Data Mining: Concepts and Techniques (3rd ed.) — Chapter 6

Data Mining: Concepts and Techniques (3rd ed.) — Chapter 6 — Jiawei Han, Micheline Kamber, and Jian Pei University of Illinois at Urbana-Champaign & Simon Fraser University 2011 Han, Kamber & Pei. All rights reserved. 1

Chapter 5: Mining Frequent Patterns, Association and Correlations: Basic Concepts and Methods Basic Concepts Frequent Itemset Mining Methods Which Patterns Are Interesting?—Pattern Evaluation Methods Summary 2

What Is Frequent Pattern Analysis? Frequent pattern: a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set First proposed by Agrawal, Imielinski, and Swami [AIS93] in the context of frequent itemsets and association rule mining Motivation: Finding inherent regularities in data What products were often purchased together?— Beer and diapers?! What are the subsequent purchases after buying a PC? What kinds of DNA are sensitive to this new drug? Can we automatically classify web documents? Applications Basket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis. 3

Why Is Freq. Pattern Mining Important? Freq. pattern: An intrinsic and important property of datasets Foundation for many essential data mining tasks Association, correlation, and causality analysis Sequential, structural (e.g., sub-graph) patterns Pattern analysis in spatiotemporal, multimedia, timeseries, and stream data Classification: discriminative, frequent pattern analysis Cluster analysis: frequent pattern-based clustering Data warehousing: iceberg cube and cube-gradient Semantic data compression: fascicles Broad applications 4

Basic Concepts: Frequent Patterns Tid Items bought 10 Beer, Nuts, Diaper 20 Beer, Coffee, Diaper 30 Beer, Diaper, Eggs 40 Nuts, Eggs, Milk 50 Nuts, Coffee, Diaper, Eggs, Milk Customer buys both Customer buys diaper Customer buys beer itemset: A set of one or more items k-itemset X {x1, , xk} (absolute) support, or, support count of X: Frequency or occurrence of an itemset X (relative) support, s, is the fraction of transactions that contains X (i.e., the probability that a transaction contains X) An itemset X is frequent if X’s support is no less than a minsup threshold 5

Basic Concepts: Association Rules Ti d Items bought 10 Beer, Nuts, Diaper 20 Beer, Coffee, Diaper 30 Beer, Diaper, Eggs 40 50 Nuts, Eggs, Milk Nuts, Coffee, Diaper, Eggs, Milk Customer Customer buys both buys diaper Customer buys beer Find all the rules X Y with minimum support and confidence support, s, probability that a transaction contains X Y confidence, c, conditional probability that a transaction having X also contains Y Association rules: (many Let minsup 50%, minconf 50% Freq.more!) Pat.: Beer:3, Nuts:3, Diaper:4, Beer Diaper (60%, Eggs:3, {Beer, Diaper}:3 100%) 6

Closed Patterns and MaxPatterns A long pattern contains a combinatorial number of subpatterns, e.g., {a1, , a100} contains (1001) (1002) (110000) 2100 – 1 1.27*1030 sub-patterns! Solution: Mine closed patterns and max-patterns instead An itemset X is closed if X is frequent and there exists no super-pattern Y כ X, with the same support as X (proposed by Pasquier, et al. @ ICDT’99) An itemset X is a max-pattern if X is frequent and there exists no frequent super-pattern Y כ X (proposed by Bayardo @ SIGMOD’98) Closed pattern is a lossless compression of freq. patterns Reducing the # of patterns and rules 7

Closed Patterns and MaxPatterns Exercise. DB { a1, , a100 , a1, , a50 } What is the set of closed itemset? a1, , a100 : 1 a1, , a50 : 2 What is the set of max-pattern? Min sup 1. a1, , a100 : 1 What is the set of all patterns? !! 8

Computational Complexity of Frequent Itemset Mining How many itemsets are potentially to be generated in the worst case? The number of frequent itemsets to be generated is senstive to the minsup threshold When minsup is low, there exist potentially an exponential number of frequent itemsets The worst case: MN where M: # distinct items, and N: max length of transactions The worst case complexty vs. the expected probability Ex. Suppose Walmart has 104 kinds of products The chance to pick up one product 10-4 The chance to pick up a particular set of 10 products: 10 -40 What is the chance this particular set of 10 products to be frequent 103 times in 109 transactions? 9

