Sequential Patterns

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Sequential PatternsProcess Mining

• Current State of Research
• Edgar de Graaf
• LIACS

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Mining Sequential Patterns

• Sequential Patterns
• Sequence Databases
• AprioriAll
• PrefixSpan
• Gap Constraints

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Sequential Patterns

• lt(a,b)(c)(a,b,d)gt
• lt a1, a2, a3 gt
• lt(3)(4,5)(8)gt contained in lt(7)(3,8)(9)(4,5,6)(8)gt
  
• lt(3)(4,5)(8)gt not contained in lt(7)(3,8)(9)(4)(5,6
  )(8)gt

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Sequential databases
The Database with sequences
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Sequential databases
lt(3)(4,5)(8)gt
Support count 0
A Generated Candidate Pattern
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Sequential databases
lt(3)(4,5)(8)gt
Support count 0
1
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Sequential databases
Support count 1
lt(3)(4,5)(8)gt
Not Contained ? Not Counted
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Sequential databases
Contained
Support count 1
2
3
4
5
Contained
Contained
IF Minimal Support 50 THEN lt(3)(4,5)(8)gt
frequent
Contained
Contained
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Lifting order (1)

• Notation by examples
• ltA,B,Cgt, a ordered list of sets sequence
• Every set A,B and C is unordered. E.g. A
  (x,y,z) (y,z,x) (z,y,x)
• x,y,z is an extension we ignore the order when
  counting frequency

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Lifting order (2)

• lt(t1)(t2)(t3)(t4)gt and
• lt(t1)(t3)(t2)(t4)gt frequent
• ?
• lt(t1)(t3,t2)(t4)gt is frequent
• Says t3 and t2 occurs frequent in-between t1 and
  t4 in either order

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Lifting Order (3)

• lt(t1)(t2)(t3)(t4)gt and
• lt(t1)(t3)(t2)(t4)gt infrequent
• suppose (t1)t3,t2(t4) frequent
• Says often t3 and t2 occur in-between t1 and t4

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Existing Algorithms

• AprioriAll the first algorithm based on the
  anti-monotone principles
• PrefixSpan currently the fastest algorithm
  around, it uses projected databases

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AprioriAll (1)

• AprioriAll(DB, min_sup)
• L1 frequent sequences size 1
• k 2
• while(Lk-1 is not empty)
• Ck candidateGeneration(Lk-1,k)
• Ck candidatePruning(Ck, k)
• Lk supportBasedPruning(Ck)
• k

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AprioriAll (2)

• candidateGeneration(Lk-1, k)
• Ck ø
• for each a in Lk-1
• for each b in Lk-1
• if(all n, 1 n k-2 an bn)
• toevoegen aan Ck de sequences
• a1ak-2, ak-1, bk-1 en
• a1ak-2, bk-1, ak-1

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PrefixSpan (1)

• Assume that the prefix lt(a,b)(c)gt
• Scan de projected database to find every frequent
  item x such that
• lt(a,b)(c,x)gt is frequent or
• lt(a,b)(c)(x)gt is frequent
• Append the x to the prefix and output the pattern
• Now call recursively e.g. PrefixSpan(lt(a,b)(c,x)gt
  , newProjDB)

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PrefixSpan (2)

• A projected DB only stores the postfix
• E.g. if prefix lt(a,b)gt then we store lt(a,b,x)gt
  as lt( _, x)gt
• New projected DB Old projected DB sequences
  without prefix

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PrefixSpan (3)

• Faster than AprioriAll
• No non-existing candidates
• Testing on a shrinking projected DB

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Gap Constraint

• Simple idea between sequence-item-sets a maximal
  distance
• lt(a)(c)(d)(e)gt, e.g. pattern lt(a)(e)gt and gap
  1 then this sequence is not counted

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Process Mining

• What is process mining?
• Using D/F tables and graphs
• Genetic Algorithms
• Problem areas
• Using sequential patterns

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What is process mining? (1)

• The ordering of events is known e.g. lt(task
  A)(task B)(task C)gt
• Process mining constructs a petri net

pay
ready
claim
register
to_be_evaluated
send_letter
Source Workflow Management by W. van der Aalst
and K. van Hee. (1997)
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What is process mining? (2)

• Usability of process mining
• Given the audit trails, what is the workflow
  network?
• Mined workflow network original design? (Delta
  Analysis)
• Mined workflow network better than the original
  design? (Performance Analysis)

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Using D/F tables and graphs (1)

• For every task a D/F table
• Intuition if A is often followed by B then the
  probability of A causing B increases

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Using D/F tables and graphs (2)

• A D/F graph is constructed
• IF((A?B N) AND (A gt B s) AND
• (B lt A s) THEN connection A to B
• More complicated rules deal with recursion and
  short loops

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Using D/F tables and graphs (3)

• D/F Graph example

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Using D/F tables and graphs (4)

• AND/OR-Splits
• OR if neither C gt B or B gt C is higher
• than the threshold
• AND if both are higher than threshold

B
A
C
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Genetic Algorithms (1)

• Create a initial population of workflows
• Calculate their fitness using audit trails
• Create a child
• Mutate the child
• Repeat 3 to 4 to create the new population
• Go to 2

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Genetic Algorithms (2)

• Advantages
• Can deal with duplicate tasks and non-free
  choice.
• Disadvantages
• The structure of the chromosome
• How do we measure fitness?
• How do we do cross-over and mutation?

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Problem Areas (1)

• Hidden tasks
• Duplicate tasks when tasks have the same name

B
C
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Problem Areas (2)

• Mining non-free-choice

A
D
C
B
E
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Problem Areas (3)

• Mining Loops
• ABCDBCD

D
A
B
C
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Problem Areas (4)

• Delta analysis how do we compare two models?
• Other problems time, dealing with noise and
  incompleteness.

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Using sequential patterns

• Mining loops?
• Fitness measure in a GA?
• Use in delta analysis?
• Generate the important frequent subsequences to
  help the designer

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Further research in sequences

• How about gaps between items in different item
  sets?
• What type of frequent subsequences to use in
  fitness?
• Lifting order, is it useful in workflow
  generation?
• Further research of lifting order

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The End

• Thank you for your attention
• Edgar de Graaf
• edegraaf_at_liacs.nl