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Data Mining: Association Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary What Is Association Mining? Association rule mining: Finding frequent patterns, associations, correlations, or causal structures among sets of items or objects in transaction databases, relational databases, and other information repositories. Applications: Basket data analysis, cross-marketing, catalog design, loss-leader analysis, clustering, classification, etc. Examples. Rule form: “Body ead [support, confidence]”. buys(x, “diapers”) buys(x, “beers”) [0.5%, 60%] major(x, “CS”) ^ takes(x, “DB”) grade(x, “A”) [1%, 75%] Association Rule: Basic Concepts Given: (1) database of transactions, (2) each transaction is a list of items (purchased by a customer in a visit) Find: all rules that correlate the presence of one set of items with that of another set of items E.g., 98% of people who purchase tires and auto accessories also get automotive services done Applications Maintenance Agreement (What the store should do to boost Maintenance Agreement sales) Home Electronics (What other products should the store stocks up?) Attached mailing in direct marketing Detecting “ping-pong”ing of patients, faulty “collisions” Rule Measures: Support and Confidence Customer buys both Find all the rules X & Y Z with minimum confidence and support support, s, probability that a transaction contains {X Y Z} confidence, c, conditional Customer buys beer probability that a transaction having {X Y} also contains Z Transaction ID Items Bought Let minimum support 50%, and minimum confidence 50%, we have 2000 A,B,C A C (50%, 66.6%) 1000 A,C C A (50%, 100%) 4000 A,D 5000 B,E,F Customer buys diaper Association Rule Mining: A Road Map Boolean vs. quantitative associations (Based on the types of values handled) buys(x, “SQLServer”) ^ buys(x, “DMBook”) buys(x, “DBMiner”) [0.2%, 60%] age(x, “30..39”) ^ income(x, “42..48K”) buys(x, “PC”) [1%, 75%] Single dimension vs. multiple dimensional associations Single level vs. multiple-level analysis What brands of beers are associated with what brands of diapers? Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary Mining Association Rules— An Example Transaction ID 2000 1000 4000 5000 Items Bought A,B,C A,C A,D B,E,F For rule A C: Min. support 50% Min. confidence 50% Frequent Itemset Support {A} 75% {B} 50% {C} 50% {A,C} 50% support = support({A C}) = 50% confidence = support({A C})/support({A}) = 66.6% The Apriori principle: Any subset of a frequent itemset must be frequent Mining Frequent Itemsets: the Key Step Find the frequent itemsets: the sets of items that have minimum support A subset of a frequent itemset must also be a frequent itemset i.e., if {AB} is a frequent itemset, both {A} and {B} should be a frequent itemset Iteratively find frequent itemsets with cardinality from 1 to k (k-itemset) Use the frequent itemsets to generate association rules. The Apriori Algorithm Join Step: Ck is generated by joining Lk-1with itself Prune Step: Any (k-1)-itemset that is not frequent cannot be a subset of a frequent k-itemset Pseudo-code: Ck: Candidate itemset of size k Lk : frequent itemset of size k L1 = {frequent items}; for (k = 1; Lk !=; k++) do begin Ck+1 = candidates generated from Lk; for each transaction t in database do Lk+1 increment the count of all candidates in Ck+1 that are contained in t = candidates in Ck+1 with min_support end return k Lk; The Apriori Algorithm — Example Database D TID 100 200 300 400 itemset sup. C1 {1} 2 {2} 3 Scan D {3} 3 {4} 1 {5} 3 Items 134 235 1235 25 C2 itemset sup L2 itemset sup 2 2 3 2 {1 {1 {1 {2 {2 {3 C3 itemset {2 3 5} Scan D {1 3} {2 3} {2 5} {3 5} 2} 3} 5} 3} 5} 5} 1 2 1 2 3 2 L1 itemset sup. {1} {2} {3} {5} 2 3 3 3 C2 itemset {1 2} Scan D L3 itemset sup {2 3 5} 2 {1 {1 {2 {2 {3 3} 5} 3} 5} 5} How to Generate Candidates? Suppose the items in Lk-1 are listed in an order Step 1: self-joining Lk-1 insert into Ck select p.item1, p.item2, …, p.itemk-1, q.itemk-1 from Lk-1 p, Lk-1 q where p.item1=q.item1, …, p.itemk-2=q.itemk-2, p.itemk-1 < q.itemk-1 Step 2: pruning forall itemsets c in Ck do forall (k-1)-subsets s of c do if (s is not in Lk-1) then delete c from Ck