Chapter 5: Mining Frequent Patterns, Association and Correlations: Basic Concepts and Methods Basic Concepts Frequent Itemset Mining Methods Which Patterns Are Interesting?—Pattern Evaluation Methods Summary 10

Scalable Frequent Itemset Mining Methods Apriori: A Candidate Generation-and-Test Approach Improving the Efficiency of Apriori FPGrowth: A Frequent Pattern-Growth Approach ECLAT: Frequent Pattern Mining with Vertical Data Format 11

The Downward Closure Property and Scalable Mining Methods The downward closure property of frequent patterns Any subset of a frequent itemset must be frequent If {beer, diaper, nuts} is frequent, so is {beer, diaper} i.e., every transaction having {beer, diaper, nuts} also contains {beer, diaper} Scalable mining methods: Three major approaches Apriori (Agrawal & Srikant@VLDB’94) Freq. pattern growth (FPgrowth—Han, Pei & Yin @SIGMOD’00) Vertical data format approach (Charm—Zaki & Hsiao @SDM’02) 12

Apriori: A Candidate Generation & Test Approach Apriori pruning principle: If there is any itemset which is infrequent, its superset should not be generated/tested! (Agrawal & Srikant @VLDB’94, Mannila, et al. @ KDD’ 94) Method: Initially, scan DB once to get frequent 1-itemset Generate length (k 1) candidate itemsets from length k frequent itemsets Test the candidates against DB Terminate when no frequent or candidate set can be generated 13

The Apriori Algorithm—An Example Database TDB Tid Items 10 A, C, D 20 B, C, E 30 A, B, C, E 40 B, E Supmin 2 Itemset C1 1st scan C2 L2 Itemset {A, C} {B, C} {B, E} {C, E} sup 2 2 3 2 sup {A} 2 {B} 3 {C} 3 {D} 1 {E} 3 Itemset {A, B} {A, C} {A, E} {B, C} {B, E} {C, E} sup 1 2 1 2 3 2 L1 Itemset sup {A} 2 {B} 3 {C} 3 {E} 3 C2 2nd scan Itemset {A, B} {A, C} {A, E} {B, C} {B, E} {C, E} C3 Itemset {B, C, E} 3rd scan L3 Itemset sup {B, C, E} 2 14

The Apriori Algorithm (PseudoCode) 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 increment the count of all candidates in Ck 1 that are contained in t Lk 1 candidates in Ck 1 with min support end return k Lk; 15

Implementation of Apriori How to generate candidates? Step 1: self-joining Lk Step 2: pruning Example of Candidate-generation 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} 16

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 17

Counting Supports of Candidates Using Hash Tree Subset function 3,6,9 1,4,7 Transaction: 1 2 3 5 6 2,5,8 1 2356 234 567 13 56 145 136 12 356 124 457 125 458 345 356 357 689 367 368 159 18

Candidate Generation: An SQL Implementation SQL Implementation of candidate generation 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 Use object-relational extensions like UDFs, BLOBs, and Table functions for efficient implementation [See: S. Sarawagi, S. Thomas, and R. Agrawal. Integrating association rule mining with relational database systems: Alternatives and implications. SIGMOD’98] 19

Scalable Frequent Itemset Mining Methods Apriori: A Candidate Generation-and-Test Approach Improving the Efficiency of Apriori FPGrowth: A Frequent Pattern-Growth Approach ECLAT: Frequent Pattern Mining with Vertical Data Format Mining Close Frequent Patterns and Maxpatterns 20

Further Improvement of the Apriori Method Major computational challenges Multiple scans of transaction database Huge number of candidates Tedious workload of support counting for candidates Improving Apriori: general ideas Reduce passes of transaction database scans Shrink number of candidates Facilitate support counting of candidates 21

