Mining Association Rules from Stars

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Mining Association Rules from Stars

Department of Information & Computer Education, NTNU

Eric Ka Ka Ng, Ada Wai-Chee Fu, and Ke Wang, 2002 IEEE International Conference on Data Mining (ICDM'02), December 09 - 12 2002, Mae

bashi City, Japan.

Advisor： Jia-Ling Koh

Speaker： Chen-Yi Lin

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Introductions Problem Definition The Proposed Method Experimental Results Conclusions


Outline

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Introductions

In real life, a database is typically made up of multiple tables and one important case is where some of the tables form a star schema.


Dimension table

Fact table (FT)

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Problem Definition (1/2)

Dimension table contains primary key (tid), some other attributes and no foreign keys.– The attributes in the dimension tables are uniqu

e.– The attributes take categorical values.

Fact table (FT)– stores the tids from dimension tables as foreign

keys.


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Problem Definition (2/2)

Dimension table and its binary representation

tidcategorical value

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The Proposed Method (1/8)

tid_list is an ordered list of elements of the form tid(count).– : e.g. – : e.g. – : e.g. – –

)( iA xtid 2,5)( 313 aaxtid A )(Xtid A )()()( jAiAjiA xtidxtidxxtid nakeyB _ 2,4_ 531 bbakeyB ixtidB _ XtidB _


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Minsup=5

count=6count=5

Hence the itemset is frequent6131 yyxx


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Binding multiple Dimension Tables– (1) To assign each combination of tid from A a

nd tid from B in FT a new tid– (2) and to set the tid in the tid_lists for items in

AB to the corresponding new tid.


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The set of frequent itemsets with items from tables A and/or B

An example of “binding” order

The set of frequent itemsets with items from tables A


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The Proposed Method (5/8) 1,1,2 4311 aaaxtid A 1,1,1,1 54211 ttttxtid AB

(1)

(2)


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The fact table FT is scanned once and the information is stored into a data structure– Prefix Tree

• each node has a label (a tid) and a counter.


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Prefix tree structure representing

tid counter


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Collapsing the prefix tree


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Experimental Results (1/5)

All experiments are conducted on SUN Ultra-Enterprise Generic_106541-18 with SunOS 5.7 and 8192MB Main Memory.

Programs are written in C++.


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In the first dataset, items in A and B are strongly related, such that frequent itemsets contain items across A and B, while items in C are not involved.

In the second dataset, items in A, B and C are all strongly related, so that maximal frequent itemsets always contain items from all of A, B and C.


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Running time for (A, B) related and (A, B, C) related datasets


masl: implementing tid_list as a linked list structuremasb: implementing tid_list as a fixed-size bitmap and an array of countfpt: the join-before-mine approach with FP-tree algorithm [HPY00]

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Mixture datasets– 10% of transactions contain frequent itemsets fr

om only A, B, C, respectively.– 15% contain frequent itemsets from AB, BC, A

C, respectively.– 10% contain frequent itemsets from ABC.– 15% are random noise.


18Running time for mixture datasets



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Conclusions


In the paper, the proposed method is a new algorithm for mining association rules on a star schema without performing the natural join.

The proposed method can be generalized to be applied to a snowflake structure.

Mining Association Rules from Stars

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