How to Count Supports of Candidates? Why counting supports of candidates a problem? The total number of candidates can be very huge One transaction may contain many candidates Method: Candidate itemsets are stored in a hash-tree Leaf node of hash-tree contains a list of itemsets and counts Interior node contains a hash table Subset function: finds all the candidates contained in a transaction Example of Generating Candidates L3={abc, abd, acd, ace, bcd} Self-joining: L3*L3 abcd from abc and abd acde from acd and ace Pruning: acde is removed because ade is not in L3 C4={abcd} Methods to Improve Apriori’s Efficiency Hash-based itemset counting: A k-itemset whose corresponding hashing bucket count is below the threshold cannot be frequent Transaction reduction: A transaction that does not contain any frequent k-itemset is useless in subsequent scans Partitioning: Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB Sampling: mining on a subset of given data, lower support threshold + a method to determine the completeness Dynamic itemset counting: add new candidate itemsets only when all of their subsets are estimated to be frequent Visualization of Association Rule Using Plane Graph Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary Multiple-Level Association Rules Food Items often form hierarchy. Items at the lower level are expected to have lower support. Rules regarding itemsets at appropriate levels could be quite useful. Transaction database can be encoded based on dimensions and levels We can explore shared multilevel mining bread milk skim Fraser TID T1 T2 T3 T4 T5 2% wheat white Sunset Items {111, 121, 211, 221} {111, 211, 222, 323} {112, 122, 221, 411} {111, 121} {111, 122, 211, 221, 413} Mining Multi-Level Associations A top_down, progressive deepening approach: First find high-level strong rules: milk bread [20%, 60%]. Then find their lower-level “weaker” rules: 2% milk wheat bread [6%, 50%]. Variations at mining multiple-level association rules. Level-crossed association rules: 2% milk Wonder wheat bread Association rules with multiple, alternative hierarchies: 2% milk Wonder bread Multi-level Association: Uniform Support vs. Reduced Support Uniform Support: the same minimum support for all levels + One minimum support threshold. No need to examine itemsets containing any item whose ancestors do not have minimum support. – Lower level items do not occur as frequently. If support threshold too high miss low level associations too low generate too many high level associations Reduced Support: reduced minimum support at lower levels There are 4 search strategies: Level-by-level independent Level-cross filtering by k-itemset Level-cross filtering by single item Controlled level-cross filtering by single item Uniform Support Multi-level mining with uniform support Level 1 min_sup = 5% Level 2 min_sup = 5% Milk [support = 10%] 2% Milk Skim Milk [support = 6%] [support = 4%] Back Reduced Support Multi-level mining with reduced support Level 1 min_sup = 5% Level 2 min_sup = 3% Milk [support = 10%] 2% Milk Skim Milk [support = 6%] [support = 4%] Back Multi-level Association: Redundancy Filtering Some rules may be redundant due to “ancestor” relationships between items. Example milk wheat bread [support = 8%, confidence = 70%] 2% milk wheat bread [support = 2%, confidence = 72%] We say the first rule is an ancestor of the second rule. A rule is redundant if its support is close to the “expected” value, based on the rule’s ancestor. Multi-Level Mining: Progressive Deepening A top-down, progressive deepening approach: First mine high-level frequent items: milk (15%), bread (10%) Then mine their lower-level “weaker” frequent itemsets: 2% milk (5%), wheat bread (4%) Different min_support threshold across multilevels lead to different algorithms: If adopting the same min_support across multilevels then toss t if any of t’s ancestors is infrequent. If adopting reduced min_support at lower levels then examine only those descendents whose ancestor’s support is frequent/non-negligible. Progressive Refinement of Data Mining Quality Why progressive refinement? Mining operator can be expensive or cheap, fine or rough Trade speed with quality: step-by-step refinement. Superset coverage property: Preserve all the positive answers—allow a positive false test but not a false negative test. Two- or multi-step mining: First apply rough/cheap operator (superset coverage) Then apply expensive algorithm on a substantially reduced candidate set (Koperski & Han, SSD’95). Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary Multi-Dimensional Association: Concepts Single-dimensional rules: buys(X, “milk”) buys(X, “bread”) Multi-dimensional rules: 2 dimensions or predicates Inter-dimension association rules (no repeated predicates) age(X,”19-25”) occupation(X,“student”) buys(X,“coke”) hybrid-dimension association rules (repeated predicates) age(X,”19-25”) buys(X, “popcorn”) buys(X, “coke”) Categorical Attributes finite number of possible values, no ordering among values Quantitative Attributes numeric, implicit ordering among values Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary Interestingness Measurements Objective measures Two popular measurements: support; and confidence Subjective measures (Silberschatz & Tuzhilin, KDD95) A rule (pattern) is interesting if it is unexpected (surprising to the user); and/or actionable (the user can do something with it) Criticism to Support and Confidence Example 1: (Aggarwal & Yu, PODS98) Among 5000 students 3000 play basketball 3750 eat cereal 2000 both play basket ball and eat cereal play basketball eat cereal [40%, 66.7%] is misleading because the overall percentage of students eating cereal is 75% which is higher than 66.7%. play basketball not eat cereal [20%, 33.3%] is far more accurate, although with lower support and confidence basketball not basketball sum(row) cereal 2000 1750 3750 not cereal 1000 250 1250 sum(col.) 3000 2000 5000 Criticism to Support and Confidence (Cont.) Example 2: X and Y: positively correlated, X and Z, negatively related support and confidence of X=>Z dominates We need a measure of dependent or correlated events corrA, B P( A B) P( A) P( B) X 1 1 1 1 0 0 0 0 Y 1 1 0 0 0 0 0 0 Z 0 1 1 1 1 1 1 1 Rule Support Confidence X=>Y 25% 50% X=>Z 37.50% 75% P(B|A)/P(B) is also called the lift of rule A => B Other Interestingness Measures: Interest Interest (correlation, lift) P( A B) P( A) P( B) taking both P(A) and P(B) in consideration P(A^B)=P(B)*P(A), if A and B are independent events A and B negatively correlated, if the value is less than 1; otherwise A and B positively correlated X 1 1 1 1 0 0 0 0 Y 1 1 0 0 0 0 0 0 Z 0 1 1 1 1 1 1 1 Itemset Support Interest X,Y X,Z Y,Z 25% 37.50% 12.50% 2 0.9 0.57 Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary Constraint-Based Mining Interactive, exploratory mining giga-bytes of data? Could it be real? — Making good use of constraints! What kinds of constraints can be used in mining? Knowledge type constraint: classification, association, etc. Data constraint: SQL-like queries Find product pairs sold together in Vancouver in Dec.’98. Dimension/level constraints: in relevance to region, price, brand, customer category. Rule constraints small sales (price < $10) triggers big sales (sum > $200). Interestingness constraints: strong rules (min_support 3%, min_confidence 60%). Mining Association Rules in Large Databases Association rule mining Mining single-dimensional Boolean association rules from transactional databases Mining multilevel association rules from transactional databases Mining multidimensional association rules from transactional databases and data warehouse From association mining to correlation analysis Constraint-based association mining Summary Summary Association rule mining probably the most significant contribution from the database community in KDD A large number of papers have been published Many interesting issues have been explored An interesting research direction Association analysis in other types of data: spatial data, multimedia data, time series data, etc. References R. Agarwal, C. Aggarwal, and V. V. V. Prasad. A tree projection algorithm for generation of frequent itemsets. In Journal of Parallel and Distributed Computing (Special Issue on High Performance Data Mining), 2000. R. Agrawal, T. Imielinski, and A. Swami. 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