Partition: Scan Database Only Twice Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB Scan 1: partition database and find local frequent patterns Scan 2: consolidate global frequent patterns A. Savasere, E. Omiecinski and S. Navathe, VLDB’95 DB1 sup1(i) σDB1 DB2 sup2(i) σDB2 DBk supk(i) σDBk DB sup(i) σDB

DHP: Reduce the Number of Candidates A k-itemset whose corresponding hashing bucket count is below Candidates: a, b, c, d, e Hash entries {ab, ad, ae} {bd, be, de} count 35 88 . . . the threshold cannot be frequent itemset s ad, {ab, ae} {bd, be, de} . . . 10 {yz, qs, 2Hash wt} Table Frequent 1-itemset: a, b, d, e ab is not a candidate 2-itemset if the sum of count of {ab, ad, ae} is below support threshold J. Park, M. Chen, and P. Yu. An effective hash-based algorithm for mining association rules. SIGMOD’95 23

Sampling for Frequent Patterns Select a sample of original database, mine frequent patterns within sample using Apriori Scan database once to verify frequent itemsets found in sample, only borders of closure of frequent patterns are checked Example: check abcd instead of ab, ac, , etc. Scan database again to find missed frequent patterns H. Toivonen. Sampling large databases for association rules. In VLDB’96 24

DIC: Reduce Number of Scans ABCD ABC ABD ACD BCD AB AC BC AD BD CD Once both A and D are determined frequent, the counting of AD begins Once all length-2 subsets of BCD are determined frequent, the counting of BCD begins Transactions A B C D Apriori {} Itemset lattice S. Brin R. Motwani, J. Ullman, and S. Tsur. Dynamic itemset DIC counting and implication rules for market basket data. SIGMOD’97 1-itemsets 2-itemsets 1-itemsets 2-items 3-items 25

Scalable Frequent Itemset Mining Methods Apriori: A Candidate Generation-and-Test Approach Improving the Efficiency of Apriori FPGrowth: A Frequent Pattern-Growth Approach ECLAT: Frequent Pattern Mining with Vertical Data Format Mining Close Frequent Patterns and Maxpatterns 26

Pattern-Growth Approach: Mining Frequent Patterns Without Candidate Generation Bottlenecks of the Apriori approach Breadth-first (i.e., level-wise) search Candidate generation and test Often generates a huge number of candidates The FPGrowth Approach (J. Han, J. Pei, and Y. Yin, SIGMOD’ 00) Depth-first search Avoid explicit candidate generation Major philosophy: Grow long patterns from short ones using local frequent items only “abc” is a frequent pattern Get all transactions having “abc”, i.e., project DB on abc: DB abc “d” is a local frequent item in DB abc abcd is a frequent pattern 27

Construct FP-tree from a Transaction Database TID items Items bought (ordered) frequent 100 200 300 400 500 {f, a, c, d, g, i, m, p} {f, c, a, m, p} {a, b, c, f, l, m, o} {f, c, a, b, m} min support 3 {b, f, h, j, o, w} {f, b} {b, c, k, s, p} {c, b, p} {} {a, f, c, e, l, p, m, n} {f, c, a, m, p} Header Table 1. Scan DB once, find f:4 c:1 Item frequency head frequent 1-itemset f 4 (single item pattern) c 4 c:3 b:1 b:1 2. Sort frequent items in a 3 b 3 frequency descending a:3 p:1 m 3 order, f-list p 3 m:2 b:1 3. Scan DB again, construct FP-tree F-list f-c-a-b-m-p p:2 m:1 28

Partition Patterns and Databases Frequent patterns can be partitioned into subsets according to f-list F-list f-c-a-b-m-p Patterns containing p Patterns having m but no p Patterns having c but no a nor b, m, p Pattern f Completeness and non-redundency 29

Find Patterns Having P From P-conditional Database Starting at the frequent item header table in the FP-tree Traverse the FP-tree by following the link of each frequent item p Accumulate all of transformed prefix paths of item p to form p’s conditional pattern base {} Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 f:4 c:3 c:1 b:1 a:3 b:1 p:1 m:2 b:1 p:2 m:1 Conditional pattern bases item cond. pattern base c f:3 a fc:3 b fca:1, f:1, c:1 m fca:2, fcab:1 p fcam:2, cb:1 30

