Chapter 7. Advanced Frequent Pattern Mining.ppt

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Data Mining:
Concepts and Techniques
(3rd ed.)
Chapter 7
Subrata Kumer Paul
Assistant Professor, Dept. of CSE, BAUET
sksubrata96@gmail.com

September 24, 2023 Data Mining: Concepts and Techniques 2

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Chapter 7 : Advanced Frequent Pattern Mining
 Pattern Mining: A Road Map
 Pattern Mining in Multi-Level, Multi-Dimensional Space
 Constraint-Based Frequent Pattern Mining
 Mining High-Dimensional Data and Colossal Patterns
 Mining Compressed or Approximate Patterns
 Pattern Exploration and Application
 Summary

Research
on
Pattern
Mining:
A
Road
Map
4

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 Mining Multi-Level Association
 Mining Multi-Dimensional Association
 Mining Quantitative Association Rules
 Mining Rare Patterns and Negative Patterns
 Summary

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Mining Multiple-Level Association Rules
 Items often form hierarchies
 Flexible support settings
 Items at the lower level are expected to have lower
support
 Exploration of shared multi-level mining (Agrawal &
Srikant@VLB’95, Han & Fu@VLDB’95)
uniform support
Milk
[support = 10%]
2% Milk
[support = 6%]
Skim Milk
[support = 4%]
Level 1
min_sup = 5%
Level 2
min_sup = 5%
Level 1
min_sup = 5%
Level 2
min_sup = 3%
reduced support

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Multi-level Association: Flexible Support and
Redundancy filtering
 Flexible min-support thresholds: Some items are more valuable but
less frequent
 Use non-uniform, group-based min-support
 E.g., {diamond, watch, camera}: 0.05%; {bread, milk}: 5%; …
 Redundancy Filtering: Some rules may be redundant due to
“ancestor” relationships between items
 milk  wheat bread [support = 8%, confidence = 70%]
 2% milk  wheat bread [support = 2%, confidence = 72%]
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

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 Summary

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Mining Multi-Dimensional Association
 Single-dimensional rules:
buys(X, “milk”)  buys(X, “bread”)
 Multi-dimensional rules:  2 dimensions or predicates
 Inter-dimension assoc. rules (no repeated predicates)
age(X,”19-25”)  occupation(X,“student”)  buys(X, “coke”)
 hybrid-dimension assoc. rules (repeated predicates)
age(X,”19-25”)  buys(X, “popcorn”)  buys(X, “coke”)
 Categorical Attributes: finite number of possible values, no
ordering among values—data cube approach
 Quantitative Attributes: Numeric, implicit ordering among
values—discretization, clustering, and gradient approaches

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 Summary

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Mining Quantitative Associations
Techniques can be categorized by how numerical attributes,
such as age or salary are treated
1. Static discretization based on predefined concept
hierarchies (data cube methods)
2. Dynamic discretization based on data distribution
(quantitative rules, e.g., Agrawal & Srikant@SIGMOD96)
3. Clustering: Distance-based association (e.g., Yang &
Miller@SIGMOD97)
 One dimensional clustering then association
4. Deviation: (such as Aumann and Lindell@KDD99)
Sex = female => Wage: mean=$7/hr (overall mean = $9)

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Static Discretization of Quantitative Attributes
 Discretized prior to mining using concept hierarchy.
 Numeric values are replaced by ranges
 In relational database, finding all frequent k-predicate sets
will require k or k+1 table scans
 Data cube is well suited for mining
 The cells of an n-dimensional
cuboid correspond to the
predicate sets
 Mining from data cubes
can be much faster
(income)
(age)
()
(buys)
(age, income) (age,buys) (income,buys)
(age,income,buys)

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Quantitative Association Rules Based on Statistical
Inference Theory [Aumann and Lindell@DMKD’03]
 Finding extraordinary and therefore interesting phenomena, e.g.,
(Sex = female) => Wage: mean=$7/hr (overall mean = $9)
 LHS: a subset of the population
 RHS: an extraordinary behavior of this subset
 The rule is accepted only if a statistical test (e.g., Z-test) confirms the
inference with high confidence
 Subrule: highlights the extraordinary behavior of a subset of the pop.
of the super rule
 E.g., (Sex = female) ^ (South = yes) => mean wage = $6.3/hr
 Two forms of rules
 Categorical => quantitative rules, or Quantitative => quantitative rules
 E.g., Education in [14-18] (yrs) => mean wage = $11.64/hr
 Open problem: Efficient methods for LHS containing two or more
quantitative attributes

