Mining Frequent Patterns, Association and Correlations�( Basic Concepts and Methods)

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Mining Frequent Patterns, Association and Correlations�( Basic Concepts and Methods)

• Basic Concepts
• Frequent Itemset Mining Methods
• Which Patterns Are Interesting?—Pattern Evaluation Methods
• Summary

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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.

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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, time-series, 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

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Basic Concepts: Frequent Patterns

• itemset: A set of one or more items
• k-itemset X = {x₁, …, x_k}
• (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

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Basic Concepts: Association Rules

• 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

Let minsup = 50%, minconf = 50%

Freq. Pat.: Beer:3, Nuts:3, Diaper:4, Eggs:3, {Beer, Diaper}:3

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Customer

buys diaper

Customer

buys both

Customer

buys beer

Nuts, Eggs, Milk

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Nuts, Coffee, Diaper, Eggs, Milk

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Beer, Diaper, Eggs

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Beer, Coffee, Diaper

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Beer, Nuts, Diaper

10

Items bought

Tid

• Association rules: (many more!)
• Beer 🡪 Diaper (60%, 100%)
• Diaper 🡪 Beer (60%, 75%)

Closed Patterns and Max-Patterns

• A long pattern contains a combinatorial number of sub-patterns, 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

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Closed Patterns and Max-Patterns

• Exercise. DB = {<a₁, …, a₁₀₀>, < a₁, …, a₅₀>}
• Min_sup = 1.
• What is the set of closed itemset?
• <a₁, …, a₁₀₀>: 1
• < a₁, …, a₅₀>: 2
• What is the set of max-pattern?
• <a₁, …, a₁₀₀>: 1
• What is the set of all patterns?
• !!

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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: M^N 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?

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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

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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

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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)

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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

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The Apriori Algorithm—An Example

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Database TDB

1^st scan

C₁

L₁

L₂

C₂

C₂

2^nd scan

C₃

L₃

3^rd scan

Sup_min = 2

The Apriori Algorithm (Pseudo-Code)

C_k: Candidate itemset of size k

L_k : frequent itemset of size k

​

L₁ = {frequent items};

for (k = 1; L_k !=∅; k++) do begin

C_k+1 = candidates generated from L_k;

for each transaction t in database do

increment the count of all candidates in C_k+1 that are contained in t

L_k+1 = candidates in C_k+1 with min_support

end

return ∪_k L_k;

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Implementation of Apriori

• How to generate candidates?
• Step 1: self-joining L_k
• 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}

​

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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

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Counting Supports of Candidates Using Hash Tree

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Transaction: 1 2 3 5 6

1 + 2 3 5 6

1 2 + 3 5 6

1 3 + 5 6

Candidate Generation: An SQL Implementation

• SQL Implementation of candidate generation
• Suppose the items in L_k-1 are listed in an order
• Step 1: self-joining L_k-1

insert into C_k

select p.item₁, p.item₂, …, p.item_k-1, q.item_k-1

from L_k-1 p, L_k-1 q

where p.item₁=q.item₁, …, p.item_k-2=q.item_k-2, p.item_k-1 < q.item_k-1

• Step 2: pruning

forall itemsets c in C_k do

forall (k-1)-subsets s of c do

if (s is not in L_k-1) then delete c from C_k

• 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]

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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

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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

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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

DB₂

DB_k

+

= DB

+

+

sup₁(i) < σDB₁

sup₂(i) < σDB₂

sup_k(i) < σDB_k

sup(i) < σDB

DHP: Reduce the Number of Candidates

• A k-itemset whose corresponding hashing bucket count is below the threshold cannot be frequent
• Candidates: a, b, c, d, e
• Hash entries
• {ab, ad, ae}
• {bd, be, de}
• …
• 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

