1. Mining Frequent Patterns in Data Streams at Multiple Time Granularities CS525 Paper Presentation Presented by: Pei Zhang, Jiahua Liu, Pengfei Geng and Salah Ahmed Authors: Chris Giannella, Jiawei Han, Jian Pei, Xifeng Yan, Philip S. Yu

2. Part 1 Introduction Problem definition and analysis FP-Stream

3. Introduction Frequent pattern mining has been widely studied and used on static transaction data set, but it is challenging to extend it to data streams. Why it is difficult to mine frequent patterns in data streams? — Mining frequent itemsets is a set of join operations.

4. Problem definition and analysis Our task is to find the complete set of grequent patterns in a data stream. Apriori algorithm: count only those itemsets whose every proper subset is frequent. Problems to use Apriori-like algorithm — Join is a blocking operator — Infrequent items can become frequent later on and hence cannot be ignored.

5. Definition The frequency of an itemset I over a time period T is the number of transactions in T in which I occurs. The support of I is the frequency divide by the total number of transactions observed in I. I is frequent if its support is no less than min_support σ. I is sub frequent if its support is less than σ but no less than the maximun support error ε. Otherwise, I is infrequent.

6. FP-Stream This paper propose a time sensitive streaming model: FP-Stream, which includes two major components: 1.A global frequent pattern tree held in main memory. 2.Tilted time windows embedded in this pattern tree.

7. Part 2 Mining Time-Sensitive Frequent Patterns in Data Streams Maintaining Tilted-Time Windows

8. Natural tilted-time window People are often interested in recent changes. Recent changes are depicted at a fine granularity, but long term changes at a Coarse granularity.

9. Frequent patterns for tilted-time windows To mine a variety of frequent patterns associated with time more flexibly, a frequent pattern set can be maintained.

10. Pattern tree For each tilted-time window, one can register window-based count for each frequent pattern. Each node represents a pattern and its frequency is recorded in the node

11. FP-Stream Usually frequent patterns do not change dramatically over time. Overlap may occur To save space, embed the tilted-time window structure into each node

12. Maintaining Tilted-Time Windows With the arrival of new data In order to make the table compact Tilted-time window maintenance mechanism is needed

13. Logarithmic Tilted-time Window In the natural tilted-time window, at most 59 (4+24+31) tilted windows need to be maintained for a period of one month. We can reduce the number of tilted-time windows using logarithmic tilted-time windows schema According to logarithmic tilted-time window model, with one year of data and the finest precision at quarter, it needs units of time instead of units.

14. Logarithmic Tilted-time Window Break the stream of transactions into fixed sized batches B 1, B 2, B 3, …, B n … B n is most current batch, B 1 is the oldest For i ≥ j, let B(i, j) denotes U i k=j B k f I (i, j) denote the frequency of I in B(i, j) Frequencies for itemset I with ratio 2 (the growth rate of window size): Maintain intermediate buffer windows

15. Logarithmic Tilted-time Window Updating Given a new batch of transactions B Replace level 0: f(n, n) with f(B) Shift f(n, n) back to the next finest level of time (level 1) Check status of intermediate window for level 1: Not full. Place f(n-1, n-1) in the intermediate window, stop the algorithm Full. f(n-1, n-1) + f(intermediate window) is shifted back to level 2 Continue this process until shifting stops

16. Logarithmic Tilted-time Window Updating…Example

17. Part 3 Tail Pruning Type I Pruning Type II Pruning Algorithm

18. Tail Pruning Let be the tilted-time windows where is the oldest. is the window size of. Drop tail sequences when the following condition holds,

19. Type I and Type II Pruning Type I Pruning: If I is found in B but is not in the FP-stream structure, no superset is in the structure. Hence, if, then none of the supersets need be examined. Type II Pruning: If all of I’s tilted-time window table entries are pruned (and I is dropped), then any superset will also be dropped.

20. An Algorithm FP-streaming: Incremental update of the FP-stream structure with incoming stream data 1. Initialize the FP-tree to empty. 2. Sort each incoming transaction t, according to f list, and then insert it into the FP-tree without pruning any items. 3. When all the transactions in B i are accumulated, update the FP- stream as follows. Mine itemsets out of the FP-tree using FP-growth algorithm Scan the FP-stream structure

21. Part 4 Experimental Set-Up Experimental Results Discussion

22. Experiments Set-Ups Experiments are performed using Sun UltraSPARC-Iii Processors, 512 MB RAM Dataset Generation 3 Million Transactions 1k Distinct Items Streams are broken into batches of size 50k transactions For every 5 batches 200 random permutations are applied

23. FP-stream time requirements Item permutations causes the behavior to jump at every 5 batches Stability is regained quickly. Required time increases as the average itemset length increases.

24. FP-stream space requirements The overall space requirements are very attracting in call cases. It was less than 3MB.

25. FP-stream average itemset length The average itemset length does not increase with the increase of average transaction length This result was also verified by Apriori running on 50k transactions.

26. FP-stream total number of itemsets The total number of itemsets increase with the increase of average transaction length. This result was also verified by Apriori running on 50k transactions.

27. Discussion Further compression is possible. If the support is stable for lots of entries, the table can be compressed. If the tilted time windows of parent node and child node are the same, only one tilted time window can be maintained. It is a very nice idea to mine time sensitive frequent patterns. Mining and maintaining frequent patterns become realistic even with limited main memory.

28. Feedback Comments and Questions

29. Thank You