From Conditional Pattern-bases to Conditional FPtrees For each pattern-base Accumulate the count for each item in the base Construct the FP-tree for the frequent items of the pattern base Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 {} f:4 c:3 c:1 b:1 a:3 b:1 p:1 m:2 b:1 p:2 m:1 m-conditional pattern base: fca:2, fcab:1 All frequent patterns relate to m {} m, f:3 fm, cm, am, fcm, fam, cam, c:3 fcam a:3 m-conditional FP-tree 31

Recursion: Mining Each Conditional FPtree {} {} Cond. pattern base of “am”: (fc:3) f:3 c:3 f:3 c:3 a:3 am-conditional FP-tree Cond. pattern base of “cm”: (f:3) {} f:3 m-conditional FP-tree cm-conditional FP-tree {} Cond. pattern base of “cam”: (f:3) f:3 cam-conditional FP-tree 32

A Special Case: Single Prefix Path in FPtree Suppose a (conditional) FP-tree T has a shared single prefix-path P Mining can be decomposed into two parts {} a1:n1 a2:n2 Reduction of the single prefix path into one node Concatenation of the mining results of the two parts a3:n3 b1:m1 C2:k2 r1 {} C1:k1 C3:k3 r1 a1:n1 a2:n2 a3:n3 b1:m1 C2:k2 C1:k1 C3:k3 33

Benefits of the FP-tree Structure Completeness Preserve complete information for frequent pattern mining Never break a long pattern of any transaction Compactness Reduce irrelevant info—infrequent items are gone Items in frequency descending order: the more frequently occurring, the more likely to be shared Never be larger than the original database (not count node-links and the count field) 34

The Frequent Pattern Growth Mining Method Idea: Frequent pattern growth Recursively grow frequent patterns by pattern and database partition Method For each frequent item, construct its conditional pattern-base, and then its conditional FP-tree Repeat the process on each newly created conditional FP-tree Until the resulting FP-tree is empty, or it contains only one path—single path will generate all the combinations of its sub-paths, each of which is a frequent pattern 35

Scaling FP-growth by Database Projection What about if FP-tree cannot fit in memory? DB projection First partition a database into a set of projected DBs Then construct and mine FP-tree for each projected DB Parallel projection vs. partition projection techniques Parallel projection Project the DB in parallel for each frequent item Parallel projection is space costly All the partitions can be processed in parallel Partition projection Partition the DB based on the ordered frequent items Passing the unprocessed parts to the subsequent partitions 36

Partition-Based Projection Parallel projection needs a lot of disk space Partition projection saves it Tran. DB fcamp fcabm fb cbp fcamp p-proj DB m-proj DB b-proj DB a-proj DB c-proj DB f-proj DB fcam fcab f fc f cb fca cb fcam fca am-proj DB cm-proj DB fc f fc f fc f 37

Performance of FPGrowth in Large Datasets 100 D2 FP-growth 120 D1 Apriori runtime 80 70 D2 TreeProjection 100 Runtime (sec.) Run time(sec.) 140 D1 FP-grow th runtime 90 60 Data set T25I20D10K 50 40 30 20 80 Data set T25I20D100K 60 40 20 10 0 0 0 0.5 1 1.5 2 Support threshold(%) 2.5 FP-Growth vs. Apriori 3 0 0.5 1 1.5 2 Support threshold (%) FP-Growth vs. TreeProjection 38

Advantages of the Pattern Growth Approach Divide-and-conquer: Lead to focused search of smaller databases Other factors No candidate generation, no candidate test Compressed database: FP-tree structure No repeated scan of entire database Decompose both the mining task and DB according to the frequent patterns obtained so far Basic ops: counting local freq items and building sub FPtree, no pattern search and matching A good open-source implementation and refinement of FPGrowth FPGrowth (Grahne and J. Zhu, FIMI'03) 39

