【数据挖掘】决策树之CART (Classification and Regression Trees)分类与回归树
决策树是一种简单的机器学习方法，它是完全透明的分类观测方法，经过训练后由一系列if-then判断语句组成一棵树。
#!/usr/bin/python
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']] 上例代码中为构建决策树的训练数据。
class decisionnode:#决策树节点结构
def __init__(self,col=-1,value=None,results=None,tb=None,fb=None):
self.col=col#被测试规则索引
self.value=value#要被测试的值
self.results=results#测试结果
#tb,fb是决策树节点，tb为true时的节点，fb为false的节点
self.tb=tb
self.fb=fb
#训练决策树：CART (Classification and Regression Trees)分类与回归树
#1）建立根节点
#2）遍历表中所有数据，选择最好的变量划分数据
def devideset(rows,column,value):#column为栏位在row的索引，value为此栏位的值
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
#根据split_function划分
set1=[row for row in rows if split_function(row)]
set2=[row for row in rows if not split_function(row)]
return (set1,set2)
#没row中最后一个栏位的个数
def uniquecount(rows):
result={}
for row in rows:
r = row[len(row) - 1]
if r not in result: result[r]=0
results[r]+=1
return result
#整个rows随机放置item到错误category中的可能性
def giniimpurity(rows):
total = len(rows)
counts=uniquecount(rows)
imp=0
for k1 in counts:
#计算k1放到错误category中的可能性
p1=float(counts[k1])/total
for k2 in counts:
if k1==k2:continue
p2=float(counts[k2])/total
imp+=p1*p2
return imp
#sum(p(x)*log2(p(x)))
def entropy(rows):
from math import log
log2=lambda x:log(x)/log(2)
results=uniquecounts(rows)
ent=0.0
for r in results.keys():
p=float(results[r])/len(rows)
ent+=p*log2(p)
return ent
决策树的构建
1）遍历数据中的每个item，找出最优的规则
2）对最优的规则建立节点，递归构建其左右子树
#递归构建决策树
def buildtree(rows,scoref=entropy):
if len(rows)==0:return decisionnode()
current_score=scoref(rows)
#设置变量，跟踪最好的规则
best_gain=0
best_criteria=None
best_sets=None
#record的栏 item数
column_count=len(row[0])-1
for col in range(0,column_count):
#生成
column_values={}
for row in rows:
column_values[row[col]]=1
#尝试为rows中的每个记录的第col个field划分set
for value in column_values.keys():
#划分后的set
(set1,set2)=devideset(rows,col,value)
#划分后的长度比例
p=float(len(set1))/len(rows)
#权重得分
gain=current_score-p*scoref(set1)-(1-p)*scoref(set2)
#找到了最好的规则
if gain>best_gain and len(set1)>0 and len(set2)>0:
best_gain=gain
best_criteria=(col,value)
best_sets=(set1,set2)
#取最好的规则，并对划分后的子集合进行递归构建决策树
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))
#利用决策树来对observation进行归类
def classify(observation,tree):
if tree.results != None:
return tree.results
v = observation[tree.col]
branch = None
#查找分支，此处算法与划分set规则一致
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,brance)