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 Summary

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Negative and Rare Patterns
 Rare patterns: Very low support but interesting
 E.g., buying Rolex watches
 Mining: Setting individual-based or special group-based
support threshold for valuable items
 Negative patterns
 Since it is unlikely that one buys Ford Expedition (an
SUV car) and Toyota Prius (a hybrid car) together, Ford
Expedition and Toyota Prius are likely negatively
correlated patterns
 Negatively correlated patterns that are infrequent tend to
be more interesting than those that are frequent

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Defining Negative Correlated Patterns (I)
 Definition 1 (support-based)
 If itemsets X and Y are both frequent but rarely occur together, i.e.,
sup(X U Y) < sup (X) * sup(Y)
 Then X and Y are negatively correlated
 Problem: A store sold two needle 100 packages A and B, only one
transaction containing both A and B.
 When there are in total 200 transactions, we have
s(A U B) = 0.005, s(A) * s(B) = 0.25, s(A U B) < s(A) * s(B)
 When there are 105 transactions, we have
s(A U B) = 1/105, s(A) * s(B) = 1/103 * 1/103, s(A U B) > s(A) * s(B)
 Where is the problem? —Null transactions, i.e., the support-based
definition is not null-invariant!

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Defining Negative Correlated Patterns (II)
 Definition 2 (negative itemset-based)
 X is a negative itemset if (1) X = Ā U B, where B is a set of positive
items, and Ā is a set of negative items, |Ā|≥ 1, and (2) s(X) ≥ μ
 Itemsets X is negatively correlated, if
 This definition suffers a similar null-invariant problem
 Definition 3 (Kulzynski measure-based) If itemsets X and Y are
frequent, but (P(X|Y) + P(Y|X))/2 < є, where є is a negative pattern
threshold, then X and Y are negatively correlated.
 Ex. For the same needle package problem, when no matter there are
200 or 105 transactions, if є = 0.01, we have
(P(A|B) + P(B|A))/2 = (0.01 + 0.01)/2 < є

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 Summary

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Constraint-based (Query-Directed) Mining
 Finding all the patterns in a database autonomously? — unrealistic!
 The patterns could be too many but not focused!
 Data mining should be an interactive process
 User directs what to be mined using a data mining query
language (or a graphical user interface)
 Constraint-based mining
 User flexibility: provides constraints on what to be mined
 Optimization: explores such constraints for efficient mining —
constraint-based mining: constraint-pushing, similar to push
selection first in DB query processing
 Note: still find all the answers satisfying constraints, not finding
some answers in “heuristic search”

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Constraints in Data Mining
 Knowledge type constraint:
 classification, association, etc.
 Data constraint — using SQL-like queries
 find product pairs sold together in stores in Chicago this
year
 Dimension/level constraint
 in relevance to region, price, brand, customer category
 Rule (or pattern) constraint
 small sales (price < $10) triggers big sales (sum >
$200)
 Interestingness constraint
 strong rules: min_support  3%, min_confidence 
60%

Meta-Rule Guided Mining
 Meta-rule can be in the rule form with partially instantiated predicates
and constants
P1(X, Y) ^ P2(X, W) => buys(X, “iPad”)
 The resulting rule derived can be
age(X, “15-25”) ^ profession(X, “student”) => buys(X, “iPad”)
 In general, it can be in the form of
P1 ^ P2 ^ … ^ Pl => Q1 ^ Q2 ^ … ^ Qr
 Method to find meta-rules
 Find frequent (l+r) predicates (based on min-support threshold)
 Push constants deeply when possible into the mining process (see
the remaining discussions on constraint-push techniques)
 Use confidence, correlation, and other measures when possible
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Constraint-Based Frequent Pattern Mining
 Pattern space pruning constraints
 Anti-monotonic: If constraint c is violated, its further mining can
be terminated
 Monotonic: If c is satisfied, no need to check c again
 Succinct: c must be satisfied, so one can start with the data sets
satisfying c
 Convertible: c is not monotonic nor anti-monotonic, but it can be
converted into it if items in the transaction can be properly
ordered
 Data space pruning constraint
 Data succinct: Data space can be pruned at the initial pattern
mining process
 Data anti-monotonic: If a transaction t does not satisfy c, t can be
pruned from its further mining