Further Improvements of Mining Methods AFOPT (Liu, et al. @ KDD’03) A “push-right” method for mining condensed frequent pattern (CFP) tree Carpenter (Pan, et al. @ KDD’03) Mine data sets with small rows but numerous columns Construct a row-enumeration tree for efficient mining FPgrowth (Grahne and Zhu, FIMI’03) Efficiently Using Prefix-Trees in Mining Frequent Itemsets, Proc. ICDM'03 Int. Workshop on Frequent Itemset Mining Implementations (FIMI'03), Melbourne, FL, Nov. 2003 TD-Close (Liu, et al, SDM’06) 40

Extension of Pattern Growth Mining Methodology Mining closed frequent itemsets and max-patterns CLOSET (DMKD’00), FPclose, and FPMax (Grahne & Zhu, Fimi’03) Mining sequential patterns PrefixSpan (ICDE’01), CloSpan (SDM’03), BIDE (ICDE’04) Mining graph patterns gSpan (ICDM’02), CloseGraph (KDD’03) Constraint-based mining of frequent patterns Convertible constraints (ICDE’01), gPrune (PAKDD’03) Computing iceberg data cubes with complex measures H-tree, H-cubing, and Star-cubing (SIGMOD’01, VLDB’03) Pattern-growth-based Clustering MaPle (Pei, et al., ICDM’03) Pattern-Growth-Based Classification Mining frequent and discriminative patterns (Cheng, et al, ICDE’07) 41

Scalable Frequent Itemset Mining Methods Apriori: A Candidate Generation-and-Test Approach Improving the Efficiency of Apriori FPGrowth: A Frequent Pattern-Growth Approach ECLAT: Frequent Pattern Mining with Vertical Data Format Mining Close Frequent Patterns and Maxpatterns 42

ECLAT: Mining by Exploring Vertical Data Format Vertical format: t(AB) {T11, T25, } tid-list: list of trans.-ids containing an itemset Deriving frequent patterns based on vertical intersections t(X) t(Y): X and Y always happen together t(X) t(Y): transaction having X always has Y Using diffset to accelerate mining Only keep track of differences of tids t(X) {T1, T2, T3}, t(XY) {T1, T3} Diffset (XY, X) {T2} Eclat (Zaki et al. @KDD’97) Mining Closed patterns using vertical format: CHARM (Zaki & Hsiao@SDM’02) 43

Scalable Frequent Itemset Mining Methods Apriori: A Candidate Generation-and-Test Approach Improving the Efficiency of Apriori FPGrowth: A Frequent Pattern-Growth Approach ECLAT: Frequent Pattern Mining with Vertical Data Format Mining Close Frequent Patterns and Maxpatterns 44

Mining Frequent Closed Patterns: CLOSET Flist: list of all frequent items in support ascending order Divide search space Patterns having d Patterns having d but no a, etc. Find frequent closed pattern recursively Flist: d-a-f-e-c Min sup 2 TID 10 20 30 40 50 Items a, c, d, e, f a, b, e c, e, f a, c, d, f c, e, f Every transaction having d also has cfa cfad is a frequent closed pattern J. Pei, J. Han & R. Mao. “CLOSET: An Efficient Algorithm for Mining Frequent Closed Itemsets", DMKD'00.

CLOSET : Mining Closed Itemsets by PatternGrowth Itemset merging: if Y appears in every occurrence of X, then Y is merged with X Sub-itemset pruning: if Y כ X, and sup(X) sup(Y), X and all of X’s descendants in the set enumeration tree can be pruned Hybrid tree projection Bottom-up physical tree-projection Top-down pseudo tree-projection Item skipping: if a local frequent item has the same support in several header tables at different levels, one can prune it from the header table at higher levels Efficient subset checking

MaxMiner: Mining Max-Patterns 1st scan: find frequent items 2nd scan: find support for Items 10 A, B, C, D, E 20 B, C, D, E, 30 A, C, D, F AB, AC, AD, AE, ABCDE BC, BD, BE, BCDE Potential CD, CE, CDE, DE maxpatterns Since BCDE is a max-pattern, no need to check A, B, C, D, E Tid BCD, BDE, CDE in later scan R. Bayardo. Efficiently mining long patterns from databases. SIGMOD’98

