构建FP-growth算法高效发现频繁项集

1、构建FP树

1.1创建FP树的结构

#创建FP树的数据结构
#FP树的类定义
class treeNode:
    def __init__(self, nameValue, numOccur, parentNode):
        self.name = nameValue
        self.count = numOccur
        self.nodeLink = None
        self.parent = parentNode      #needs to be updated
        self.children = {}

    def inc(self, numOccur):
        self.count += numOccur

    def disp(self, ind=1):
        print ('  '*ind, self.name, ' ', self.count)
        for child in self.children.values():
            child.disp(ind+1)

if __name__ == '__main__':
    #创建一个单节点
    rootNode = treeNode('pyramid',9,None)
    #增加一个子节点
    rootNode.children['eye'] = treeNode('eye',13,None)
    #显示子节点
    rootNode.disp()
    #添加一个子节点
    rootNode.children['phoenix'] = treeNode('phoenix',3,None)
    rootNode.disp()
'''
  pyramid   9
     eye   13
  pyramid   9
     eye   13
     phoenix   3

'''

1.2构建FP树

1.2.1加载数据集

def loadSimpDat():
    simpDat = [['r', 'z', 'h', 'j', 'p'],
               ['z', 'y', 'x', 'w', 'v', 'u', 't', 's'],
               ['z'],
               ['r', 'x', 'n', 'o', 's'],
               ['y', 'r', 'x', 'z', 'q', 't', 'p'],
               ['y', 'z', 'x', 'e', 'q', 's', 't', 'm']]
    return simpDat

def createInitSet(dataSet):
    retDict = {}
    for trans in dataSet:
        retDict[frozenset(trans)] = 1
    return retDict

if __name__ == '__main__':
    data = loadSimpDat()
    data = createInitSet(data)
    print(data)
'''
{frozenset({'z', 'h', 'r', 'p', 'j'}): 1, frozenset({'s', 'v', 'z', 'u', 'w', 't', 'y', 'x'}): 1, frozenset({'z'}): 1, frozenset({'s', 'o', 'r', 'n', 'x'}): 1, 
frozenset({'p', 'z', 't', 'r', 'y', 'q', 'x'}): 1, frozenset({'e', 's', 'z', 't', 'm', 'y', 'q', 'x'}): 1}
'''

1.2.2统计每个商品出现的次数

def createTree(dataSet, minSup=1): #create FP-tree from dataset but don't mine
    #头指针表，存储每个元素出现的频率
    headerTable = {}
    #go over dataSet twice
    for trans in dataSet:#first pass counts frequency of occurance
        for item in trans:
            headerTable[item] = headerTable.get(item, 0) + dataSet[trans]
    print(headerTable)

if __name__ == '__main__':
    data = loadSimpDat()
    data = createInitSet(data)
    createTree(data)
'''
{'r': 3, 'h': 1, 'z': 5, 'p': 2, 'j': 1, 'x': 4, 's': 3, 'u': 1, 'v': 1, 'y': 3, 't': 3, 'w': 1, 'o': 1, 'n': 1, 'q': 2, 'm': 1, 'e': 1}
'''

1.2.3过滤支持度小于最小支持度的商品

  #删除支持度小于最小支持度的商品
    for k in headerTable.keys():  #remove items not meeting minSup
        if headerTable[k] < minSup:
            del(headerTable[k])
    freqItemSet = set(headerTable.keys())
    print ('freqItemSet: ',freqItemSet)
    '''
    freqItemSet:  {'n', 't', 'q', 'e', 'p', 'w', 'h', 'r', 'u', 'j', 'o', 'x', 'v', 'm', 'z', 'y', 's'}
    '''
    if len(freqItemSet) == 0:
        return None, None  #if no items meet min support -->get out

1.2.4将剩下的商品重新组合成节点的形式

  for k in headerTable:
        headerTable[k] = [headerTable[k], None] #reformat headerTable to use Node link
    print ('headerTable: ',headerTable)
    '''
    headerTable:  {'p': [2, None], 'h': [1, None], 'r': [3, None], 'j': [1, None], 'z': [5, None], 't': [3, None], 'w': [1, None], 'u': [1, None], 
    'x': [4, None], 'v': [1, None], 'y': [3, None], 's': [3, None], 'n': [1, None], 'o': [1, None], 'q': [2, None], 'e': [1, None], 'm': [1, None]}

    '''