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Pattern Space Pruning with Anti-Monotonicity Constraints
 A constraint C is anti-monotone if the super
pattern satisfies C, all of its sub-patterns do so
too
 In other words, anti-monotonicity: If an itemset
S violates the constraint, so does any of its
superset
 Ex. 1. sum(S.price)  v is anti-monotone
 Ex. 2. range(S.profit)  15 is anti-monotone
 Itemset ab violates C
 So does every superset of ab
 Ex. 3. sum(S.Price)  v is not anti-monotone
 Ex. 4. support count is anti-monotone: core
property used in Apriori
TID Transaction
10 a, b, c, d, f
20 b, c, d, f, g, h
30 a, c, d, e, f
40 c, e, f, g
TDB (min_sup=2)
Item Profit
a 40
b 0
c -20
d 10
e -30
f 30
g 20
h -10

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Pattern Space Pruning with Monotonicity Constraints
 A constraint C is monotone if the pattern
satisfies C, we do not need to check C in
subsequent mining
 Alternatively, monotonicity: If an itemset S
satisfies the constraint, so does any of its
superset
 Ex. 1. sum(S.Price)  v is monotone
 Ex. 2. min(S.Price)  v is monotone
 Ex. 3. C: range(S.profit)  15
 Itemset ab satisfies C
 So does every superset of ab
TID Transaction
10 a, b, c, d, f
20 b, c, d, f, g, h
30 a, c, d, e, f
40 c, e, f, g
TDB (min_sup=2)
Item Profit
a 40
b 0
c -20
d 10
e -30
f 30
g 20
h -10

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Data Space Pruning with Data Anti-monotonicity
 A constraint c is data anti-monotone if for a pattern
p cannot satisfy a transaction t under c, p’s
superset cannot satisfy t under c either
 The key for data anti-monotone is recursive data
reduction
 Ex. 1. sum(S.Price)  v is data anti-monotone
 Ex. 2. min(S.Price)  v is data anti-monotone
 Ex. 3. C: range(S.profit)  25 is data anti-
monotone
 Itemset {b, c}’s projected DB:
 T10’: {d, f, h}, T20’: {d, f, g, h}, T30’: {d, f, g}
 since C cannot satisfy T10’, T10’ can be pruned
TID Transaction
10 a, b, c, d, f, h
20 b, c, d, f, g, h
30 b, c, d, f, g
40 c, e, f, g
TDB (min_sup=2)
Item Profit
a 40
b 0
c -20
d -15
e -30
f -10
g 20
h -5

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Pattern Space Pruning with Succinctness
 Succinctness:
 Given A1, the set of items satisfying a succinctness
constraint C, then any set S satisfying C is based on
A1 , i.e., S contains a subset belonging to A1
 Idea: Without looking at the transaction database,
whether an itemset S satisfies constraint C can be
determined based on the selection of items
 min(S.Price)  v is succinct
 sum(S.Price)  v is not succinct
 Optimization: If C is succinct, C is pre-counting pushable

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Naïve Algorithm: Apriori + Constraint
TID Items
100 1 3 4
200 2 3 5
300 1 2 3 5
400 2 5
Database D itemset sup.
{1} 2
{2} 3
{3} 3
{4} 1
{5} 3
itemset sup.
{1} 2
{2} 3
{3} 3
{5} 3
Scan D
C1
L1
itemset
{1 2}
{1 3}
{1 5}
{2 3}
{2 5}
{3 5}
itemset sup
{1 2} 1
{1 3} 2
{1 5} 1
{2 3} 2
{2 5} 3
{3 5} 2
itemset sup
{1 3} 2
{2 3} 2
{2 5} 3
{3 5} 2
L2
C2 C2
Scan D
C3 L3
itemset
{2 3 5}
Scan D itemset sup
{2 3 5} 2
Constraint:
Sum{S.price} < 5

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Constrained Apriori : Push a Succinct Constraint
Deep
TID Items
100 1 3 4
200 2 3 5
300 1 2 3 5
400 2 5
Database D itemset sup.
{1} 2
{2} 3
{3} 3
{4} 1
{5} 3
itemset sup.
{1} 2
{2} 3
{3} 3
{5} 3
Scan D
C1
L1
itemset
{1 2}
{1 3}
{1 5}
{2 3}
{2 5}
{3 5}
itemset sup
{1 2} 1
{1 3} 2
{1 5} 1
{2 3} 2
{2 5} 3
{3 5} 2
itemset sup
{1 3} 2
{2 3} 2
{2 5} 3
{3 5} 2
L2
C2 C2
Scan D
C3 L3
itemset
{2 3 5}
Scan D itemset sup
{2 3 5} 2
Constraint:
min{S.price } <= 1
not immediately
to be used

