python机器学习笔记（11）—— FP-growth
0x00 什么是FP-growth算法？
在使用google时，我们在输入关键词后，它会自动给我们可能的补全项。FP-growth就可以实现这个功能。FP-growth是用于高效发现频繁集的算法。它两次扫描数据，其中第一次是构建FP树，第二次是从中挖掘频繁项集。
- 优点：速度一般较快。
- 缺点：大数据集下运算较慢。
- 适用数据范围：数值型或标量型。
0x01 构建FP树
FP树的特点是可能会出现重复的项，并且重复项会有指针相连。树的容器结构如下：
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)
然后是构建树的代码：
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
createTree()首先计算并移除不满足支持度的项目，然后初始化头指针列表，利用updateTree()函数生成树节点。
updateTree()则首先判断项目是否在其子节点中，在则增加子节点计数；不在则生成该子节点，使用updateHeader()函数生成节点间指针，并对子节点递归。
updataHeader()是一个简单的循环，找到该节点的最后一次重复位置。
测试结果如下：
import fpGrowth
simpDat = fpGrowth.loadSimpDat()
print 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']]
initSet = fpGrowth.createInitSet(simpDat)
print initSet
# {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}
myFPtree, myHeaderTab = fpGrowth.createTree(initSet,3)
myFPtree.disp()
# 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
0x02 从FP树中挖掘频繁规则
首先我们需要得到给定某元素结尾的所有路径。
def ascendTree(leafNode, prefixPath): #ascends from leaf node to root
if leafNode.parent != None:
prefixPath.append(leafNode.name)
ascendTree(leafNode.parent, prefixPath)
def findPrefixPath(basePat, treeNode): #treeNode comes from header table
condPats = {}
while treeNode != None:
prefixPath = []
ascendTree(treeNode, prefixPath)
if len(prefixPath) > 1:
condPats[frozenset(prefixPath[1:])] = treeNode.count
treeNode = treeNode.nodeLink
return condPats
代码还是相当直观的，就不作解释（作者写了个卵用没有的basePat变量是方便读者理解么……）。
然后递归查找频繁集：
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)
比较难以理解的部分可能是preFix这个参数。这个参数在每次递归之前都会加入用于生成上面所说的 给定某元素结尾的所有路径 的这个元素，然后把加入该元素后的集合append到返回参数中。
运行效果是这样的：
freqItems = []
fpGrowth.mineTree(myFPtree, myHeaderTab, 3, set([]), freqItems)
# 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
print freqItems
# [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'])]