SEQUENTIAL PATTERNS & THE GSP ALGORITHM

BY: JOE CASABONA

INTRO

• What are Sequential Patterns?• Why don't ARs suffice?• The General Sequential Pattern Algorithm

o Finding Frequent Setso Candidate Generationo Rule Generation

WHAT ARE SEQUENTIAL PATTERNS?

"Finding statistically relevant patterns between data examples where the values are delivered in a sequence." [3]

Very similar to Association Rules, but sequence in this case matters. There may be times when order is important. 

SEQUENTIAL PATTERN EXAMPLES

In Transaction Processing:     Do customers usually buy a new controller or a game first after buying an Xbox?

In Text Mining:    Order of the words important for finding linguistic orlanguage patterns [1]

OBJECTIVE

Given a set S of input data sequences, find all sequences that have a user-specified minimum support. This is called a 'frequent sequence' or sequential pattern. [1]

We will use the Generalized Sequential Pattern Algorithm (GSP)

GSP

Similar to Apriori Algorithm•  Find individual items with minSupport (1-

sequences)• Use them to find 2-sequences• Continue using k-sequences to find

(k+1)-sequences• Stop when there are no more frequent

sequences. Difference is in Candidate Generation 

GSP: CANDIDATE GENERATION

Input : Frequent Set k-1 (F[k-1])Output: Candidate Set C[k] How it works: • Join F[k-1] with F[k-1]•  Get rid of infrequent sequences (prune)• Note: Order of items matter 

CANDIDATE EXAMPLE

F[3] = <{1, 2} {4}>, <{1, 2} {5}>, <{1} {4, 5}>, <{1, 4} {6}>, <{2} {4, 5}>, <{2} {4} {6}> After Join: <{1, 2} {4, 5}>, <{1, 2} { 4} {6}> After Prune: <{1, 2} {4, 5}>  C[4]=  <{1, 2} {4, 5}>

RULE GENERATION

Objective not to generate rules, but it can be done.  Sequential Rule: Apply confidence to  Frequent Sequences Label Sequential Rules: Replace some elements in X with *

RERERENCES

[1] The Book I am using: Liu, Bing. Web Data Mining, Chapter 2: Association Rules and Sequential Patterns. Springer, December, 2006  Wikipedia:[2] "GSP Algorithm." http://en.wikipedia.org/wiki/GSP_AlgorithmJune 3, 2008

[3] "Sequence Mining." http://en.wikipedia.org/wiki/Sequence_miningOct. 30, 2008