Research issues on association rule mining Loo Kin Kong 26 th February, 2003

Plan Recent trends on data mining Association rule interestingness Association rule mining on data streams Research directions Conclusion

Association rules First proposed in [Agarwal et al. 94] Given a database D of transactions, which contains only binary attributes For an itemset x, the support of x is defined as supp(x) = fraction of D containing x An association rule is in the form I  J, where: I  J =  supp(I  J)   supp supp(I  J) / supp(I)   conf

Recent trends on association rule mining Association rule interestingness Association rule mining on data streams Privacy preserving [Rizvi el al. 02] New data structures to improve the efficiency of finding frequent itemsets [Relue et al. 01]

Association rule interestingness – overview Problem with association rule mining: Too many rules mined Mined rules may contain redundancy or trivial rules Subjective approaches aim at: Minimizing human effort involved Objective approaches aim at: Based on some predefined interestingness measure, filter rules that are uninteresting

Subjective approaches Rule templates [Klemettinen et al. 94] A rule template specifies what attributes to occur in the LHS and RHS of a rule e.g., any rule in the form “” & (any number of conditions)  “” is uninteresting By elimination [Sahar 99] For a rule r = A  B, r ’ = a  b is an ancestor rule if a  A and b  B. r’ is said to cover r. An ancestor rule can be classified as one of the following: True-Not-Interesting (TNI) Not-True-Interesting (NTI) Not-True-Not-Interesting (NTNI) True-Interesting (TI)

Objective approaches Statistical / problem-specific measures Entropy gain, lift, … Pruning redundant rules by the maximum entropy principle [Jaroszewica 02]

Probability A finite probability space is a pair (S,P), in which S is a finite non-empty set P is a mapping P:S  [0,1], satisfying  s  S P(s) = 1 Each s  S is called an event P(s), also denoted by p s, is the probability of the event s The self-information of s is defined as I(s) = – log P(s)

Entropy A partition U is a collection of mutually exclusive elements whose union equals S Each element contains one or more events The measure of uncertainty that any event of a partition U would occur is called the entropy of the partitioning U H( U ) = – p 1 log p 1 – p 2 log p 2 – … – p N log p N Where p 1,..., p N are respectively the probabilities of events a 1,..., a N of U H( U ) is maximum if p 1 = p 2 =... = p N = 1/N

The maximum entropy method (MEM) The MEM determines the probabilities p i of the events in a partition U, subject to various given constraints. By MEM, when some of the p i ’ s are unknown, they must be chosen to maximize the entropy of U, subject to the given constraints.

Definitions A constraint C is a pair C = ( I, p), where: I is an itemset p  [0,1] is the probability of I occurring in a transaction The set of constraints generated by an association rule I  J is defined as C( I  J ) = {( I, supp( I )), ( I  J, supp( I  J ))} A rule K  J is a sub-rule of I  J if K  I

I -nonredundancy A rule I  J is considered I -nonredundant with respect to R, where R is a set of association rules, if: I = , or I (C I, J (R), I  J ) is larger than some threshold, where I () is either I act () or I pass (), C I, J (R) is the constraints induced by all sub-rules of I  J in R

Pruning redundant association rules Input: A set R of association rules 1. For each singleton A i in the database 2. R i = {   A i } 3. k = 1 4. For each rule I  A i  R, | I |=k, do 5. If I  A i is I -nonredundant w.r.t. R i then 6. R i = R i  { I  A i } 7. k = k+1 8. Goto 4 9. R =  R i

Association rule interestingness: let’s face it... “Interesting” is a subjective sense... Domain knowledge is needed at some stage to determine what is interesting... in fact, one may argue that there does not exist a truly objective interestingness measure... It is because we try to model what is interesting... but “objective” interestingness measures are still worth studying Can act as a filter before any human intervention is required

Interesting or uninteresting? Consider the association rule: r = I  J, supp(r) = 1%, conf(r) = 100% A question: Do you think whether r is interesting or uninteresting? Considering the support and/or confidence of one single rule may not be enough to determine whether a rule is interesting or not So we try to compare a rule with some other rule(s)

Observation: comparing a family of rules For a maximal frequent itemset I: The set of rules I’  {i}, where i  I, I’  I \ {i} forms a family of rules For example, for the maximal frequent itemset {abcde}, abcd  econf = supp({abcde})/supp({abcd}) abc  econf = supp({abce})/supp({abc}) abd  econf = supp({abde})/supp({abd})... are in a family

abcd e abcdabceabdeacdebcde bcdabeaceadebcebdecdeabcabdacd bcbdcdaebecedeabacad abcde 

