Tutorial on Assignment 3 in Data Mining 2008 Association Rule Mining. Gyozo Gidofalvi Uppsala Database Laboratory

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1 Tutorial on Assignment 3 in Data Mining 2008 Association Rule Mining Gyozo Gidofalvi Uppsala Database Laboratory

2 Announcements Monday the 15 th of December, has been added as a possible date for examination of assignment 3 and/or 4. Updated course home page with assignment 3 material. 11/26/2008 Gyozo Gidofalvi 2

3 Outline Association rules and Apriori-based frequent itemset mining Frequent pattern growth based frequent itemset mining Amos II / AmosQL crash course Frequent itemset mining - elements of a DB implementation using Amos II / AmosQL The assignment 11/26/2008 Gyozo Gidofalvi 3

4 Association Rules and Apriori-Based Frequent Itemset Mining

5 Association Rules The Basic Idea By examining transactions, or shop carts, we can find which items are commonly purchased together. This knowledge can be used in advertising or in goods placement in stores. Association rules have the general form: I 1 I 2 where I 1 and I 2 are disjoint sets of items that for example can be purchased in a store. The rule should be read as: Given that someone has bought the items in the set I 1 they are likely to also buy the items in the set I 2. 11/26/2008 Gyozo Gidofalvi 5

6 Large Itemsets An itemset is a set of single items from the database of transactions. If some items often occur together they can form an association rule. The support of an itemset expresses how often the itemset appears in a single transaction in the database, i.e., the support of an itemset I is the ratio of transactions in which the itemset is a subset. Supp I = Number of transactions containing I Total number of transactions An itemset is considered to be a large itemset if its support is above some threshold. 11/26/2008 Gyozo Gidofalvi 6

7 Finding the Large Itemsets The Brute Force Approach Just take all items and form all possible combinations of them and count away. Unfortunately, this will take some time... A better approach: The Apriori Algorithm Basic idea: An itemset can only be a large itemset if all its subsets are large itemsets 11/26/2008 Gyozo Gidofalvi 7

8 Example Assume that we have a transaction database with 100 transactions and we have the items a, b and c. Assume that the minimum support is set to 0.60, which gives us a minimum support count of 60. Itemset Count {a} 65 {b} 50 {c} 80 Since the count of {b} is below the minimum support count no itemset containing b can be a large itemset. This means that when we look for itemsets of size 2 we do not have to look for any sets containing b, which in turn leaves us with the only possible candidate {a,c}. 11/26/2008 Gyozo Gidofalvi 8

9 The Apriori Algorithm A general outline of the algorithm is the following: 1. Count all itemsets of size K. 2. Prune the unsupported itemsets of size K. 3. Generate new candidates of size K Prune the new candidates based on supported subsets. 5. Repeat from 1 until no more candidates or large itemsets are found. 6. When all supported itemsets have been found, generate the rules. 11/26/2008 Gyozo Gidofalvi 9

10 Candidate Generation Assume that we have the large itemsets of size 2 {a,b}, {b,c}, {a,c} and {c,d} From these sets we can form the candidates of size 3 {a,b,c}, {a,c,d} and {b,c,d} But... Why not {a,b,d}? Answer: 11/26/2008 Gyozo Gidofalvi 10

11 Candidate Pruning Again, assume that we have the large 2-itemsets {a,b}, {b,c}, {a,c} and {c,d} And the 3-candidates {a,b,c}, {a,c,d} and {b,c,d} Can all of these 3-candidates be large itemsets? Answer: 11/26/2008 Gyozo Gidofalvi 11

12 Find Out if the Itemset is Large When we have found our final candidates we can simply count all occurrences of the itemset in the transaction database and then remove those that have too low support count. If at least one of the candidates have enough support count we loop again until we can find no more candidates or large itemsets. 11/26/2008 Gyozo Gidofalvi 12

13 Rule Metrics When we have our large itemsets we want to form association rules from them. As we said earlier the association rule has the form I 1 I 2 The support, Supp tot, of the rule is the support of the itemset I tot where I tot = I 1 U I 2 The confidence, C, of the rule is C = Supp tot Supp I1 11/26/2008 Gyozo Gidofalvi 13

14 Rule Metrics (cont.) How can we interpret the support and the confidence of a rule? The support is how common the rule is in the transaction database. The confidence is how often the left hand side of the rule is associated with the right hand side. In what situations can we have a rule with: High support and low confidence? Low support and high confidence? High support and high confidence? 11/26/2008 Gyozo Gidofalvi 14

