FP树与python实现

FP-growth算法可以高效的发现频繁项集，但是该算法不能去发现关联规则，FP-growth算法 只需要对数据库进行两次扫描，一般情况下其算法效率高于Apriori算法两个数量级。

一颗FP树是如下图1所示：

跟别的树没什么区别，只是增加了相似节点的链接。

FP树的定义：

class treeNode :
    def __init__(self,nameValue,numOccur,parentNode):
        self.name = nameValue
        self.count = numOccur
        self.nodeLink = None
        self.parent = parentNode
        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)

disp()函数主要是以文本显示出树的结构。在实现中，我们需要一个头指针表来指向给定类型第一个实例，如下图2：

这个算法核心部分就是建立FP树，下面是建树代码：

def createTree(dataSet, minSup=1): #create FP-tree from dataset but don't mine
    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]
    for k in headerTable.keys():  #remove items not meeting minSup
        if headerTable[k] < minSup:
            del(headerTable[k])
    freqItemSet = set(headerTable.keys())
    #print 'freqItemSet: ',freqItemSet
    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
    retTree = treeNode('Null Set', 1, None) #create tree
    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:
            orderedItems = [v[0] for v in sorted(localD.items(), key=lambda p: p[1], reverse=True)]
            updateTree(orderedItems, retTree, headerTable, count)#populate tree with ordered freq itemset
    return retTree, headerTable #return tree and header table

def updateTree(items, inTree, headerTable, count):
    if items[0] in inTree.children:#check if orderedItems[0] in retTree.children
        inTree.children[items[0]].inc(count) #incrament count
    else:   #add items[0] to inTree.children
        inTree.children[items[0]] = treeNode(items[0], count, inTree)
        if headerTable[items[0]][1] == None: #update header table
            headerTable[items[0]][1] = inTree.children[items[0]]
        else:
            updateHeader(headerTable[items[0]][1], inTree.children[items[0]])
    if len(items) > 1:#call updateTree() with remaining ordered items
        updateTree(items[1::], inTree.children[items[0]], headerTable, count)

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

参考着图2 我们可以比较清楚理解建树过程：headerTable就是头指针表，维护这张表是为了后面发现频繁项集中用到做准备。这里有一些实现细节东西，我们对所有的元素项先进行计数，如果不满足最低支持度，直接删掉不用加入FP树中。updateTree()函数时更新树，updateHeader()是维护headerTable头指针表 。

从一棵FP树中挖掘频繁项集：

class treeNode :
    def __init__(self,nameValue,numOccur,parentNode):
        self.name = nameValue
        self.count = numOccur
        self.nodeLink = None
        self.parent = parentNode
        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)

def createTree(dataSet,minSup=1):
    headerTable = {}
    for trans in dataSet:
        for item in trans:
            headerTable[item] = headerTable.get(item,0)+ dataSet[trans]
    for k in headerTable.keys():
        if headerTable[k] < minSup:
            del(headerTable[k])
    freqItemSet = set(headerTable.keys())
    if len(freqItemSet) == 0 : return None,None
    for k in headerTable:
        headerTable[k] = [headerTable[k],None]
    retTree = treeNode('Null Set',1,None)
    for tranSet ,count in dataSet.items():
        localD = {}
        for item in tranSet:
            if item in freqItemSet:
                localD[item] = headerTable[item][0]
        if len(localD) > 0:
            orderedItems = [v[0] for v in sorted(localD.items(),key = lambda p:p[1],reverse = True)]
            updateTree(orderedItems,retTree,headerTable,count)
    return retTree,headerTable

def updateTree(items,inTree,headerTable,count):
    if items[0] in inTree.children:
        inTree.children[items[0]].inc(count)
    else:
        inTree.children[items[0]] = treeNode(items[0],count,inTree)
        if headerTable[items[0]][1] ==None:
            headerTable[items[0]][1] = inTree.children[items[0]]
        else:
            updateHeader(headerTable[items[0]][1], inTree.children[items[0]])
    if len(items) > 1:
        updateTree(items[1::], inTree.children[items[0]], headerTable, count)

def updateHeader(nodeToTest,targetNode):
    while (nodeToTest.nodeLink !=  None):
        nodeToTest = nodeToTest.nodeLink
    nodeToTest.nodeLink = targetNode