1.2.5创建FP树

#FP树构建函数
'''
dataSet:数据集
minSup=1：最小支持度
'''
def createTree(dataSet, minSup=1): #create FP-tree from dataset but don't mine
    #头指针表，存储每个元素出现的频率
    headerTable = {}
    #go over dataSet twice
    for trans in dataSet:#first pass counts frequency of occurance
        for item in trans:
            headerTable[item] = headerTable.get(item, 0) + dataSet[trans]
    #删除支持度小于最小支持度的商品
    for k in list(headerTable.keys()):  #remove items not meeting minSup
        if headerTable[k] < minSup:
            del(headerTable[k])
    freqItemSet = set(headerTable.keys())
    print ('freqItemSet: ',freqItemSet)
    '''
    freqItemSet:  {'n', 't', 'q', 'e', 'p', 'w', 'h', 'r', 'u', 'j', 'o', 'x', 'v', 'm', 'z', 'y', 's'}
    '''
    if len(freqItemSet) == 0:
        return None, None  #if no items meet min support -->get out
    for k in headerTable:
        headerTable[k] = [headerTable[k], None] #reformat headerTable to use Node link
    print ('headerTable: ',headerTable)
    '''
    headerTable:  {'p': [2, None], 'h': [1, None], 'r': [3, None], 'j': [1, None], 'z': [5, None], 't': [3, None], 'w': [1, None], 'u': [1, None], 
    'x': [4, None], 'v': [1, None], 'y': [3, None], 's': [3, None], 'n': [1, None], 'o': [1, None], 'q': [2, None], 'e': [1, None], 'm': [1, None]}

    '''
    retTree = treeNode('Null Set', 1, None) #create tree

    #第二次遍历数据集
    for tranSet, count in dataSet.items():  #go through dataset 2nd time
        localD = {}
        for item in tranSet:  #put transaction items in order
            if item in freqItemSet:
                localD[item] = headerTable[item][0]
                if len(localD) > 0:
                    # p: p[1]按照value排序
                    # p: p[0]按照key排序
                    #reverse=True降序排列
                    orderedItems = [v[0] for v in sorted(localD.items(), key=lambda p: p[1], reverse=True)]
                    '''
                    orderedItems:['z', 'x', 'y', 's', 't', 'q', 'm', 'e']
                  '''
                    updateTree(orderedItems, retTree, headerTable, count)#populate tree with ordered freq itemset
    return retTree, headerTable #return tree and header table


# print(localD.items())
    '''
    dict_items([('e', 1), ('y', 3), ('s', 3), ('z', 5), ('m', 1), ('t', 3), ('x', 4), ('q', 2)])
    '''


# if __name__ == '__main__':
#     data = loadSimpDat()
#     data = createInitSet(data)
#     createTree(data)
'''
{'r': 3, 'h': 1, 'z': 5, 'p': 2, 'j': 1, 'x': 4, 's': 3, 'u': 1, 'v': 1, 'y': 3, 't': 3, 'w': 1, 'o': 1, 'n': 1, 'q': 2, 'm': 1, 'e': 1}
'''

'''
items:按照出现次数已排好序的商品列表
inTree：节点树
headerTable：商品节点集
count：频繁项集出现的次数
'''
def updateTree(items, inTree, headerTable, count):
    #测试第一个元素项是否作为子节点存在
    if items[0] in inTree.children:#check if orderedItems[0] in retTree.children
        #如果存在就更新该元素项的计数
        inTree.children[items[0]].inc(count) #incrament count
    else:   #add items[0] to inTree.children
        #如果不存在，则将该元素作为一个新节点添加到树中
        inTree.children[items[0]] = treeNode(items[0], count, inTree)
        #如果头指针表的值为None
        if headerTable[items[0]][1] == None: #update header table
            #将该元素节点添加到头指针表中
            headerTable[items[0]][1] = inTree.children[items[0]]
        else:
            #如果头指针表已经存在，则更新头指针表
            updateHeader(headerTable[items[0]][1], inTree.children[items[0]])
    #如果元素项的长度大于1
    if len(items) > 1:#call updateTree() with remaining ordered items
        #每次不断的调用自身，每次调用去掉列表的第一个元素
        updateTree(items[1::], inTree.children[items[0]], headerTable, count)
    return inTree



#头指针更新
#确保节点链接指向树中该元素项的每个实例
#构成一个链表
#头指针从nodelink开始，一直沿着nodelink到达链表末尾
def updateHeader(nodeToTest, targetNode):   #this version does not use recursion
    while (nodeToTest.nodeLink != None):    #Do not use recursion to traverse a linked list!
        nodeToTest = nodeToTest.nodeLink
    nodeToTest.nodeLink = targetNode


if __name__ == '__main__':
    data = loadSimpDat()
    data = createInitSet(data)
    MyFPtree,MyHeaderTable=createTree(data,3)
    MyFPtree.disp()

