Temporal Database Paper Reading

1
Temporal DatabasePaper Reading

• R95922007 ???? ???
• Efficient Mining Strategy for Frequent Serial
  Episodes in Temporal Database, K Huang, C Chang

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Introduction

• Discover frequent serial episodes to find
  relationships between events.
• - explain the problems that cause a particular
  event
• - predict future result
• Episode a partially ordered collection of
  events occurring together.
• - the user defines how close is close enough
• - win the width of the time window

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Three classes of episodes

• Introduced by Mannila et al.
• Serial episodes
• - patterns of a total order in the sequence
• Parallel episodes
• - no constraints on the relative order
• Composite episodes
• - serial combination of parallel episodes

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Examples episodes
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Algorithms (old)

• Presented by Mannila et al.
• Finding parallel and serial episodes that are
  frequent enough.
• WINEPI
• - consider the support of an episode
• MINEPI
• - consider the number of minimal occurrences
• of an episode

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WINEPI

• Consider the Sequence SA3A4B5B6.
• support the number of sliding windows with
  width win.
• Given win3, there are six windows
• W1A3, W2A3A4, W3A3A4B5,
• W4A4B5B6, W5B5B6, W6B6 .
• ltA,Bgt is supported by two windows.

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MINEPI

• Consider the Sequence SA3A4B5B6.
• minimal occurrences an interval that contains
  episode a, but no proper sub-interval does.
• ltAgt has mo support 2.
• - interval 3,3 and 4,4.
• ltA,Bgt has mo support 1.
• - interval 4,5.

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Complex sequences

• Several events occurring at one time
• Example
• A temporal database is a complex sequence with
  temporal attributes.

A D B A B E C E A B F A C E B D F D
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Algorithms (new)

• Extend the algorithm to deal with complex
  sequences.
• MINEPI
• - depth-first enumeration to generate the
  frequent episodes by equalJoin and temporalJoin.
• EMMA
• - Episodes Mining using Memory Anchor
• - utilizes memory anchors to accelerate mining
  task

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More about MINEPI

• Breath-first manner
• - enumerate longer episodes from shorter ones
• Parameters
• - maxwin maximum window width for an episode
• - minsup minimal frequent for frequent
  episode
• Temporal Join
• - connects events from different time intervals

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Example MINEPI

• S A1A2B3A4B5, maxwin4, minsup2
• Find frequent 1-episode first
• - mo(A)1,1,2,2,4,4, mo(B)3,3,5,5
• Temporal Join with maxwin4
• - possibles of ltA,Bgt 1,3,2,3,2,5,4,5
• - mo(ltA,Bgt)2,3,4,5 (choose minimal ones)
• - support(ltA,Bgt)1,4,2,5,4,5
• - support count 3, counting distinct start
  point

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MINEPI

• Must deal with complex sequences.
• Depth-first manner for memory saving
• Equal Join
• - connects events at the same interval
• Bound List
• For a serial episode Pltp1,,pkgt
• - tsi,tei S contains P in time tsi,tei
• For an event Y
• - ti,ti S contains P in time ti

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Example bound list

• maxwin 4.
• Bound list of ltA,B,Cgt 1,4,3,6.
• Bound list of ltCgt 4,4,6,6.

1 2 3 4 5 6 7 8
A D B A B E C E A B F A C E B D F D
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Operations

• Given Pltp1,,pkgt and an event f.
• - P.boundlist ts1,te1,,tsn,ten
• - f.boundlist ts1,ts1,,tsm,tsm
• Equal Join P1P?fltp1,,pk?fgt.
• - P1.boundlist are tsi,tei such that
• teitsj for some j (1?j?m)
• Temporal Join P2P.fltp1,,pk,fgt.
• - P2.boundlist are tsi,tsj such that
• tsj-tsiltmaxwin and tsjgttei for some j (1?j?m)

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Drawbacks of MINEPI

• Huge amount of combinations
• - Consider I 1-frequent episodes
• - O(I2) checking for temporal joins and equal
  joins
• Unnecessary joins
• - should skip temporal joins for a prefix if the
  number
• of extendable matching bounds lt minsup
  TDB
• Duplicate joins
• - episode ltABC,ABCgt need 41 joins
• ltAgt?ltABgt?ltABCgt?ltABC,Agt?ltABC,ABgt?ltABC,ABCgt