CHARM: Mining by Exploring Vertical Data Format Vertical format: t(AB) {T11, T25, } tid-list: list of trans.-ids containing an itemset Deriving closed patterns based on vertical intersections t(X) t(Y): X and Y always happen together t(X) t(Y): transaction having X always has Y Using diffset to accelerate mining Only keep track of differences of tids t(X) {T1, T2, T3}, t(XY) {T1, T3} Diffset (XY, X) {T2} Eclat/MaxEclat (Zaki et al. @KDD’97), VIPER(P. Shenoy et al.@SIGMOD’00), CHARM (Zaki & Hsiao@SDM’02)

Visualization of Association Rules: Plane Graph 49

Visualization of Association Rules: Rule Graph 50

Visualization of Association Rules (SGI/MineSet 3.0) 51

Chapter 5: Mining Frequent Patterns, Association and Correlations: Basic Concepts and Methods Basic Concepts Frequent Itemset Mining Methods Which Patterns Are Interesting?—Pattern Evaluation Methods Summary 52

Interestingness Measure: Correlations (Lift) play basketball eat cereal [40%, 66.7%] is misleading The overall % of students eating cereal is 75% 66.7%. play basketball not eat cereal [20%, 33.3%] is more accurate, although with lower support and confidence Measure of dependent/correlated events: lift P( A B ) lift P ( A) P( B) 2000 / 5000 lift ( B, C ) 0.89 3000 / 5000 * 3750 / 5000 lift ( B, C ) Basketba ll Not basketball Sum (row) Cereal 2000 1750 3750 Not cereal 1000 250 1250 Sum(col.) 3000 2000 5000 1000 / 5000 1.33 3000 / 5000 *1250 / 5000 53

Are lift and 2 Good Measures of Correlation? “Buy walnuts buy milk [1%, 80%]” is misleading if 85% of customers buy milk Support and confidence are not good to indicate correlations Over 20 interestingness measures have been proposed (see Tan, Kumar, Sritastava @KDD’02) Which are good ones? 54

Null-Invariant Measures 55

Comparison of Interestingness Measures Null-(transaction) invariance is crucial for correlation analysis Lift and 2 are not null-invariant 5 null-invariant measures Milk No Milk Sum (row) Coffee m, c m, c c No Coffee m, c m, c c Sum(col. m m ) Null-transactions w.r.t. m and c March 11, 2023 Kulczynski measure (1927) Data Mining: Concepts and Null-invariant Subtle: They disagree56

Analysis of DBLP Coauthor Relationships Recent DB conferences, removing balanced associations, low sup, etc. Advisor-advisee relation: Kulc: high, coherence: low, cosine: middle Tianyi Wu, Yuguo Chen and Jiawei Han, “ Association Mining in Large Databases: A Re-Examination of Its Measures ”, Proc. 2007 Int. Conf. Principles and Practice of Knowledge Discovery in Databases (PKDD'07), Sept. 2007 57

Which Null-Invariant Measure Is Better? IR (Imbalance Ratio): measure the imbalance of two itemsets A and B in rule implications Kulczynski and Imbalance Ratio (IR) together present a clear picture for all the three datasets D4 through D6 D4 is balanced & neutral D5 is imbalanced & neutral D6 is very imbalanced & neutral

Chapter 5: Mining Frequent Patterns, Association and Correlations: Basic Concepts and Methods Basic Concepts Frequent Itemset Mining Methods Which Patterns Are Interesting?—Pattern Evaluation Methods Summary 59

Summary Basic concepts: association rules, supportconfident framework, closed and max-patterns Scalable frequent pattern mining methods Apriori (Candidate generation & test) Projection-based (FPgrowth, CLOSET , .) Vertical format approach (ECLAT, CHARM, .) Which patterns are interesting? Pattern evaluation methods 60