   Null Set   1
     z   5
       r   1
       x   3
         t   3
           y   2
             s   2
           r   1
             y   1
     x   1
       r   1
         s   1

上树中给出了对应的元素项以及对应的频率计数值，每个缩进表示所处的树的深度

1.3从FP树中挖掘频繁项集

1.3.1抽取条件模式基

条件模式基：以所查找元素结尾的所有路径的集合，每一条路径都是前缀路径，一条前缀路径是所查找元素项与根节点的所有内容。

#发现以给定元素项结尾的所有路径的函数
#迭代上溯整棵树
#从末尾节点开始遍历，保存节点的名字，一直遍历到根节点
def ascendTree(leafNode, prefixPath): #ascends from leaf node to root
    if leafNode.parent != None:
        prefixPath.append(leafNode.name)
        ascendTree(leafNode.parent, prefixPath)

#遍历链表到达结尾
def findPrefixPath(basePat, treeNode): #treeNode comes from header table
    #条件模式基字典
    condPats = {}
    while treeNode != None:
        prefixPath = []
        ascendTree(treeNode, prefixPath)
        #如果前缀路径大于1
        if len(prefixPath) > 1:
            print("len(prefixPath) > 1",prefixPath）
            print("prefixPath[1:]",prefixPath[1:])
            condPats[frozenset(prefixPath[1:])] = treeNode.count
        treeNode = treeNode.nodeLink
    return condPats

以y结尾的条件模式基

if __name__ == '__main__':
    data = loadSimpDat()
    data = createInitSet(data)
    MyFPtree,MyHeaderTable=createTree(data,3)
    path = findPrefixPath('y', MyHeaderTable['y'][1]);
    print("path-->",path)

freqItemSet:  {'z', 'x', 't', 'r', 's', 'y'}
headerTable:  {'z': [5, None], 'r': [3, None], 'x': [4, None], 't': [3, None], 's': [3, None], 'y': [3, None]}
len(prefixPath) > 1 ['y', 's', 't', 'x', 'z']
prefixPath[1:] ['s', 't', 'x', 'z']
len(prefixPath) > 1 ['y', 'r', 't', 'x', 'z']
prefixPath[1:] ['r', 't', 'x', 'z']
path--> {frozenset({'s', 'x', 'z', 't'}): 2, frozenset({'x', 'r', 'z', 't'}): 1}

以r结尾的条件模式基

if __name__ == '__main__':
    data = loadSimpDat()
    data = createInitSet(data)
    MyFPtree,MyHeaderTable=createTree(data,3)
    path = findPrefixPath('r', MyHeaderTable['r'][1]);
    print("path-->",path)

len(prefixPath) > 1 ['r', 'z']
prefixPath[1:] ['z']
len(prefixPath) > 1 ['r', 'x']
prefixPath[1:] ['x']
len(prefixPath) > 1 ['r', 'x', 'z']
prefixPath[1:] ['x', 'z']
path--> {frozenset({'z'}): 1, frozenset({'x'}): 1, frozenset({'x', 'z'}): 1}

求出所有的元素的条件模式基

if __name__ == '__main__':
    data = loadSimpDat()
    data = createInitSet(data)
    MyFPtree,MyHeaderTable=createTree(data,3)
    freqItemSet= {'x', 'y', 't', 's', 'z', 'r'}
    for i in freqItemSet:
        path = findPrefixPath(i, MyHeaderTable[i][1]);
        print(i,"path-->",path)
'''
y path--> {frozenset({'x'}): 2, frozenset({'x', 'z'}): 2, frozenset({'t'}): 2, frozenset({'x', 't'}): 4, frozenset({'x', 't', 'z'}): 2}
x path--> {frozenset({'z'}): 4}
s path--> {frozenset({'x', 'y'}): 1, frozenset({'x', 'z', 'y'}): 2, frozenset({'x'}): 2, frozenset({'x', 't', 'y'}): 1, frozenset({'x', 't', 'z', 'y'}): 1}
r path--> {frozenset({'z'}): 1, frozenset({'x', 's'}): 1, frozenset({'x', 't', 'y'}): 1, frozenset({'x', 't', 'z', 'y'}): 1}
z path--> {}
t path--> {frozenset({'x', 's', 'z', 'y'}): 1, frozenset({'x'}): 4, frozenset({'x', 'z'}): 2}
'''