15 Frequent Pattern Growth Based Frequent Itemset Mining

16 The Frequent Pattern Growth Approach to FIM The bottleneck of Apriori is candidate generation and testing. High cost of mining long itemsets! Idea: Instead of bottom up, in a top-down fashion extend frequent patterns by adding a single locally frequent item to it Question: What does locally mean? Answer: To find the frequent itemsets that contain an item i, the only transactions that need to be considered are transactions that contain i. Definition: A frequent item i-related projected transaction table, is denoted as PT_i, that collects all frequent items (larger than i) in the transactions containing i. Let s look at an example! 11/26/2008 Gyozo Gidofalvi 16

17 Example Transactions Relational format Frequent items Filtered transactions Items co-occuring with item 1 Frequent items Projected table on item 1 Frequent items Items co-occuring with item 3 (and 1) Projected table on item 3 (and 1) 11/26/2008 Gyozo Gidofalvi 17

18 Frequent itemset tree depth-first Discover all frequent itemsets by recursively filtering and projecting transactions in a depth-first-search manner until there are frequent items in the filtered/projected table. 11/26/2008 Gyozo Gidofalvi 18

19 Amos II / AmosQL Crash Course

20 Amos II / AmosQL Resources Amos II: extensible, main-memory Object-Relational Database Management System (ORDBMS) Runs on PCs on Windows and Linux AmosQL: object-relational and functional query language Homepage: Tutorial: 11/26/2008 Gyozo Gidofalvi 20

21 Basic Amos II Data Model 11/26/2008 Gyozo Gidofalvi 21

22 Objects Regard database as set of objects Built-in atomic types, literals: String, Integer, Real, Boolean Collection types: bags, e.g., bag( Tore ) and vectors, e.g., {1,2,3} Surrogate types: Objects have unique object identifiers (OIDs), e.g. OID[45] Explicit creation and deletion AmosQL Example: Amos> create type Person; Amos> create Person instances :tore; creates new object, say OID[45], and binds environment variable :tore to it. 11/26/2008 Gyozo Gidofalvi 22

23 Types Classification of objects Objects are grouped by the types to which they belong (are instances of) Organized in type/subtype Directed Acyclic Graph Defines that OIDs of one type is subset of OIDs of other types 11/26/2008 Gyozo Gidofalvi 23

24 Functions Define semantics of objects: Properties of objects Relationships among objects (mappings between arguments and results) Views on objects Stored procedures for objects More than one argument allowed Bag valued results allowed, e.g, FrequentItems Tuple valued results allowed 11/26/2008 Gyozo Gidofalvi 24

25 Vectors Constructor: {} Amos> set :v = {1,2,3}; Indexing: Amos> :v[1]; Conversion between vectors and bags: Amos> in(:v); Amos> vectorof(in(:v)); Useful vector operators: dim, concat 11/26/2008 Gyozo Gidofalvi 25

26 Defining Set Operations On Vectors Amos> create function vintersect(vector v1, vector v2) -> vector as sort(select i from object i where i in v1 and i in v2); Amos> create function vdiff(vector v1, vector v2) -> vector as sort(select i from object i where i in v1 and notany (select where i in v2)); Amos> create function vunion(vector v1, vector v2) -> vector as sort(select distinct i from object i where i in v1 or i in v2); Amos> create function vcontain (vector v1, vector v2) -> boolean as select true where dim(v2) = dim(vintersect(v1, v2)); 11/26/2008 Gyozo Gidofalvi 26

27 Example: Association Rule DB Amos> create function FIS(vector) -> integer as stored; Amos> add FIS({'beer'})=5; Amos> add FIS({'other'})=2; Amos> add FIS({'diapers'})=3; Amos> add FIS({'beer','diapers'})=2; Amos> add FIS({'beer','other'})=1; Amos> add FIS({'beer','diapers','other'})=1; Amos> add FIS({'diapers','other'})=1; Amos> create function showfis() -> bag of <vector, integer> as select is, supp from vector is, integer supp where FIS(is)=supp; Amos> create function ARconf(vector prec, vector cons) -> real as FIS(vunion(prec,cons))/FIS(prec); Amos> ARconf({'beer'},{'diapers'}); Amos> ARconf({ diapers'},{'beer'}); 11/26/2008 Gyozo Gidofalvi 27

