# Mining Sequential Patterns Generalizations and Performance

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```					Mining Sequential Patterns:
Generalizations and Performance
Improvements

R. Srikant R. Agrawal

Presented by: M.H. Lin
Outline
   Motivation
   Objective
   Introduction
   Problem Statement
   The New Algorithm: GSP
   Performance Evaluation
   Conclusion
   Personal Opinion
Motivation
   The problem of mining sequential patterns was
recently introduced.
   Limitations of the AprioriAll [Agrawal, 1995]
   Absence of time constraints
   Rigid definition of a transaction
   Absence of taxonomies
Objective
   We present GSP, a new algorithm that
discovers these generalized sequential patterns
   Empirically compared the performance of GSP
with the AprioriAll algorithm.
Introduction
   Instance
   A database of sequences, called data-sequences
   Each sequence is a list of transactions ordered by transaction-
time
   Each transaction is a set of items
   Definitions:
   A sequential pattern consists a list of itemsets
   Support:the number of data-sequences that contain the
pattern
   Problem:
   To discover all the sequential patterns with a user-specified
minimum support
Example Of A Sequential Pattern
   Database of book-club, each data-sequence
corresponds to a given customer’s all book
selection, each transaction contains the books
selected by the given customer in one order

   A sequential pattern:
5% of customers bought ‘Foundation’, then
‘Foundation and Empire’ and ‘Ringworld’,
then ‘Second Foundation’
Features of A Sequential Pattern
   E.g: 5% cust. bought ‘Foundation’, then ‘Foundation and Empire’ and
‘Ringworld’, then ‘Second Foundation’
   The Maximum and/or minimum time gaps between adjacent
elements.
   Eg: the time between buying ‘Foundation’, and then ‘Foundation and
Empire’ and ‘Ringworld’ should be within 3 months
   A sliding time window over the sequence-pattern elements
   E.g.: one week
   Mo: BK-a Sa: BK-b Next Su: BK-c ;
   This data-sequence supports the pattern “BK-a” and “ BK-b”, then
“BK-c”
   User-defined Taxonomies
   Example
 coming soon….
A User-defined Taxonomy

A customer who bought Foundation,then Perfect Spy, would support the
following patterns:
•Foundation, then Perfect Spy
•Asimov, then Perfect Spy
•Science Fiction, then Le Carre

…
The Old Algorithm--AprioriAll
   A 3-phase algorithm
   Phase 1: finds all frequent itemsets with min. support
   Phase 2: transforms the DB s.t. each transaction only
contains the frequent itemsets
   Phase 3: finds sequential patterns
   Pros.
   Can Discover all frequent sequential patterns
   Cons.
   Computationally expensive: space, time
   Not feasible to incorporate sliding windows
Problem Statement
   Definitions:
   Let I = {i1,i2,…,im} be a set of literals, called items
   Let T be a directed acyclic graph on the literals.
   An itemset is a non-empty set of items
   A sequence is an ordered list of itemsets
   We denote a sequence s by <s1s2…sn>, where sj is an itemset.
   We denote an element of sequence by (x1,x2,…,xm), where xj is
an item.
   A sequence <a1a2…an> is a subsequence of another sequence
<b1b2…bm> if there exist integers i1<i2<…<in such that a1  bi1 ,
a2 bi2 , …, an bin.

   E.g:<(3)(4,5)(8)> is a subsequence of <(7)(3,8)(9)(4,5,6)(8)>
   E.g:<(3)(5)> is not a subsequence of <(3,5)>
Problem Statement(contd.)
   A data-sequence contains a sequence s if s is a
subsequence of the data-sequence.
   Plus taxonomies:
   a transaction T contains an item x I if x is in T or x is an
ancestor of some item in T.
   Plus sliding windows:
   A data-sequence d = <d1…dm> contains a sequence s = <s1…sn>
if there exist integers l1≤u1<l2≤u2<…<ln ≤un such that
   1. si is contained in      , 1 ≤ i ≤ n , and
   2. transaction-time(dui) – transaction-time(dli) ≤window-size , 1 ≤ i ≤
n
   Plus time constraints:
   3. transaction-time(dli) - transaction-time(dui-1) > min-gap, 2 ≤ i ≤ n,
and
   4. transaction-time(dui) - transaction-time(dli-1) ≤ max-gap, 2 ≤ i ≤ n.
Problem Definition
   Input:
   Database D : data sequences
   Taxonomy T : a DAG, not a tree
   User-specified min-gap and max-gap time
constraints
   A user-specified sliding window size
   A user-specified minimum support
   Goal:
   To find all sequences whose support is greater than
the given support
Example