1.3.2通过条件模式基创建条件FP树

def mineTree(inTree, headerTable, minSup, preFix, freqItemList):
    #按照value排序的key
    #默认升序排列，按照元素项出现的次数从小到大排列
    bigL = [v[0] for v in sorted(headerTable.items(), key=lambda p: p[1][0])]#(sort header table)
    #从出现次数最小的元素开始（头指针表的底端开始）
    for basePat in bigL:  #start from bottom of header table
        newFreqSet = preFix.copy()
        newFreqSet.add(basePat)
        print ('频繁项集: ',newFreqSet )   #append to set)
        freqItemList.append(newFreqSet)
        #得到每个元素的条件模式基
        condPattBases = findPrefixPath(basePat, headerTable[basePat][1])
        print ('条件模式基 :',basePat, condPattBases)
        #2. construct cond FP-tree from cond. pattern base
        #根据条件模式基创建条件FP树
        myCondTree, myHead = createTree(condPattBases, minSup)
        print ('头指针列表 ', myHead)
        #挖掘条件FP树
        if myHead != None: #3. mine cond. FP-tree
            print ('产生的条件树 ',newFreqSet)
            myCondTree.disp(1)
            mineTree(myCondTree, myHead, minSup, newFreqSet, freqItemList)

if __name__ == '__main__':
    minSup = 3
    preFix = set([])
    freqItemList = []
    data = loadSimpDat()
    data = createInitSet(data)
    MyFPtree,MyHeaderTable=createTree(data,3)
    mineTree( MyFPtree,MyHeaderTable, minSup, preFix, freqItemList)