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

def ascendTree(leafNode,prefixPath):
    if leafNode.parent !=None:
        prefixPath.append(leafNode.name)
        ascendTree(leafNode.parent, prefixPath)

def findPrefixPath(basePat,treeNode):
    condPats={}
    while treeNode != None:
        prefixPath = []
        ascendTree(treeNode, prefixPath)
        if len(prefixPath) > 1:
            condPats[frozenset(prefixPath[1:])] = treeNode.count
        treeNode = treeNode.nodeLink
    return condPats

def mineTree(inTree,headerTable,minSup,preFix,freqItemList):
    bigL = [v[0] for v in sorted(headerTable.items(),key=lambda p:p[1])]
    for basePat in bigL:
        newFreqSet = preFix.copy()
        newFreqSet.add(basePat)
        freqItemList.append(newFreqSet)
        condPattBases = findPrefixPath(basePat, headerTable[basePat][1])
        myCondTree,myHead = createTree(condPattBases, minSup)
        if myHead!= None:
            print 'conditional tree for: ',newFreqSet
            myCondTree.disp(1)
            mineTree(myCondTree, myHead, minSup, newFreqSet, freqItemList)

if __name__ == "__main__":
    simpDat = loadSimpDat()
    print simpDat
    initSet = createInitSet(simpDat)
    print initSet
    myFPtree , myHeaderTab = createTree(initSet, 3)
    myFPtree.disp()
    print findPrefixPath('t', myHeaderTab['t'][1])
    freqItems = []
    mineTree(myFPtree, myHeaderTab, 3, set([]), freqItems)
    print freqItems
    

输出结果：

[['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']]
{frozenset(['e', 'm', 'q', 's', 't', 'y', 'x', 'z']): 1, frozenset(['x', 's', 'r', 'o', 'n']): 1, frozenset(['s', 'u', 't', 'w', 'v', 'y', 'x', 'z']): 1, frozenset(['q', 'p', 'r', 't', 'y', 'x', 'z']): 1, frozenset(['h', 'r', 'z', 'p', 'j']): 1, frozenset(['z']): 1}
  Null Set    1
   x    1
    s    1
     r    1
   z    5
    x    3
     y    3
      s    2
       t    2
      r    1
       t    1
    r    1
{frozenset(['y', 'x', 's', 'z']): 2, frozenset(['y', 'x', 'r', 'z']): 1}
conditional tree for:  set(['y'])
  Null Set    1
   x    3
    z    3
conditional tree for:  set(['y', 'z'])
  Null Set    1
   x    3
conditional tree for:  set(['s'])
  Null Set    1
   x    3
conditional tree for:  set(['t'])
  Null Set    1
   y    3
    x    3
     z    3
conditional tree for:  set(['x', 't'])
  Null Set    1
   y    3
conditional tree for:  set(['z', 't'])
  Null Set    1
   y    3
    x    3
conditional tree for:  set(['x', 'z', 't'])
  Null Set    1
   y    3
conditional tree for:  set(['x'])
  Null Set    1
   z    3
[set(['y']), set(['y', 'x']), set(['y', 'z']), set(['y', 'x', 'z']), set(['s']), set(['x', 's']), set(['t']), set(['y', 't']), set(['x', 't']), set(['y', 'x', 't']), set(['z', 't']), set(['y', 'z', 't']), set(['x', 'z', 't']), set(['y', 'x', 'z', 't']), set(['r']), set(['x']), set(['x', 'z']), set(['z'])]