1 Finding Recent Frequent Itemsets Adaptively over Online Data Streams J. H, Chang and W.S. Lee, in Proc. Of the 9th ACM International Conference on Knowledge Discovery and Data Ming, Adviser: Jia-Ling Koh Speaker: Shu-Ning Shin Date:

2 Introduction This paper proposes a method of finding recent frequent itemsets ： –Significant itemsets are maintained by a prefix- tree lattice structure called monitoring lattice. –Decaying the old occurrence count of each itemset as time goes by. –Minimize the number of significant itemsets ： delayed-insertion pruning operations

3 Preliminaries (1) Data Stream can be defined ： –I={i 1, i 2, …, i n } ： a set of current items. –e ： itemset, a set of item. –Tid ： transaction id, T k generate at the kth turn. –D k =, When new transaction D k is generated. –|D| k ： the number of transactions in D k. –C k (e) ： the number of transactions in D k that contain the itemset e. –S k (e) ： Support of itemset e in D k.

4 Preliminaries (2) Decay rate ： the reducing rate of a weight for a fixed decay-unit. d=b -(1/h), (b>1, h ≧ 1, b -1 ≦ d<1) –decay-unit ： the chunk of information to be decayed together. –decay-base b ： the amount of weight reduction per a decay-unit and greater than 1. –decay-base-life h ： defined by the number of decay-units that makes the current weight be b -1.

5 Preliminaries (3) The total number of transactions |D| k in the current data stream D k ： –The value of |D| k converges to 1/(1-d) as the value k increases infinitely. The count C k (e) of an itemset e in the current data stream D k ：

6 Count Estimation of an itemset (1) The maximum possible count of an itemset is estimated by the minimum value among the maximum possible counts of all of its subsets.

7 Count Estimation of an itemset (2) Definition 1 ： – ： a set of itemset e ’ s subsets – ： a set of e ’ s m-subsets – ： a set of counts for e ’ s m-subsets Definition 2 ： –Union-itemset is composed of all items that are members of either e 1 or e 2. –Intersection-itemset is composed of all items that are members of both e 1 and e 2.

8 exclusively distributed (LED) ： the items of an itemset appear together in as many transactions as possible. most exclusively distributed (MED) ： the items of an itemset appear exclusively as many transactions as possible. The maximum count of n-itemset e ： Count Estimation of an itemset (3)

9 Count Estimation of an itemset (4) Two itemsets e 1, e 2 ： The minimum count of C min (e) can be estimated by (n-1)-subset union ： Estimation error ： –E(e)=C max (e)-C min (e)

10 estDec Method (1) Every node in a monitoring lattice maintains a triple (cnt, err, MRtid) for its corresponding itemset e ： –cnt ： count of e. –err ： maximum error count of e –Mrtid ： the most recent transacrion id that contain e

11 estDec Method (2) estDec Method is composed of four phase ： –Phase Ⅰ： parameter updating phase –Phase Ⅱ： count updating phase –Phase Ⅲ： Delayed insertion phase –Phase Ⅳ： frequent itemset selection phase

12 estDec Method (3) Phase II ： the counts of those itemsets in ML that appear in T k are updated. –S prn ： threshold for pruning. –If a 1-itemset is pruned from ML, it is impossible to estimate its count later. Phase I ： |D| k is updated.

13 estDec Method (4) Phase III ： Find new itemset that has high possibility to become frequent. Two cases insert new itemset to a ML ： –new 1-itemset, the cnt of 1-itemset is actual. –Itemset e C max (e)/|D| k ≧ S ins, S ins ： threshold for delayed-insertion. cntt_for_subsets=(1-d |e|-1 )/(1-d) max_xnt_before_subsets=Sins*(|D| k-(|e|-1) )*d |e|-1 ) C upper (e)=Max_xnt_before_subsets+ Cntt_for_subsets

14 estDec Method (5) Phase IV ： produces all current frequent itemsets in ML. –itemset e is frequent if its current support (cnt * d (k-MRtid) )/|D| k is greater than S min –its current support error ： (err*d (k-MRtid) )/|D| k

15 estDec Method (6) Force-pruning operation ： –all insignificant itemsets in ML can be pruned –perform when the current size of ML reaches a threshold.

16 Experimental (1) Performance of the estDec method for the data set T10.I4.D1000K –S ins is denoted p%, the actual value=S min *p%. –Force-pruning operation perform in every 1,000 transactions. –(a) memory usage (b) performance time of Phases I~III (c) performance time of Phases IV

17 Experimental (2) Accuracy of mining result –Average support error ASE(R estDec |R dApriori )

18 Experimental (3) The adaptability of the estDec method for the change of information in a data stream. –Coverage rate CR(X) |R| ： total nmber of frequent itemdets in ML