决策树-py

my_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’]]

class decisionnode:
def init(self,col=-1,value=None,results=None,tb=None,fb=None):
self.col=col
self.value=value
self.results=results
self.tb=tb
self.fb=fb

Divides a set on a specific column. Can handle numeric

or nominal values

def divideset(rows,column,value):

Make a function that tells us if a row is in

the first group (true) or the second group (false)

split_function=None
if isinstance(value,int) or isinstance(value,float):
split_function=lambda row:row[column]>=value
else:
split_function=lambda row:row[column]==value

Divide the rows into two sets and return them

set1=[row for row in rows if split_function(row)]
set2=[row for row in rows if not split_function(row)]
return (set1,set2)

Create counts of possible results (the last column of

each row is the result)

def uniquecounts(rows):
results={}
for row in rows:
# The result is the last column
r=row[len(row)-1]
if r not in results: results[r]=0
results[r]+=1
return results

Probability that a randomly placed item will

be in the wrong category

def giniimpurity(rows):
total=len(rows)
counts=uniquecounts(rows)
imp=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

Entropy is the sum of p(x)log(p(x)) across all

the different possible results

def entropy(rows):
from math import log
log2=lambda x:log(x)/log(2)
results=uniquecounts(rows)

Now calculate the entropy

ent=0.0
for r in results.keys():
p=float(results[r])/len(rows)
ent=ent-p*log2§
return ent

def printtree(tree,indent=’’):

Is this a leaf node?

if tree.results!=None:
print str(tree.results)
else:
# Print the criteria
print str(tree.col)+’:’+str(tree.value)+’? ’

  # Print the branches
  print indent+'T->',
  printtree(tree.tb,indent+'  ')
  print indent+'F->',
  printtree(tree.fb,indent+'  ')

def getwidth(tree):
if tree.tbNone and tree.fbNone: return 1
return getwidth(tree.tb)+getwidth(tree.fb)

def getdepth(tree):
if tree.tbNone and tree.fbNone: return 0
return max(getdepth(tree.tb),getdepth(tree.fb))+1

from PIL import Image,ImageDraw

def drawtree(tree,jpeg=‘tree.jpg’):
w=getwidth(tree)*100
h=getdepth(tree)*100+120

img=Image.new(‘RGB’,(w,h),(255,255,255))
draw=ImageDraw.Draw(img)

drawnode(draw,tree,w/2,20)
img.save(jpeg,‘JPEG’)

def drawnode(draw,tree,x,y):
if tree.results==None:
# Get the width of each branch
w1=getwidth(tree.fb)*100
w2=getwidth(tree.tb)*100

# Determine the total space required by this node
left=x-(w1+w2)/2
right=x+(w1+w2)/2

# Draw the condition string
draw.text((x-20,y-10),str(tree.col)+':'+str(tree.value),(0,0,0))

# Draw links to the branches
draw.line((x,y,left+w1/2,y+100),fill=(255,0,0))
draw.line((x,y,right-w2/2,y+100),fill=(255,0,0))

# Draw the branch nodes
drawnode(draw,tree.fb,left+w1/2,y+100)
drawnode(draw,tree.tb,right-w2/2,y+100)

else:
txt=’ \n’.join([’%s:%d’%v for v in tree.results.items()])
draw.text((x-20,y),txt,(0,0,0))

def classify(observation,tree):
if tree.results!=None:
return tree.results
else:
v=observation[tree.col]
branch=None
if isinstance(v,int) or isinstance(v,float):
if v>=tree.value: branch=tree.tb
else: branch=tree.fb
else:
if v==tree.value: branch=tree.tb
else: branch=tree.fb
return classify(observation,branch)

def prune(tree,mingain):

If the branches aren’t leaves, then prune them

if tree.tb.resultsNone:
prune(tree.tb,mingain)
if tree.fb.resultsNone:
prune(tree.fb,mingain)

If both the subbranches are now leaves, see if they

should merged

if tree.tb.results!=None and tree.fb.results!=None:
# Build a combined dataset
tb,fb=[],[]
for v,c in tree.tb.results.items():
tb+=[[v]]*c
for v,c in tree.fb.results.items():
fb+=[[v]]*c

# Test the reduction in entropy
delta=entropy(tb+fb)-(entropy(tb)+entropy(fb)/2)

if delta<mingain:
  # Merge the branches
  tree.tb,tree.fb=None,None
  tree.results=uniquecounts(tb+fb)

def mdclassify(observation,tree):
if tree.results!=None:
return tree.results
else:
v=observation[tree.col]
if vNone:
tr,fr=mdclassify(observation,tree.tb),mdclassify(observation,tree.fb)
tcount=sum(tr.values())
fcount=sum(fr.values())
tw=float(tcount)/(tcount+fcount)
fw=float(fcount)/(tcount+fcount)
result={}
for k,v in tr.items(): result[k]=vtw
for k,v in fr.items(): result[k]=vfw
return result
else:
if isinstance(v,int) or isinstance(v,float):
if v>=tree.value: branch=tree.tb
else: branch=tree.fb
else:
if vtree.value: branch=tree.tb
else: branch=tree.fb
return mdclassify(observation,branch)

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 buildtree(rows,scoref=entropy):
if len(rows)==0: return decisionnode()
current_score=scoref(rows)

Set up some variables to track the best criteria

best_gain=0.0
best_criteria=None
best_sets=None

column_count=len(rows[0])-1
for col in range(0,column_count):
# Generate the list of different values in
# this column
column_values={}
for row in rows:
column_values[row[col]]=1
# Now try dividing the rows up for each value
# in this column
for value in column_values.keys():
(set1,set2)=divideset(rows,col,value)

  # Information gain
  p=float(len(set1))/len(rows)
  gain=current_score-p*scoref(set1)-(1-p)*scoref(set2)
  if gain>best_gain and len(set1)>0 and len(set2)>0:
    best_gain=gain
    best_criteria=(col,value)
    best_sets=(set1,set2)

Create the sub branches

if best_gain>0:
trueBranch=buildtree(best_sets[0])
falseBranch=buildtree(best_sets[1])
return decisionnode(col=best_criteria[0],value=best_criteria[1],
tb=trueBranch,fb=falseBranch)
else:
return decisionnode(results=uniquecounts(rows))