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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'])]
FP树与python实现
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