   minimum support: 2 data-sequences
   With the AprioriAll
   <(Ringworld)(Ringworld Engineers)>
   Sliding-window of 7 days adds the pattern
   <(Foundation, Ringworld)(Ringworld Engineers)>
   Max-gap of 30 days
   both patterns dropped
   Add the taxonomy, no sliding-window or time constraints, one is
   <(Foundation)(Asimov)>
GSP:Basic Structure
   Phase 1: makes the first pass over database
   To yield all the 1-element frequent sequences
   Phase 2: the kth pass:
   starts with seed set found in the (k-1)th pass to generate
candidate sequences, which has one more item than a seed
sequence;
   A new pass over D to find the support for these candidate
sequences
   These frequent candidates become the seed for the next pass
   Phase 3: terminates when
   no more frequent sequences are found
   no candidate sequences are generated
GSP: implementation
   Generating Candidates:
   To generate as few candidates as possible while
maintaining completeness
   Counting Candidates:
   To determine the candidate sequence’s support
   Implementing Taxonomies
Candidate Generation
   Definition:
   K-sequence : a sequence with k items,
   Lk : the set of frequent k-sequences,
   Ck : the set of candidate k-sequences
   Goal: given the set of all frequent (k-1)-sequences,
generate a candidate set of all frequent k-sequences
   Algorithm:
   Join Phase: joining Lk-1 with Lk-1 . s1 can join with s2 if (s1 – first
item) is the same as (s2 – last item)
   Prune Phase: delete candidate sequences that have a
contiguous (k-1) subsequence whose support count is less
than the minimum support
Candidate Generation: Example

   Join phase:
   <(1,2)(3)> joins with <(2)(3,4)> => <(1,2)(3,4)>
   <(1,2)(3)> joins with <(2)(3)(5)> => <(1,2)(3)(5)>
   Prune phase:
   <(1,2)(3)(5)> is dropped => <(1)(3)(5)> is not in L3
Counting Candidates
   Problem: given a set of candidate sequences C
and a data sequence d, find all sequences in C
that are contained in d.
   Two techniques are used
   Hash-tree data structure: to reduce the number of
candidates in C that need to be checked.
   Transformation the representation of the data-
sequences d : to find whether a specific candidate
is a subsequence of d efficiently.
Hash-Tree Structure
   Purpose: reducing the number of candidates
   Leaf node: a list of sequences
   Interior node: a hash table
   Operations:
   Adding candidate sequences to the hash-tree
   Finding the candidates contained in a data-
sequence
   Min-gap
   Max-gap
   Sliding window size
Representation Transformation
   Purpose: to efficiently find the first occurrence of an
element
   Transform the data sequences into transaction-links,
each link is identified by one item
   E.g.:max-gap=30,min-gap=5,window-size=0,<(1,2)(3)(4)>
   E.g.:window-size:7,find(2,6) after time=20
Implementing Taxonomies
   Basic Idea:
   to replace each data-sequence d with an “extended sequence”
d’, where each transaction di ’ contains all the items in the
corresponding transaction di ,as well as all their ancestors.
   E.g.:<(Foundation, Ringworld)(Second Foundation)> =>
<Foundation,Ringworld,Asimov,Niven,Science Fiction)(Second
Foundation,Asimov,Science Fiction)>
   Optimizations
   Pre-compute the ancestors of each item, drop infrequent
ancestors before a new pass
   Not count patterns with an element that contains an item x
and its ancestor y
   Problem: redundancy
   E.g.
Performance Evaluation
   Comparison of GSP and AprioriAll
   Result: 2 to 20 times faster
   Contributing factors:
   Fewer candidates
   Directly finding the candidates
   Scale-up:
   scales linearly with the number of data-sequences
   Effects of Time Constraints and Sliding
Windows:
   there was no performance degradation
Experiment Result
Experiment Result(contd.)
Experiment Result(contd.)
Experiment Result(contd.)
Experiment Result(contd.)
Conclusion
   GSP is a Generalized Sequence Mining Algorithm
   Discovering all the sequential patterns
   Good Customizability
   Has been incorporated into IBM’s data mining product
Personal Opinion
   Hash-tree Structure: main memory limitation
   Multi-pass over the database
   Apply GSP to CIS data

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