28 Frequent Itemset Mining Elements of a DB Implementation Using Amos II / AmosQL

29 Transactions Function (table) to store transactions: Amos> create function transact(integer tid)->bag of integer as stored; Population of the transaction table: Amos> add transact(1)=in({1,2,3}); remove transact(1)=2; Selection of a transaction: Amos> transact(1); Transactions as a bag of tuples: Amos> create function transact_bt()->bag of <integer, integer> as select tid, item from integer tid, integer item where transact(tid)=item; Materialized transaction table as a vector: Amos> create function transact_vt()->vector of <integer, integer> as vectorof(transact_bt()); 11/26/2008 Gyozo Gidofalvi 29

30 Support Counting Function to calculate the supports of items in vt: Amos> create function itemsupps_vt(vector of <integer, integer> vt) as groupby ((select i,t from integer i, integer t where <t,i> in vt), #'count'); ->bag of <integer, integer> 11/26/2008 Gyozo Gidofalvi 30

31 Item-Related Projection Function to calculate the pitem-related projected minsuppfiltered materialized transaction table Amos> create function irpft(vector of <integer, integer> vt, integer minsupp, integer pitem) as vselect tid, item ->vector of <integer, integer> from integer tid, integer item, integer i, integer s where <tid, item> in vt and freqitems_vt(vt, minsupp)=<i,s> and item = i and tid = itemsuppby_vt(vt, pitem) and item > pitem; 11/26/2008 Gyozo Gidofalvi 31

32 Subset Generation Function to filter a vector v to contain only elements that are larger than p Amos> create function vlarger(vector of integer v, integer p) ->vector of integer as vselect c from integer c where c in v and c>p; Recursive function to calculate all subsets of the set of elements in a vector c (to be called with empty vector p) Amos> create function subsets_rec(vector of integer p, vector of integer c) ->vector of integer as begin result (select res from vector of integer res, vector of integer newp, integer i where res = p or (res = subsets_rec(newp, vlarger(c,i)) and newp = concat(p,{i}) and i in c)); end; 11/26/2008 Gyozo Gidofalvi 32

33 The Assignment

34 The Assignment You can choose your favorite programming language, but NOT MATLAB since it is not suitable for this assignment. Since you can choose your own language you cannot expect help in language issues. You are going to run the solution on UNIX so please make sure that your solution is runnable on the University's UNIX system. The program must run in a few minutes since we are going to run it during the examination. Too slow programs will be rejected. 11/26/2008 Gyozo Gidofalvi 34

35 The Assignment (cont.) The algorithm is easy to get wrong and then you will get a superexponential behaviour that causes the execution time to blow up! Please make sure you understand the algorithm before you start programming. There are example runs on the course's home page. Your solution must be able to get these results before the examination. (Oh, and we will make other trial runs ;-) Finally, please read the instructions carefully, especially the parts about the command line interface and the rule sorting. 11/26/2008 Gyozo Gidofalvi 35

36 Exercise Find the rules with support 0.5 and confidence 0.75 in the following database: TID Transaction 1 {a b c d} 2 {a c d} 3 {a b c} 4 {b c d} 5 {a b c} 6 {a b c} 7 {c d e} 8 {a c} 11/26/2008 Gyozo Gidofalvi 36

37 Reference and Further Reading Mining Associations between Sets of Items in Large Databases. R. Agrawal, T. Imielinski, and A. Swami. In Proceedings of the ACM SIGMOD International Conference on the Management of Data, pp , May Fast Algorithms for Mining Association Rules. R. Agrawal and R. Srikant. In Proceedings of the 20th International Conference on Very Large Databases, pp , September An Effective Hash Based Algorithm for Mining Association Rules. J. S. Park, M.-S. Chen, and P. S. Yu. In Proceedings of the ACM SIGMOD International Conference on the Management of Data, pp , May Mining Frequent Patterns without Candidate Generation. J. Han, H. Pei, and Y. Yin. In Proceedings of the ACM-SIGMOD International Conference on Management of Data (SIGMOD'00), pp. 1-12, May Efficient Frequent Pattern Mining in Relational Databases. X. Shang, K.-U. Sattler, and I. Geist. 5. Workshop des GI-Arbeitskreis Knowledge Discovery (AK KD) im Rahmen der LWA /26/2008 Gyozo Gidofalvi 37