Mining Association Rules from Stars Department of Information & Computer Education, NTNU Mining Association Rules from Stars Eric Ka Ka Ng, Ada Wai-Chee Fu, and Ke Wang, 2002 IEEE International Conference on Data Mining (ICDM'02), December 09 - 12 2002, Maebashi City, Japan. Advisor：Jia-Ling Koh Speaker：Chen-Yi Lin

Outline Introductions Problem Definition The Proposed Method Department of Information & Computer Education, NTNU Outline Introductions Problem Definition The Proposed Method Experimental Results Conclusions

Department of Information & Computer Education, NTNU 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)

Problem Definition (1/2) Department of Information & Computer Education, NTNU Problem Definition (1/2) Dimension table contains primary key (tid), some other attributes and no foreign keys. The attributes in the dimension tables are unique. The attributes take categorical values. Fact table (FT) stores the tids from dimension tables as foreign keys.

Problem Definition (2/2) Department of Information & Computer Education, NTNU Problem Definition (2/2) categorical value tid Dimension table and its binary representation

The Proposed Method (1/8) Department of Information & Computer Education, NTNU The Proposed Method (1/8) tid_list is an ordered list of elements of the form tid(count). : e.g.

The Proposed Method (2/8) Department of Information & Computer Education, NTNU The Proposed Method (2/8) Minsup=5 count=6 count=5 Hence the itemset is frequent

The Proposed Method (3/8) Department of Information & Computer Education, NTNU The Proposed Method (3/8) Binding multiple Dimension Tables (1) To assign each combination of tid from A and 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.

The Proposed Method (4/8) Department of Information & Computer Education, NTNU The Proposed Method (4/8) The set of frequent itemsets with items from tables A and/or B The set of frequent itemsets with items from tables A An example of “binding” order

The Proposed Method (5/8) Department of Information & Computer Education, NTNU The Proposed Method (5/8) (1) (2)

The Proposed Method (6/8) Department of Information & Computer Education, NTNU The Proposed Method (6/8) 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.

The Proposed Method (7/8) Department of Information & Computer Education, NTNU The Proposed Method (7/8) counter tid Prefix tree structure representing

The Proposed Method (8/8) Department of Information & Computer Education, NTNU The Proposed Method (8/8) Collapsing the prefix tree

Experimental Results (1/5) Department of Information & Computer Education, NTNU 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++.

Experimental Results (2/5) Department of Information & Computer Education, NTNU Experimental Results (2/5) 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.

Experimental Results (3/5) Department of Information & Computer Education, NTNU Experimental Results (3/5) masl: implementing tid_list as a linked list structure masb: implementing tid_list as a fixed-size bitmap and an array of count fpt: the join-before-mine approach with FP-tree algorithm [HPY00] Running time for (A, B) related and (A, B, C) related datasets

Experimental Results (4/5) Department of Information & Computer Education, NTNU Experimental Results (4/5) Mixture datasets 10% of transactions contain frequent itemsets from only A, B, C, respectively. 15% contain frequent itemsets from AB, BC, AC, respectively. 10% contain frequent itemsets from ABC. 15% are random noise.

Experimental Results (5/5) Department of Information & Computer Education, NTNU Experimental Results (5/5) Running time for mixture datasets

Department of Information & Computer Education, NTNU 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.