Ref: Basic Concepts of Frequent Pattern Mining (Association Rules) R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. SIGMOD'93 (Max-pattern) R. J. Bayardo. Efficiently mining long patterns from databases. SIGMOD'98 (Closed-pattern) N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Discovering frequent closed itemsets for association rules. ICDT'99 (Sequential pattern) R. Agrawal and R. Srikant. Mining sequential patterns. ICDE'95 61

Ref: Apriori and Its Improvements R. Agrawal and R. Srikant. Fast algorithms for mining association rules. VLDB'94 H. Mannila, H. Toivonen, and A. I. Verkamo. Efficient algorithms for discovering association rules. KDD'94 A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining association rules in large databases. VLDB'95 J. S. Park, M. S. Chen, and P. S. Yu. An effective hash-based algorithm for mining association rules. SIGMOD'95 H. Toivonen. Sampling large databases for association rules. VLDB'96 S. Brin, R. Motwani, J. D. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for market basket analysis. SIGMOD'97 S. Sarawagi, S. Thomas, and R. Agrawal. Integrating association rule mining with relational database systems: Alternatives and implications. SIGMOD'98 62

Ref: Depth-First, Projection-Based FP Mining R. Agarwal, C. Aggarwal, and V. V. V. Prasad. A tree projection algorithm for generation of frequent itemsets. J. Parallel and Distributed Computing, 2002. G. Grahne and J. Zhu, Efficiently Using Prefix-Trees in Mining Frequent Itemsets, Proc. FIMI'03 B. Goethals and M. Zaki. An introduction to workshop on frequent itemset mining implementations. Proc. ICDM’03 Int. Workshop on Frequent Itemset Mining Implementations (FIMI’03), Melbourne, FL, Nov. 2003 J. Han, J. Pei, and Y. Yin. Mining frequent patterns without candidate generation. SIGMOD’ 00 J. Liu, Y. Pan, K. Wang, and J. Han. Mining Frequent Item Sets by Opportunistic Projection. KDD'02 J. Han, J. Wang, Y. Lu, and P. Tzvetkov. Mining Top-K Frequent Closed Patterns without Minimum Support. ICDM'02 J. Wang, J. Han, and J. Pei. CLOSET : Searching for the Best Strategies for Mining Frequent Closed Itemsets. KDD'03 63

Ref: Vertical Format and Row Enumeration Methods M. J. Zaki, S. Parthasarathy, M. Ogihara, and W. Li. Parallel algorithm for discovery of association rules. DAMI:97. M. J. Zaki and C. J. Hsiao. CHARM: An Efficient Algorithm for Closed Itemset Mining, SDM'02. C. Bucila, J. Gehrke, D. Kifer, and W. White. DualMiner: A Dual-Pruning Algorithm for Itemsets with Constraints. KDD’02. F. Pan, G. Cong, A. K. H. Tung, J. Yang, and M. Zaki , CARPENTER: Finding Closed Patterns in Long Biological Datasets. KDD'03. H. Liu, J. Han, D. Xin, and Z. Shao, Mining Interesting Patterns from Very High Dimensional Data: A Top-Down Row Enumeration Approach, SDM'06. 64

Ref: Mining Correlations and Interesting Rules S. Brin, R. Motwani, and C. Silverstein. Beyond market basket: Generalizing association rules to correlations. SIGMOD'97. M. Klemettinen, H. Mannila, P. Ronkainen, H. Toivonen, and A. I. Verkamo. Finding interesting rules from large sets of discovered association rules. CIKM'94. R. J. Hilderman and H. J. Hamilton. Knowledge Discovery and Measures of Interest. Kluwer Academic, 2001. C. Silverstein, S. Brin, R. Motwani, and J. Ullman. Scalable techniques for mining causal structures. VLDB'98. P.-N. Tan, V. Kumar, and J. Srivastava. Selecting the Right Interestingness Measure for Association Patterns. KDD'02. E. Omiecinski. Alternative Interest Measures for Mining Associations. TKDE’03. T. Wu, Y. Chen, and J. Han, “Re-Examination of Interestingness Measures in Pattern Mining: A Unified Framework", Data Mining and Knowledge Discovery, 21(3):371397, 2010 65