Observation: comparing a family of rules (cont’d) The blue half of the lattice is obtained by appending the item “e” to each node in the orange half The family of rules captures how the item “e” affects the support of the orange half of the lattice Idea: We may compare confidences of rules in a family to find any “unusually” high or low confidences We can use some statistical tests to perform the comparison; no need for complicated statistical models (e.g., MEM)

Association rule mining on data streams In some new applications, data come as a continuous “ stream ” The sheer volume of a stream over its lifetime is huge Queries require timely answer Examples: Stock ticks Network traffic measurements A method for finding approximate frequency counts on data streams is proposed in [Manku et al. 02]

Goals of the paper The algorithm ensures that All itemsets whose true frequency exceeds sN are reported (i.e., no false negative) No itemset whose true frequency is less than ( s-  ) N is output Estimated frequencies are less than the true frequencies by at most  N Some notations: Let N denote the current length of the stream Let s  (0,1) denote the support threshold Let   (0,1) denote the error tolerance

The simple case: finding frequent items Each transaction in the stream contains only 1 item 2 algorithms were proposed, namely: Sticky Sampling Algorithm Lossy Counting Algorithm Features of the algorithms: Sampling techniques are used Frequency counts found are approximate but error is guaranteed not to exceed a user-specified tolerance level For Lossy Counting, all frequent items are reported

Lossy Counting Algorithm Incoming data stream is conceptually divided into buckets of  1/  transactions Counts are kept in a data structure D Each entry in D is in the form ( e, f,  ), where: e is the item f is the frequency of e in the stream since the entry is inserted in D  is the maximum count of e in the stream before e is added to D

Lossy Counting Algorithm (cont ’ d) 1. D   ; N  0 2. w   1/  ; b  1 3. e  next transaction; N  N if (e,f,  ) exists in D do 5. f  f else do 7. insert (e,1,b-1) to D 8. endif 9. if N mod w = 0 do 10. prune(D, b); b  b endif 12. Goto 3; D: The set of all counts N: Curr. len. of stream e: Transaction (itemset) w: Bucket width b: Current bucket id 1. function prune(D, b) 2. for each entry (e,f,  ) in D do 3. if f +   b do 4. remove the entry from D 5. endif

Lossy Counting Lossy Counting guarantees that: When deletion occurs, b   N If an entry ( e, f,  ) is deleted, f e  b where f e is the actual frequency count of e Hence, if an entry ( e, f,  ) is deleted, f e   N Finally, f  f e  f +  N

The more complex case: finding frequent itemsets The Lossy Counting algorithm is extended to find frequent itemsets Transactions in the data stream contains any number of items Essentially the same as the case for single items, except: Multiple buckets (  of them say) are processed in a batch Each entry in D is in the form ( set, f,  ) Transactions read in are (wisely) expanded to its subsets

Association rule mining on data streams: food for thought Challenges to mine from data streams Fast update Data are usually not permanently stored (but may be buffered) Fast response for queries Minimized resources (e.g. number of counts kept) Possible interesting problems concerning association rule mining on data streams: More efficient/accurate algorithms for finding association rules on data streams Change mining in frequency counts

The lattice structure A bottleneck in the algorithm proposed in [Manku et al. 02] is that it needs to expand a transaction to its subsets for counting For example, for a transaction {abcde}, we may need to count the itemsets {a}, {b}, {c}, {d}, {e}, {ab}, {ac}... Hence updates are expensive (although queries can be fast)

abcd e abcdabceabdeacdebcde acdaceadebcdbcebdecdeabcabdabe aebcbdbecdcedeabacad abcde  The lattice structure (cont ’ d)

Conclusion Both association rule interestingness and mining on data streams are challenging problems Research on rule interestingness can make association rule mining a more efficient tool for knowledge discovery Association rule mining on data streams is an upcoming application and a promising direction for research

References [Agarwal et al. 94] R. Agarwal and R. Srikant. Fast Algorithms for Mining Association Rules. VLDB94. [Jaroszewica 02] S. Jaroszewica and D.A. Simovici. Pruning Redundant Association rules Using Maximum Entropy Principle. PAKDD02. [Klemettinen et al. 94] Mika Klemettinen et al. Finding Interesting Rules from Large Sets of Discovered Association Rules. CIKM94. [Manku et al. 02] G. S. Manku and R. Motwani. Approximate Frequency Counts over Data Streams. VLDB02. [Relue et al. 01] R. Relue, X. Wu and H Huang. Efficient Runtime Generation of Association Rules. CIKM01. [Rizvi el al. 02] S. J. Rizvi and J. R. Haritsa. Maintaining Data Privacy in Association Rule Mining. VLDB02. [Sahar 99] Sigal Sahar. Interestingness Via What Is Not Interesting. KDD99.

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