Reinventing the wheel：决策树算法的实现

摘要：数据描述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决策树数据结构决策树节点初始化决策树节点按数据集的列划分数据集以作为划分列的参照只有叶子节点有，代表最终划分出的子数据集结果统计信息。

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 divideset(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)=divideset(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=" 
".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