Mining Frequent Patterns in Data Streams at Multiple Time Granularities

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Mining Frequent Patterns in Data Streams at
Multiple Time Granularities

• C.Giannella, J. Han, J. Pei,
• X. Yan and P. Yu

Pele Williams
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Presentation Outline

• Objective and Definition of Key terms
• Problem Definition Research Applications
• The FP-Stream Structure
• Pruning Techniques
• Algorithm
• Experiments, Results Conclusion

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Objective

• An extension of frequent pattern mining to Data
  Streams
• Propose the FP-stream structure which enables
  the dynamic mining of time-sensitive
  frequent patterns

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Terms Frequent Pattern Mining

• An Association Rule Mining technique that is
  used to obtain all frequent itemsets (from
  items in transactions) for a given minimum
  support threshold .

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Example Frequent Pattern Mining
Pattern Tree (r3) c ( r4) s
Database 01 s c r a 02 s r n 03 n r c a
04 r s 05 r s c
Pattern Base c r s (2) c r (1)
s r(4)
Support 0.6
Frequent Pattern Tree
r5 s4
c1 c2
Rules c r s r
Header Table Item Count r 5 s
4 c 3
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Problem Definition Solutions (1 of 2)

• How can Frequent Pattern Mining be applied to
  Data Streams?
• - Mine in batches (windows) and use a
  single-pass algorithm
• How can the completeness of frequent patterns in
  data streams be ensured?
• - Store a bit more information than the
  currently frequent items

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Problem Definition Solutions (1 of 2)

• How can the entire stream be mined within limited
  time and memory contraints?
• - Retain the counts of frequent and sub-frequent
  patterns and prune regularly
• How can time-sensitive Frequent Patterns be
  mined ?
• - Use a time-tilted window

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Applicable Queries

• What is the frequent pattern set over the period
  t2 and t3
• What are the periods when (a, b) is frequent?
• Does the support of a change dramatically in the
  period from t3 to t0

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Research Applications

• Mining Alarming Incidents (MAIDS)
• Network Traffic Analysis (Intrusion Detection)
• Shopping trends
• Dynamic Tracing of Stock Fluctuation
• Sensor Network Data Analysis
• Web Click Stream mining

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The FP- Stream Structure
This object is copied from the original paper
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Tilted-Time Windows
This object is copied from the original paper
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Time Granularity Error

• For a time window request consisting of h
  batches
• Time Granularity Error h - h h/2
• Example Last 24 batches 6 hours
• Gives the last 31 batches 7 24/2

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Intermediate Buffer Windows

• A temporary location to store batch counts at
  different granularity levels. E.g.
• B 8 ? f(8, 8) f(7, 7) f(6, 5) f(4, 1) .
• B 9 ? f(9, 9) f(8, 8) f(7, 7) f(6, 5)
  f(4, 1) .
• B 10 ? f(10, 10) f(9, 9) f(8, 7) f(6, 5)
  f(4, 1).

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Intermediate Buffer Windows

• B 11? f(11, 11) f(10, 10) f(9, 9) f(8, 7)
  f(6, 5) f(4, 1).
• B 12? f(12, 12) f(11, 11) f(10, 9) f(8, 5)
  f(4, 1).
• The size of the titled-time window can grow no
  larger than 2log2N) 2

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Frequent Pattern Pruning

• Tail Pruning Drop the counts of the last m to n
  windows if the sum of their frequency is lt ?
• fI(T) ?W fI(T) fI(T)
• Type I Pruning Supersets of an infrequent
  pattern are also infrequent
• Type II Pruning Drop the tails (or the entire
  pattern) of the all supersets if the subset has
  been dropped.

This equation is copied from the original paper
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Algorithm ( 1 of 3)

• Batch 1
• Compute the frequencies of all items
• Create f_list - Frequency ordered items
• Create FP-Tree with items with FI ? B1
• Mine all Patterns off the tree
• Create FP-Stream Structure
• ( Pattern Tree Time-Tilted Windows)

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Algorithm ( 2 of 3)

• Batchi for i 2
• Empty FP-Tree
• Sort each transaction, t , according to f_list
• Insert into FP-Tree without pruning items
• Mine pattern, I off the tree
• If I is in FP-Stream Structure
• - Add FI(B) to titled-time window for I
• - Do Tail Pruning
• - Do Type II Pruning

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Algorithm ( 3 of 3)

• If I is not in FP-Stream Structure
• - If FI(B) ? B
• - Insert I into FP-Stream Structure
• - Else Do Type I Pruning
• Scan FP-Stream structure
• If I was not updated in batch B, insert 0 in Is
  tilted-time window
• Do tail Pruning
• Drop leaf nodes with empty titled-time windows

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Experiments ( 1 of 2)

• IBM Synthetic Market-Basket Data Generator
• 3M Transactions using 1K distinct items
• Each batch was 50K transactions
• s 0.5 and 0.75
• ? 0.1 s
• Randomly permutates 200 table entries every five
  batches
• 3 Data sets Length 3, 5 7

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Experiments ( 2 of 2)

• Statistics At the end of each batch
• Time Number of seconds/ batch
• Size Size of FP-Stream structure
• Num Itemset Total number of itemsets
• Ave Len Length of an itemset

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Results ( 1 of 4)

• Time Average of 1000 trans/sec

This object is copied from the original paper
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Results ( 2 of 4)

• Size Approx 350k/batch

This object is copied from the original paper
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Results ( 3 of 4)

• Ave Length Length of approx. 3

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Results ( 4 of 4)

• Num Itemsets 500 -25, 000 itemsets

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Discussion

• Introduce a fading factor for older transactions
• Compress the FP-Stream structure further
  (parent-child)
• Reordering of (sub)frequent items
• Limit the length of the titled-time Window

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Related Work

• Stream Data Classification Domingos
  Hulten(2000)
• Stream Clustering Guha (2000), OCallaghan
  (2002)
• Mining Frequent Counts in Streams Manku (2002)
  Landmark model, mine FP in data streams by
  assuming patterns are measured from the start of
  the stream up to the current moment.

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Conclusions

• A novel approach to mine time-sensitive frequent
  patterns in data streams
• Overall space requirements can easily fit into
  main memory (less that 3M)
• The algorithm does not fall behind the stream
  (2000 -180 Transactions per seconds)

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Opinion

• The use of tilted-time windows is a novel and key
  idea to the mining of data streams
• Choice of the Maximum support error, ?, at which
  the loss of support will be insignificant

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• Questions ?

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Frequent, Sub-Frequent Infrequent Patterns

• For a Period T,
• If s minimum support
• ? maximum support error (0.1s )
• Frequent s
• s gt Subfrequent ?
• Infrequent lt ?

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Natural tilted-time window
This object is copied from the original paper
One month 4 24 31 59 units
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Logarithmic tilted-time window
One Year Log2 (365 24 4) 1 17
units Rather than 366 24 4 35, 136 units
This object is copied from the original paper
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Frequent Patterns for Tilted-Time Windows
back
This object is copied from the original paper