机器学习实战--fp-growth

接着前面所学的apriori频繁集挖掘，这里介绍一种更高效的发现频繁集的算法fp-growth(frequence pattern)，对大数据量时尤其有效（近百万条数据中查找，一般电脑只需2s左右）但fp-growth算法只能用来进行发现频繁集，不能挖掘关联规则。
fp-growth算法主要由两步：
1、构建fp树
2、利用fp树发现频繁集
构建fp树：
构建fp树时，需要扫描数据集2次，第一次统计出现的次数，得到项出现的频率；第二次只考虑频繁元素。
1、创建fp树数据结构

class treeNode:
    def __init__(self, nameValue, numOccur, parentNode):
        self.name = nameValue#元素名
        self.count = numOccur#元素出现的次数
        self.nodeLink = None
        #父节点，后面得到频繁集项进行回溯时会用到
        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)

2、除了fp树外，还需要一个头指针table保存指向不同类型的首元素的指针，整个数据结构如下：

第一次遍历数据集会得到各个元素出现的次数，接下来去掉不满足最小支持度的元素项。再进行下一步的构建fp树。再构建时，读入每一个项集并将其添加到一条已经存在的路径中。如果该路径不存在，创建一条新的路径。每个事务就是一个无序集合。假设有集合｛z,x,y｝和｛y,z,x｝,那么再fp树中，相同项只会表示一次。为了解决此问题，在将集合添加到树之前，需要对每个集合进行排序。排序基于元素项的绝对出现频率进行。

#dataSet simple：{feozenset(['r', 'z', 'h', 'j', 'p']):1, frozenset(['z', 'y', 'x', 'w', 'v', 'u', 't', 's']):2}
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

基于fp树的频繁集的挖掘：

def ascendTree(leafNode, prefixPath): #ascends from leaf node to root
    if leafNode.parent != None:
        prefixPath.append(leafNode.name)
        ascendTree(leafNode.parent, prefixPath)
#treeNode: 理解为headerTable头指针链表中的节点
#创建条件模式基
def findPrefixPath(basePat, treeNode): #treeNode comes from header table
    condPats = {}
    while treeNode != None:
        prefixPath = []
        ascendTree(treeNode, prefixPath)
        #add the prefixPath count
        if len(prefixPath) > 1: 
            condPats[frozenset(prefixPath[1:])] = treeNode.count
        treeNode = treeNode.nodeLink
    return condPats
#freqItemList：频繁集项列表
#inTree:fp树
#headerTable:头指针表
def mineTree(inTree, headerTable, minSup, preFix, freqItemList):
    bigL = [v[0] for v in sorted(headerTable.items(), key=lambda p: p[1])]#(sort header table)
    for basePat in bigL:  #start from bottom of header table
        newFreqSet = preFix.copy()
        newFreqSet.add(basePat)
        #print 'finalFrequent Item: ',newFreqSet #append to set
        freqItemList.append(newFreqSet)
        condPattBases = findPrefixPath(basePat, headerTable[basePat][1])
        #print 'condPattBases :',basePat, condPattBases
        #2. construct cond FP-tree from cond. pattern base
        myCondTree, myHead = createTree(condPattBases, minSup)
        #print 'head from conditional tree: ', myHead
        if myHead != None: #3. mine cond. FP-tree
            #print 'conditional tree for: ',newFreqSet
            #myCondTree.disp(1) 
            mineTree(myCondTree, myHead, minSup, newFreqSet, freqItemList)

测试：

#minSup = 3
#simpDat = loadSimpDat()
#initSet = createInitSet(simpDat)
#myFPtree, myHeaderTab = createTree(initSet, minSup)
#myFPtree.disp()
#myFreqList = []
#mineTree(myFPtree, myHeaderTab, minSup, set([]), myFreqList)