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Understanding Association Rules and Sequential Associations in Data Mining

This lecture explores the significance of association rules in data mining, emphasizing their role in uncovering relationships between attributes. It defines the formal framework for association rules, focusing on the concepts of support and confidence as critical metrics for rule evaluation. Various applications, including market-basket analysis and sequential associations, are discussed alongside practical challenges such as sparse data and algorithm efficiency. The session also includes insights into algorithms like the A-Priori algorithm and its implications for mining frequent episodes in datasets, particularly in security contexts.

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Understanding Association Rules and Sequential Associations in Data Mining

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  1. CS 590M Fall 2001: Security Issues in Data Mining Lecture 5: Association Rules, Sequential Associations

  2. Why Association Rules? • Understand attributes, not entities • Discover relationships that • Show some dependency between attributes • Are “interesting” • Give an understanding of the data space

  3. Formal Definition • Data: • Items={i1,…,in} • Transactions T={t1,…,tm} where ti = {ij1, …, ijk} • Support: Given AI, supp(A) = |{t  T | t  A}| / |T| • Goal: Find rules AB with support ≥ s and confidence ≥ c where: • A, B  I, A  B =  • s = supp(A  B), c = supp(A  B) / supp(A)

  4. Sample: Market Basket

  5. Types of associations • Machine-learning base: classification / decision rules • Entities independent, unordered • Find rules leading to target class • To get rule sets, re-run for all classes as targets • Market-basket • Collection of related entities with same key • Can be modeled as independent entities, sparse data • Sequential • Like market basket, but group by distance rather than same key

  6. Historical Association Rule Learning • Decision tree converted to rules • ID3, as discussed in previous lecture • Direct production of decision rules • CN2, others • Problem: Algorithms don’t scale well to many practical problems

  7. Database community contribution: Market Basket Association Rules • Rakesh Agrawal, Tomasz Imielinski, and Arun Swami. Mining association rules between sets of items in large databases. In Proc. of the ACM SIGMOD Conference on Management of Data, pages 207--216, Washington, D.C., May 1993. • Rakesh Agrawal, Ramakrishnan Srikant: Fast Algorithms for Mining Association Rules in Large Databases. VLDB 1994: 487-499

  8. Database community contribution: Market Basket Association Rules • Practical problems often have sparse data • Many attributes, few items per transaction • Goal is typically search for high support • High support = broad impact • High confidence not crucial (as opposed to classification) • Very Large data sets(main-memory algorithms impractical)

  9. A-Priori Algorithm • Observation: if A has support s, then • i  A, supp(i) ≥ s • Gives bottom-up algorithm • Find single items with support ≥ s • Just look at transaction subsets with those items for pairs • Recurse

  10. A-Priori Algorithm • First, generate all large itemsets • Sets X  I such that supp(X) ≥ s (threshold) • Captures “supp(A  B) ≥ s” part of problem • Second, find high-confidence rules that are subsets of X • B = Xi , A = X-B • To find confidence, need supp(A)But A will be in all large itemsets – don’t need to go back to the database!

  11. A-Priori Algorithm L1 = {large 1-itemsets}; for ( k = 2; Lk-1  ; k++ ) Ck = select p.i1, p.iY, …, p.ik-1, q.ik-1 from Lk-1 p, Lk-1 q where p.i1 = q.i1, …, p.ik-2 = q.ik-2  transactions t  T Ct = subset(Ck, t); // Candidates contained in t  candidates c  Ct: c.count++; Lk = {c  Ck | c.count  minsup} Answer = k Lk;

  12. Frequent episodes for sequential associations • Heikki Mannila, Hannu Toivonen, and A. Inkeri Verkamo: Discovering Frequent Episodes in Sequences. In First International Conference on Knowledge Discovery and Data Mining (KDD'95), 210 - 215, Montreal, Canada, August 1995. AAAI Press. • Instead of transaction, items grouped by sliding window in time • Same basic idea as A-Priori

  13. Frequent Episodes: Definition • Event types E • Event (A,t) where A in E • Sequence S=((A1,t1),…,(An,tn)) • Frequent episode F = (Ai, …, Aj) where •  tl, tm such that t1tl<…<tm  tn tm-tl  window: • count( ((Ai,tl), …, (Aj, tm)) )  support

  14. Applications/Issues in Security • Frequent episodes in intrusion detection data • What does this tell us? • Preventing the discovery of associations • Known items to protect • What if we don’t know what we want to protect?

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