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EMMA

• Divide into three phases
• (I) Mining frequent itemset in the complex
  sequence.
• (II) Encode each frequent itemset with a unique
  ID,
• and construct a encoded horizontal database.
• (III) Mining episodes in the encoded database.
• Depth-First Search
• Memory Anchor
• - utilize the boundlists to access information
• - timelists of frequent itemsets are their
  boundlists

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Example database

• minsup 5

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Combine episodes

• Only combine existing episodes with a local
  frequent 1-tuple episode.
• - overcome the huge amount of generations
• Projected boundlist (PBL)
• - episode 3ltCgt has boundlist
• 1,1,2,2,4,4,8,8,11,11,14,14,15,15
  
• - given maxwin 4, the projected boundlist is
• 2,4,3,5,5,7,9,11,12,14,15,16,16,1
  6
• - note that TDB16

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Example PBL

• 3.timelist1,2,4,8,11,14,15.
• 1 ? 2,4
• 2 ? 3,5
• 4 ? 5,7
• 8 ? 9,11
• 11 ? 12,14
• 14 ? 15,16
• 15 ? 16,16
• with maxwin 4 and TDB16.

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Local frequent ID

• A local frequent ID has boundlist that can match
  into other episodes PBL.
• - 3.PBL2,4,3,5,5,7,9,11,12,14,15,16
  ,16,16
• - 4.BL3,3,5,5,6,6,9,9,12,12,13,13,
  16,16
• Record boundlist of ID when examining.
• - get the boundlist immediately at temporal join
• - ltC,Dgtlt3,4gt then ltC,Dgt.boundlist
• 1,3,2,3,4,5,8,9,11,12,14,16,15,16
  

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Example temporal join

• 4.BL3,3,5,5,6,6,9,9,12,12,13,13,16
  ,16.
• Recall the construction of 3.PBL
• 1 ? 2,4 3,3 in it
• 2 ? 3,5 3,3 in it (take minimal)
• 4 ? 5,7 5,5 in it
• 8 ? 9,11 9,9 in it
• 11 ? 12,14 12,12 in it
• 14 ? 15,16 16,16 in it
• 15 ? 16,16 16,16 in it
• Result 1,3,2,3,4,5,8,9,11,12,14,16,
  15,16

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Procedure emmajoin

• Recursively extend the episodes
• - until no more serial episodes can be extended
• Avoid unnecessary checking in MINEPI
• - stop when the number of extendable bounds for
  a
• serial episode is less than minsup TDB.
• Example 2ltBgt.
• - 2.BL3,3,6,6,9,9,12,12,16,16
• - 2.PBL4,6,7,9,10,12,13,15
  (TDB16)
• - do not need to extend 2 if minsup 5

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Example emmajoin

• 3.BL1,1,4,4,8,8,11,11,14,14,15,15.
  
• 7.BL1,1,4,4,8,8,11,11,14,14.
• 9.BL3,3,6,6,9,9,12,12,16,16.
• Call emmajoin to extend each 1-tuple episodes
• 3.PBL2,4,5,7,9,11,12,14,15,16,16,16
  .
• Find local frequent IDs in 3.PBL.

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Example emmajoin (cont.)

• minsup 5, maxwin 4.
• By temporal Join
• - lt3,3gt.BL1,4,8,11,11,14,14,15
• - lt3,7gt.BL1,4,8,11,11,14
• - lt3,9gt.BL1,3,4,6,8,9,11,12,14,16
• - lt3,9gt is generated from prefix 3
• - recursively call emmajoin to extendlt3,9gt
• - lt3,9gt.PBL4,4,7,7,10,11,13,14
• - there are no local frequent IDs since minsup5
• Back to call emmajoin for episode 7.

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Experiments

• On a dataset composed of 10 stocks.
• Parameters maxwin/minsup.
• - more running time when maxwin increases
• - more running time when minsup decreases
• - since the number of frequent episodes
  increases
• EMMA runs faster than MINEPI.
• MINEPI uses lesser space than EMMA.
• - EMMA needs large memory as minsup decreases

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Conclusion

• Modify MINEPI to MINEPI
• - for mining episodes in a complex sequence
• Propose EMMA
• - avoid the drawbacks of MINEPI
• EMMA is more efficient than MINEPI.
• Future work
• - only discussed serial episodes
• - parallel and composite episodes remain to be
  solved