摘要：數據描述每條數據項儲存在列表中，最后一列儲存結果多條數據項形成數據集決策樹數據結構決策樹節點初始化決策樹節點按數據集的列劃分數據集以作為劃分列的參照只有葉子節點有，代表最終劃分出的子數據集結果統計信息。

每條數據項儲存在列表中，最后一列儲存結果
多條數據項形成數據集

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

class DecisionNode:
    """決策樹節點
    """
    
    def __init__(self,col=-1,value=None,results=None,tb=None,fb=None):
        """初始化決策樹節點
        
        args：        
        col -- 按數據集的col列劃分數據集
        value -- 以value作為劃分col列的參照
        result -- 只有葉子節點有，代表最終劃分出的子數據集結果統計信息。｛‘結果’：結果出現次數｝
        rb,fb -- 代表左右子樹
        """
        self.col=col
        self.value=value
        self.results=results
        self.tb=tb
        self.fb=fb

決策樹分類的最終結果是將數據項劃分出了若干子集，其中每個子集的結果都一樣，所以這里采用｛‘結果’：結果出現次數｝的方式表達每個子集

def divideset(rows,column,value):
    """依據數據集rows的column列的值，判斷其與參考值value的關系對數據集進行拆分
       返回兩個數據集
    """
    split_function=None
    #value是數值類型
    if isinstance(value,int) or isinstance(value,float):
        #定義lambda函數當row[column]>=value時返回true
        split_function=lambda row:row[column]>=value
    #value是字符類型
    else:
        #定義lambda函數當row[column]==value時返回true
        split_function=lambda row:row[column]==value
    #將數據集拆分成兩個
    set1=[row for row in rows if split_function(row)]
    set2=[row for row in rows if not split_function(row)]
    #返回兩個數據集
    return (set1,set2)

def uniquecounts(rows):
    """計算數據集rows中有幾種最終結果，計算結果出現次數，返回一個字典
    """
    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數據集的基尼不純度
    """
    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數據集的熵
    """
    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):
    """構造決策樹
    """
    if len(rows)==0: return DecisionNode()
    current_score=scoref(rows)

    # 最佳信息增益
    best_gain=0.0
    #
    best_criteria=None
    #最佳劃分
    best_sets=None

    column_count=len(rows[0])-1
    #遍歷數據集的列，確定分割順序
    for col in range(0,column_count):
        column_values={}
        # 構造字典
        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)
            # 計算信息增益
            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)
    # 如果劃分的兩個數據集熵小于原數據集，進一步劃分它們
    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)
    # 如果劃分的兩個數據集熵不小于原數據集，停止劃分
    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):
    """對缺失數據進行分類
    
    args：
    observation -- 發生信息缺失的數據項
    tree -- 訓練完成的決策樹
    
    返回代表該分類的結果字典
    """

    # 判斷數據是否到達葉節點
    if tree.results!=None:
        # 已經到達葉節點，返回結果result
        return tree.results
    else:
        # 對數據項的col列進行分析
        v=observation[tree.col]

        # 若col列數據缺失
        if v==None:
            #對tree的左右子樹分別使用mdclassify，tr是左子樹得到的結果字典，fr是右子樹得到的結果字典
            tr,fr=mdclassify(observation,tree.tb),mdclassify(observation,tree.fb)

            # 分別以結果占總數比例計算得到左右子樹的權重
            tcount=sum(tr.values())
            fcount=sum(fr.values())
            tw=float(tcount)/(tcount+fcount)
            fw=float(fcount)/(tcount+fcount)
            result={}

            # 計算左右子樹的加權平均
            for k,v in tr.items(): 
                result[k]=v*tw
            for k,v in fr.items(): 
                # fr的結果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的結果累加到result中  
                result[k]+=v*fw
            return result

        # col列沒有缺失，繼續沿決策樹分類
        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):
    """對決策樹進行剪枝
    
    args：
    tree -- 決策樹
    mingain -- 最小信息增益
    
   返回
    """
    # 修剪非葉節點
    if tree.tb.results==None:
        prune(tree.tb,mingain)
    if tree.fb.results==None:
        prune(tree.fb,mingain)
    #合并兩個葉子節點
    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
        #計算熵減少情況
        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