Sequential Pattern Mining and GSP

Sequential Pattern Mining
University of Kashan
Fall 2017
Hamidreza Mahdavipanah
Pegah Hajian
Narges Heydarzadeh
Professor: Dr. S. M. Vahidipour

Outlines
● Introduction
● Definitions
● GSP
● Constraints that GSP supports

Studies on Sequential Pattern Mining
● First introduced by Agrawal and Srikant in 1995
○ They presented three algorithms
■ AprioriAll
■ AprioriSome
■ DynamicSome
● Then in 1996 they presented GSP algorithm which was much faster than
former algorithms and it also was generalized for more real life problems
● Pattern-growth methods: FreeSpan and PrefixSpan
● Mining closed sequential patterns: CloSpan
● ...

Applications
● Customer shopping sequences
○ First buy computer, then CD-ROM, and then digital camera, within 3
month.
● Medical treatments
● Natural disasters (e.g., earthquakes)
● Stocks and markets
● DNA sequences and gene structures

Problem Statement
We are given a database D of customer transactions. Each transaction consists of
the following fields:
We want to find all large sequences that have a certain user-specified minimum
support.
It is similar to the frequent itemsets mining, but with consideration of ordering.
customer-id transaction-time items

Example of a
database
Customer Id Transaction Time Items Bought
1 June 25 ‘93 30
1 June 30 ‘93 90
2 June 10 ‘93 10, 20
2 June 15 ‘93 30
2 June 20 ‘93 40, 60, 70
3 June 25 ‘93 30, 50, 70
4 June 25 ‘93 30
4 June 30 ‘93 40, 70
4 June 25 ‘93 90
5 June 12 ‘93 90

We convert DB
to this form
Customer Id Customer Sequence
1 <(30)(90)>
2 <(10 20) (30) (40 60 70)>
3 <(30 50 70)>
4 <(30) (40 70) (90)>
5 <(90)>

Itemset and Sequence
An itemset is a non-empty set of items.
- We denote an itemset i by (i1
i2
… im
)
A Sequence is an ordered list of items.
- We denote a sequence s by <s1
s2
… sn
>

Subsequence and supersequence
Given two sequences α = <a1
a2
… an
> and β = <b1
b2
… bm
>:
● α is called a subsequence of β, if there exists integers 1 ≤ j1
< j2
< … < jn
≤ m
such that a1
⊆ b1
, a2
⊆ b2
, …, an
⊆ bjn
● β is called a supersequence of α
Example:
α=<(a b) d> and β=<(a b c) (d e)>

Apriori Property
of Sequential
Patterns
If a sequence S is not
frequent, then none of the
super-sequences of S is
frequent.
Example:
<h b> is infrequent -> so do
<h a b> and <(a h) b>

Outline of the GSP Method
● Initially, every item in DB is a candidate of length-1
● For each level (i.e., sequences of length-k) do
○ Scan database to collect support count for each candidate sequence
○ Generate candidate length(k + 1) sequences from length-k frequent
sequences using Apriori
○ Repeat until no frequent sequence or no candidate can be found

Major strength of GSP is its
candidate pruning by Apriori
property

Finding Length-1 Sequential Patterns
● Initial candidates:
○ <a>, <b>, <c>, <d>, <e>, <f>, <g>, <h>
● Scan database once, count support for candidates

Generating Length-2 Candidates
= 36

= 15

Using Apriori : 36 + 15 = 51 length-2 candidates
Without Apriori : (8 * 8) + (8 * 7) / 2 = 92 length- candidates
Apriori prunes 44.57% candidates

Finding Length-2 Sequential Patterns
● Scan database one more time, collect support count for
each length-2 candidate
● There are 19 length-2 candidates which pass the
minimum support threshold
○ They are length-2 sequential patterns

The GSP Algorithm
● Take sequences in form of <x> as length-1 candidates
● Scan database once, find F1
, the set of length-1 sequential
patterns
● Let k = 1; while Fk
is not empty do
○ Form Ck + 1
the set of length-(k + 1) candidates from Fk
○ If Ck + 1
is not empty, scan database once, find Fk + 1
, the
set of length(k + 1) sequential patterns
○ Let k = k + 1

The Good, the Bad, and the Ugly
● The Good: benefits from the Apriori pruning which reduces
search space
● The Bad: Scans the database multiple times
● The Ugly: Generates a huge set of candidates sequences

Why GSP is called Generalized Sequential Pattern Mining?
For practical use of SPM, in 1996 Agrawal and Srikant
introduced three type of constraints that makes SPM problem
more general and practical and since GSP support these
constraints it is called Generalized sequential pattern mining.

Time Constraint
An ability for users to specify maximum and/or minimum
time gaps between adjacent elements of the sequential
pattern.

Sliding Window
That is, each element of the pattern can be contained in the
union of the items bought in a set of transactions, as long as
the difference between the maximum and minimum
transaction-times is less than the size of a sliding time
window.

Taxonomy
An ability to define a taxonomy (is-a hierarchy) over the items
in the data.

References
● R. Agrawal and R. Srikant. Mining Sequential Patterns.1995
● R. Srikant and R. Agrawal. Mining Sequential Patterns.1996
● Jian Pei, Jiawei Han, Behzad Mortazavi-Asl, Helen Pinto, PrefixSpan: Mining
Sequential Patterns Efficiently by Prefix-Projected Pattern Growth. 2001

Sequential Pattern Mining and GSP

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