
v = observations[tree.col]
if v == None:
tr = classifyWithMissingData(observations, tree.trueBranch)
fr = classifyWithMissingData(observations, tree.falseBranch)
tcount = sum(tr.values())
fcount = sum(fr.values())
tw = float(tcount)/(tcount + fcount)
fw = float(fcount)/(tcount + fcount)
result = defaultdict(int) # Problem description: http://blog.ludovf.net/python-collections-defaultdict/
for k, v in tr.items(): result[k] += v*tw
for k, v in fr.items(): result[k] += v*fw
return dict(result)
else:
branch = None
if isinstance(v, int) or isinstance(v, float):
if v >= tree.value: branch = tree.trueBranch
else: branch = tree.falseBranch
else:
if v == tree.value: branch = tree.trueBranch
else: branch = tree.falseBranch
return classifyWithMissingData(observations, branch)
# function body
if dataMissing:
return classifyWithMissingData(observations, tree)
else:
return classifyWithoutMissingData(observations, tree)
def plot(decisionTree):
"""Plots the obtained decision tree. """
def toString(decisionTree, indent=''):
if decisionTree.results != None: # leaf node
return str(decisionTree.results)
else:
szCol = 'Column %s' % decisionTree.col
if szCol in dcHeadings:
szCol = dcHeadings[szCol]
if isinstance(decisionTree.value, int) or isinstance(decisionTree.value, float):
decision = '%s >= %s?' % (szCol, decisionTree.value)
else:
decision = '%s == %s?' % (szCol, decisionTree.value)
trueBranch = indent + 'yes -> ' + toString(decisionTree.trueBranch, indent + '\t\t')
falseBranch = indent + 'no -> ' + toString(decisionTree.falseBranch, indent + '\t\t')
return (decision + '\n' + trueBranch + '\n' + falseBranch)
print(toString(decisionTree))
def dotgraph(decisionTree):
global dcHeadings
dcNodes = defaultdict(list)
"""Plots the obtained decision tree. """
def toString(iSplit, decisionTree, bBranch, szParent = "null", indent=''):
if decisionTree.results != None: # leaf node
lsY = []
for szX, n in decisionTree.results.items():
lsY.append('%s:%d' % (szX, n))
dcY = {"name": "%s" % ', '.join(lsY), "parent" : szParent}
dcSummary = decisionTree.summary
dcNodes[iSplit].append(['leaf', dcY['name'], szParent, bBranch, dcSummary['impurity'],
dcSummary['samples']])
return dcY
else:
szCol = 'Column %s' % decisionTree.col
if szCol in dcHeadings:
szCol = dcHeadings[szCol]
if isinstance(decisionTree.value, int) or isinstance(decisionTree.value, float):
decision = '%s >= %s' % (szCol, decisionTree.value)
else:
decision = '%s == %s' % (szCol, decisionTree.value)
trueBranch = toString(iSplit+1, decisionTree.trueBranch, True, decision, indent + '\t\t')
falseBranch = toString(iSplit+1, decisionTree.falseBranch, False, decision, indent + '\t\t')
dcSummary = decisionTree.summary
dcNodes[iSplit].append([iSplit+1, decision, szParent, bBranch, dcSummary['impurity'],
dcSummary['samples']])
return
toString(0, decisionTree, None)
lsDot = ['digraph Tree {',
'node [shape=box, style="filled, rounded", color="black", fontname=helvetica] ;',
'edge [fontname=helvetica] ;'
]
i_node = 0
dcParent = {}
for nSplit, lsY in dcNodes.items():
for lsX in lsY:
iSplit, decision, szParent, bBranch, szImpurity, szSamples =lsX
if type(iSplit) == int:
szSplit = '%d-%s' % (iSplit, decision)
dcParent[szSplit] = i_node
lsDot.append('%d [label=<%s<br/>impurity %s<br/>samples %s>, fillcolor="#e5813900"] ;' % (i_node,
decision.replace('>=', '≥').replace('?', ''),
szImpurity,
szSamples))
else:
lsDot.append('%d [label=<impurity %s<br/>samples %s<br/>class %s>, fillcolor="#e5813900"] ;' % (i_node,
szImpurity,
szSamples,
decision))
if szParent != 'null':
if bBranch:
szAngle = '45'
szHeadLabel = 'True'
else:
szAngle = '-45'
szHeadLabel = 'False'
szSplit = '%d-%s' % (nSplit, szParent)
p_node = dcParent[szSplit]
if nSplit == 1:
lsDot.append('%d -> %d [labeldistance=2.5, labelangle=%s, headlabel="%s"] ;' % (p_node,
i_node, szAngle, szHeadLabel))
else:
lsDot.append('%d -> %d ;' % (p_node, i_node))
i_node += 1
lsDot.append('}')
dot_data = '\n'.join(lsDot)
return dot_data
def loadCSV(file):
"""Loads a CSV file and converts all floats and ints into basic datatypes."""
def convertTypes(s):
s = s.strip()
try:
return float(s) if '.' in s else int(s)
except ValueError:
return s
reader = csv.reader(open(file, 'rt'))
dcHeader = {}
if bHeader:
lsHeader = next(reader)
for i, szY in enumerate(lsHeader):
szCol = 'Column %d' % i
dcHeader[szCol] = str(szY)
return dcHeader, [[convertTypes(item) for item in row] for row in reader]
if __name__ == '__main__':
# Select the example you want to classify
example = 2
# All examples do the following steps:
# 1. Load training data
# 2. Let the decision tree grow
# 4. Plot the decision tree
# 5. classify without missing data
# 6. Classifiy with missing data
# (7.) Prune the decision tree according to a minimal gain level
# (8.) Plot the pruned tree
if example == 1:
# the smaller examples
bHeader = False
dcHeadings, trainingData = loadCSV('tbc.csv') # sorry for not translating the TBC and pneumonia symptoms
decisionTree = growDecisionTreeFrom(trainingData)
#decisionTree = growDecisionTreeFrom(trainingData, evaluationFunction=gini) # with gini
result = plot(decisionTree)
print(result)
dot_data = dotgraph(decisionTree)
graph = pydotplus.graph_from_dot_data(dot_data)
graph.write_pdf("tbc.pdf")
graph.write_png("tbc.png")
print(classify(['ohne', 'leicht', 'Streifen', 'normal', 'normal'], decisionTree, dataMissing=False))
print(classify([None, 'leicht', None, 'Flocken', 'fiepend'], decisionTree, dataMissing=True)) # no longer unique
# Don' forget if you compare the resulting tree with the tree in my presentation: here it is a binary tree!
else:
bHeader = True
# the bigger example
dcHeadings, trainingData = loadCSV('fishiris.csv') # demo data from matlab
decisionTree = growDecisionTreeFrom(trainingData, evaluationFunction=gini)
prune(decisionTree, 0.8, notify=True) # notify, when a branch is pruned (one time in this example)
result = plot(decisionTree)
print(result)
dot_data = dotgraph(decisionTree)
graph = pydotplus.graph_from_dot_data(dot_data)
graph.write_pdf("iris.pdf")
graph.write_png("iris.png")
print(classify([6.0, 2.2, 5.0, 1.5], decisionTree)) # dataMissing=False is the default setting
print(classify([None, None, None, 1.5], decisionTree, dataMissing=True)) # no longer unique |
les arbres de décision
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