python如何实现决策树算法?（代码）

每条数据项储存在列表中，最后一列储存结果
多条数据项形成数据集

data=[[d1,d2,d3...dn,result],
      [d1,d2,d3...dn,result],
                .
                .
      [d1,d2,d3...dn,result]]

class DecisionNode:
    '''决策树节点
    '''
    
    def __init__(self,col=-1,value=None,results=None,tb=None,fb=None):
        '''初始化决策树节点
        
        args：        
        col -- 按数据集的col列划分数据集
        value -- 以value作为划分col列的参照
        result -- 只有叶子节点有，代表最终划分出的子数据集结果统计信息。｛‘结果’：结果出现次数｝
        rb,fb -- 代表左右子树
        '''
        self.col=col
        self.value=value
        self.results=results
        self.tb=tb
        self.fb=fb

决策树分类的最终结果是将数据项划分出了若干子集，其中每个子集的结果都一样，所以这里采用｛‘结果’：结果出现次数｝的方式表达每个子集

def pideset(rows,column,value):
    '''依据数据集rows的column列的值，判断其与参考值value的关系对数据集进行拆分
       返回两个数据集
    '''
    split_function=None
    #value是数值类型
    if isinstance(value,int) or isinstance(value,float):
        #定义lambda函数当row[column]>=value时返回true
        split_function=lambda row:row[column]>=value
    #value是字符类型
    else:
        #定义lambda函数当row[column]==value时返回true
        split_function=lambda row:row[column]==value
    #将数据集拆分成两个
    set1=[row for row in rows if split_function(row)]
    set2=[row for row in rows if not split_function(row)]
    #返回两个数据集
    return (set1,set2)

def uniquecounts(rows):
    '''计算数据集rows中有几种最终结果，计算结果出现次数，返回一个字典
    '''
    results={}
    for row in rows:
        r=row[len(row)-1]
        if r not in results: results[r]=0
        results[r]+=1
    return results

def giniimpurity(rows):
    '''返回rows数据集的基尼不纯度
    '''
    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

def entropy(rows):
    '''返回rows数据集的熵
    '''
    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=ent-p*log2(p)
    return ent

def build_tree(rows,scoref=entropy):
    '''构造决策树
    '''
    if len(rows)==0: return DecisionNode()
    current_score=scoref(rows)

    # 最佳信息增益
    best_gain=0.0
    #
    best_criteria=None
    #最佳划分
    best_sets=None

    column_count=len(rows[0])-1
    #遍历数据集的列，确定分割顺序
    for col in range(0,column_count):
        column_values={}
        # 构造字典
        for row in rows:
            column_values[row[col]]=1
        for value in column_values.keys():
            (set1,set2)=pideset(rows,col,value)
            p=float(len(set1))/len(rows)
            # 计算信息增益
            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)
    # 如果划分的两个数据集熵小于原数据集，进一步划分它们
    if best_gain>0:
        trueBranch=build_tree(best_sets[0])
        falseBranch=build_tree(best_sets[1])
        return DecisionNode(col=best_criteria[0],value=best_criteria[1],
                        tb=trueBranch,fb=falseBranch)
    # 如果划分的两个数据集熵不小于原数据集，停止划分
    else:
        return DecisionNode(results=uniquecounts(rows))

def print_tree(tree,indent=''):
    if tree.results!=None:
        print(str(tree.results))
    else:
        print(str(tree.col)+':'+str(tree.value)+'? ')
        print(indent+'T->',end='')
        print_tree(tree.tb,indent+'  ')
        print(indent+'F->',end='')
        print_tree(tree.fb,indent+'  ')


def getwidth(tree):
    if tree.tb==None and tree.fb==None: return 1
    return getwidth(tree.tb)+getwidth(tree.fb)

def getdepth(tree):
    if tree.tb==None and tree.fb==None: return 0
    return max(getdepth(tree.tb),getdepth(tree.fb))+1


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 mdclassify(observation,tree):
    '''对缺失数据进行分类
    
    args：
    observation -- 发生信息缺失的数据项
    tree -- 训练完成的决策树
    
    返回代表该分类的结果字典
    '''

    # 判断数据是否到达叶节点
    if tree.results!=None:
        # 已经到达叶节点，返回结果result
        return tree.results
    else:
        # 对数据项的col列进行分析
        v=observation[tree.col]

        # 若col列数据缺失
        if v==None:
            #对tree的左右子树分别使用mdclassify，tr是左子树得到的结果字典，fr是右子树得到的结果字典
            tr,fr=mdclassify(observation,tree.tb),mdclassify(observation,tree.fb)

            # 分别以结果占总数比例计算得到左右子树的权重
            tcount=sum(tr.values())
            fcount=sum(fr.values())
            tw=float(tcount)/(tcount+fcount)
            fw=float(fcount)/(tcount+fcount)
            result={}

            # 计算左右子树的加权平均
            for k,v in tr.items(): 
                result[k]=v*tw
            for k,v in fr.items(): 
                # fr的结果k有可能并不在tr中，在result中初始化k
                if k not in result: 
                    result[k]=0 
                # fr的结果累加到result中  
                result[k]+=v*fw
            return result

        # col列没有缺失，继续沿决策树分类
        else:
            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 mdclassify(observation,branch)

tree=build_tree(my_data)
print(mdclassify(['google',None,'yes',None],tree))
print(mdclassify(['google','France',None,None],tree))

def prune(tree,mingain):
    '''对决策树进行剪枝
    
    args：
    tree -- 决策树
    mingain -- 最小信息增益
    
   返回
    '''
    # 修剪非叶节点
    if tree.tb.results==None:
        prune(tree.tb,mingain)
    if tree.fb.results==None:
        prune(tree.fb,mingain)
    #合并两个叶子节点
    if tree.tb.results!=None and tree.fb.results!=None:
        tb,fb=[],[]
        for v,c in tree.tb.results.items():
            tb+=[[v]]*c
        for v,c in tree.fb.results.items():
            fb+=[[v]]*c
        #计算熵减少情况
        delta=entropy(tb+fb)-(entropy(tb)+entropy(fb)/2)
        #熵的增加量小于mingain，可以合并分支
        if delta<mingain:
            tree.tb,tree.fb=None,None
            tree.results=uniquecounts(tb+fb)

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