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Hash Table

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

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DIC: Reduce Number of Scans

• 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

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ABCD

ABC

ABD

ACD

BCD

AB

AC

BC

AD

BD

CD

A

B

C

D

{}

Itemset lattice

Transactions

1-itemsets

2-itemsets

…

Apriori

1-itemsets

2-items

3-items

DIC

S. Brin R. Motwani, J. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for market basket data. SIGMOD’97

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

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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

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Construct FP-tree from a Transaction Database

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min_support = 3

TID Items bought (ordered) frequent items

100 {f, a, c, d, g, i, m, p} {f, c, a, m, p}

200 {a, b, c, f, l, m, o} {f, c, a, b, m}

300 {b, f, h, j, o, w} {f, b}

400 {b, c, k, s, p} {c, b, p}

500 {a, f, c, e, l, p, m, n} {f, c, a, m, p}

1. Scan DB once, find frequent 1-itemset (single item pattern)
2. Sort frequent items in frequency descending order, f-list
3. Scan DB again, construct FP-tree

F-list = f-c-a-b-m-p

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

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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

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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

From Conditional Pattern-bases to Conditional FP-trees

• 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

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m-conditional pattern base:

fca:2, fcab:1

All frequent patterns relate to m

m,

fm, cm, am,

fcm, fam, cam,

fcam

🡲

🡲

{}

f:4

c:1

b:1

p:1

b:1

c:3

a:3

b:1

m:2

p:2

m:1

Header Table

Item frequency head

f 4

c 4

a 3

b 3

m 3

p 3

Recursion: Mining Each Conditional FP-tree

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Cond. pattern base of “am”: (fc:3)

Cond. pattern base of “cm”: (f:3)

{}

f:3

cm-conditional FP-tree

Cond. pattern base of “cam”: (f:3)

{}

f:3

cam-conditional FP-tree

A Special Case: Single Prefix Path in FP-tree

• Suppose a (conditional) FP-tree T has a shared single prefix-path P
• Mining can be decomposed into two parts
• Reduction of the single prefix path into one node
• Concatenation of the mining results of the two parts

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🡲

+

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)

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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

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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

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Partition-Based Projection

• Parallel projection needs a lot of disk space
• Partition projection saves it

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Performance of FPGrowth in Large Datasets

FP-Growth vs. Apriori

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Data set T25I20D10K

Data set T25I20D100K

FP-Growth vs. Tree-Projection

Advantages of the Pattern Growth Approach

• Divide-and-conquer:
• Decompose both the mining task and DB according to the frequent patterns obtained so far
• 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
• Basic ops: counting local freq items and building sub FP-tree, no pattern search and matching
• A good open-source implementation and refinement of FPGrowth
• FPGrowth+ (Grahne and J. Zhu, FIMI'03)

​

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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)

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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)

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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

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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)

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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

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Mining Frequent Closed Patterns: CLOSET

• Flist: list of all frequent items in support ascending order
• Flist: d-a-f-e-c
• Divide search space
• Patterns having d
• Patterns having d but no a, etc.
• Find frequent closed pattern recursively
• 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.

Min_sup=2

CLOSET+: Mining Closed Itemsets by Pattern-Growth

• 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

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

Potential max-patterns

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)

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Visualization of Association Rules: Plane Graph

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Visualization of Association Rules: Rule Graph

Visualization of Association Rules �(SGI/MineSet 3.0)

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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

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Are lift and χ² 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?

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Null-Invariant Measures

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Comparison of Interestingness Measures

• Null-(transaction) invariance is crucial for correlation analysis
• Lift and χ² are not null-invariant
• 5 null-invariant measures

*

Data Mining: Concepts and Techniques

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Null-transactions w.r.t. m and c

Null-invariant

Subtle: They disagree

Kulczynski measure (1927)

Analysis of DBLP Coauthor Relationships

• 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

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Advisor-advisee relation: Kulc: high, coherence: low, cosine: middle

Recent DB conferences, removing balanced associations, low sup, etc.

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, support-confident 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

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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.

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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):371-397, 2010

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