MyHeaderTable {'z': [5, <__main__.treeNode object at 0x0000016BD70FA4A8>], 'r': [3, <__main__.treeNode object at 0x0000016BD70FA470>], 'x': [4, <__main__.treeNode object at 0x0000016BD70FA748>], 'y': [3, <__main__.treeNode object at 0x0000016BD70FA780>], 't': [3, <__main__.treeNode object at 0x0000016BD70FA7B8>], 's': [3, <__main__.treeNode object at 0x0000016BD70FA7F0>]}
MyFPtree <__main__.treeNode object at 0x0000016BD6E8B198>
频繁项:  {'r'}
条件模式基 : r {frozenset({'z'}): 1, frozenset({'s', 'x'}): 1, frozenset({'y', 'x', 'z', 't'}): 1}
头指针列表:  None
频繁项:  {'y'}
条件模式基 : y {frozenset({'x', 'z'}): 3}
头指针列表:  {'x': [3, <__main__.treeNode object at 0x0000016BD70FA9E8>], 'z': [3, <__main__.treeNode object at 0x0000016BD70FA978>]}
{'y'} 产生的条件树: 
   Null Set   1
     x   3
       z   3
频繁项:  {'y', 'x'}
条件模式基 : x {}
头指针列表:  None
频繁项:  {'y', 'z'}
条件模式基 : z {frozenset({'x'}): 3}
头指针列表:  {'x': [3, <__main__.treeNode object at 0x0000016BD70FAA58>]}
{'y', 'z'} 产生的条件树: 
   Null Set   1
     x   3
频繁项:  {'y', 'x', 'z'}
条件模式基 : x {}
头指针列表:  None
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}]
myCondTree=> None
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}]
myCondTree=> <__main__.treeNode object at 0x0000016BD70FA9B0>
频繁项:  {'t'}
条件模式基 : t {frozenset({'y', 'x', 'z'}): 3}
头指针列表:  {'y': [3, <__main__.treeNode object at 0x0000016BD70FAB00>], 'x': [3, <__main__.treeNode object at 0x0000016BD70FAA20>], 'z': [3, <__main__.treeNode object at 0x0000016BD70FAA90>]}
{'t'} 产生的条件树: 
   Null Set   1
     y   3
       x   3
         z   3
频繁项:  {'y', 't'}
条件模式基 : y {}
头指针列表:  None
频繁项:  {'x', 't'}
条件模式基 : x {frozenset({'y'}): 3}
头指针列表:  {'y': [3, <__main__.treeNode object at 0x0000016BD70FABA8>]}
{'x', 't'} 产生的条件树: 
   Null Set   1
     y   3
频繁项:  {'y', 'x', 't'}
条件模式基 : y {}
头指针列表:  None
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}, {'t'}, {'y', 't'}, {'x', 't'}, {'y', 'x', 't'}]
myCondTree=> None
频繁项:  {'z', 't'}
条件模式基 : z {frozenset({'y', 'x'}): 3}
头指针列表:  {'y': [3, <__main__.treeNode object at 0x0000016BD70FAC88>], 'x': [3, <__main__.treeNode object at 0x0000016BD70FAC50>]}
{'z', 't'} 产生的条件树: 
   Null Set   1
     y   3
       x   3
频繁项:  {'y', 'z', 't'}
条件模式基 : y {}
头指针列表:  None
频繁项:  {'x', 'z', 't'}
条件模式基 : x {frozenset({'y'}): 3}
头指针列表:  {'y': [3, <__main__.treeNode object at 0x0000016BD70FABE0>]}
{'x', 'z', 't'} 产生的条件树: 
   Null Set   1
     y   3
频繁项:  {'y', 'x', 'z', 't'}
条件模式基 : y {}
头指针列表:  None
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}, {'t'}, {'y', 't'}, {'x', 't'}, {'y', 'x', 't'}, {'z', 't'}, {'y', 'z', 't'}, {'x', 'z', 't'}, {'y', 'x', 'z', 't'}]
myCondTree=> None
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}, {'t'}, {'y', 't'}, {'x', 't'}, {'y', 'x', 't'}, {'z', 't'}, {'y', 'z', 't'}, {'x', 'z', 't'}, {'y', 'x', 'z', 't'}]
myCondTree=> <__main__.treeNode object at 0x0000016BD70FACF8>
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}, {'t'}, {'y', 't'}, {'x', 't'}, {'y', 'x', 't'}, {'z', 't'}, {'y', 'z', 't'}, {'x', 'z', 't'}, {'y', 'x', 'z', 't'}]
myCondTree=> <__main__.treeNode object at 0x0000016BD70FAC18>
频繁项:  {'s'}
条件模式基 : s {frozenset({'y', 'x', 'z', 't'}): 2, frozenset({'x'}): 1}
头指针列表:  {'x': [3, <__main__.treeNode object at 0x0000016BD70FAB38>]}
{'s'} 产生的条件树: 
   Null Set   1
     x   3
频繁项:  {'s', 'x'}
条件模式基 : x {}
头指针列表:  None
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}, {'t'}, {'y', 't'}, {'x', 't'}, {'y', 'x', 't'}, {'z', 't'}, {'y', 'z', 't'}, {'x', 'z', 't'}, {'y', 'x', 'z', 't'}, {'s'}, {'s', 'x'}]
myCondTree=> None
频繁项:  {'x'}
条件模式基 : x {frozenset({'z'}): 3}
头指针列表:  {'z': [3, <__main__.treeNode object at 0x0000016BD70FAD68>]}
{'x'} 产生的条件树: 
   Null Set   1
     z   3
频繁项:  {'x', 'z'}
条件模式基 : z {}
头指针列表:  None
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}, {'t'}, {'y', 't'}, {'x', 't'}, {'y', 'x', 't'}, {'z', 't'}, {'y', 'z', 't'}, {'x', 'z', 't'}, {'y', 'x', 'z', 't'}, {'s'}, {'s', 'x'}, {'x'}, {'x', 'z'}]
myCondTree=> None
频繁项:  {'z'}
条件模式基 : z {}
头指针列表:  None
freqItemList=> [{'r'}, {'y'}, {'y', 'x'}, {'y', 'z'}, {'y', 'x', 'z'}, {'t'}, {'y', 't'}, {'x', 't'}, {'y', 'x', 't'}, {'z', 't'}, {'y', 'z', 't'}, {'x', 'z', 't'}, {'y', 'x', 'z', 't'}, {'s'}, {'s', 'x'}, {'x'}, {'x', 'z'}, {'z'}]
myCondTree=> None
   Null Set   1
     z   5
       r   1
       x   3
         y   3
           t   3
             s   2
             r   1
     x   1
       s   1
         r   1

Process finished with exit code 0

2、应用：从新闻网站点击流中挖掘

if __name__ == '__main__':
    fs = open("G:kosarak.dat")
    readlines = fs.readlines()
    mydat=[]
    for line in readlines:
        split = line.split()
        mydat.append(split)
    data = createInitSet(mydat)
    MyFPtree,MyHeaderTable=createTree(data,100000)
    myFreqList = []
    #寻找至少被十万人浏览过的报道
    mineTree(MyFPtree,MyHeaderTable,100000,set([]),myFreqList)
    print(len(myFreqList))
    print(myFreqList)