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Constrained FP-Growth: Push a Succinct
Constraint Deep
Constraint:
min{S.price } <= 1
TID Items
100 1 3 4
200 2 3 5
300 1 2 3 5
400 2 5
TID Items
100 1 3
200 2 3 5
300 1 2 3 5
400 2 5
Remove
infrequent
length 1
FP-Tree
TID Items
100 3 4
300 2 3 5
1-Projected DB
No Need to project on 2, 3, or 5

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Constrained FP-Growth: Push a Data
Anti-monotonic Constraint Deep
Constraint:
min{S.price } <= 1
TID Items
100 1 3 4
200 2 3 5
300 1 2 3 5
400 2 5
TID Items
100 1 3
300 1 3
FP-Tree
Single branch, we are done
Remove from data

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Constrained FP-Growth: Push a
Data Anti-monotonic Constraint
Deep
Constraint:
range{S.price } > 25
min_sup >= 2
FP-Tree
TID Transaction
10 a, c, d, f, h
20 c, d, f, g, h
30 c, d, f, g
B-Projected DB
B
FP-Tree
TID Transaction
10 a, b, c, d, f, h
20 b, c, d, f, g, h
30 b, c, d, f, g
40 a, c, e, f, g
TID Transaction
10 a, b, c, d, f, h
20 b, c, d, f, g, h
30 b, c, d, f, g
40 a, c, e, f, g
Item Profit
a 40
b 0
c -20
d -15
e -30
f -10
g 20
h -5
Recursive
Data
Pruning
Single branch:
bcdfg: 2

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Convertible Constraints: Ordering Data in
Transactions
 Convert tough constraints into anti-
monotone or monotone by properly
ordering items
 Examine C: avg(S.profit)  25
 Order items in value-descending
order
 <a, f, g, d, b, h, c, e>
 If an itemset afb violates C
 So does afbh, afb*
 It becomes anti-monotone!
TID Transaction
10 a, b, c, d, f
20 b, c, d, f, g, h
30 a, c, d, e, f
40 c, e, f, g
TDB (min_sup=2)
Item Profit
a 40
b 0
c -20
d 10
e -30
f 30
g 20
h -10

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Strongly Convertible Constraints
 avg(X)  25 is convertible anti-monotone w.r.t.
item value descending order R: <a, f, g, d, b,
h, c, e>
 If an itemset af violates a constraint C, so
does every itemset with af as prefix, such as
afd
 avg(X)  25 is convertible monotone w.r.t. item
value ascending order R-1: <e, c, h, b, d, g, f,
a>
 If an itemset d satisfies a constraint C, so
does itemsets df and dfa, which having d as
a prefix
 Thus, avg(X)  25 is strongly convertible
Item Profit
a 40
b 0
c -20
d 10
e -30
f 30
g 20
h -10

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Can Apriori Handle Convertible Constraints?
 A convertible, not monotone nor anti-monotone
nor succinct constraint cannot be pushed deep
into the an Apriori mining algorithm
 Within the level wise framework, no direct
pruning based on the constraint can be made
 Itemset df violates constraint C: avg(X) >=
25
 Since adf satisfies C, Apriori needs df to
assemble adf, df cannot be pruned
 But it can be pushed into frequent-pattern
growth framework!
Item Value
a 40
b 0
c -20
d 10
e -30
f 30
g 20
h -10

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Pattern Space Pruning w. Convertible Constraints
 C: avg(X) >= 25, min_sup=2
 List items in every transaction in value
descending order R: <a, f, g, d, b, h, c, e>
 C is convertible anti-monotone w.r.t. R
 Scan TDB once
 remove infrequent items
 Item h is dropped
 Itemsets a and f are good, …
 Projection-based mining
 Imposing an appropriate order on item
projection
 Many tough constraints can be converted into
(anti)-monotone
TID Transaction
10 a, f, d, b, c
20 f, g, d, b, c
30 a, f, d, c, e
40 f, g, h, c, e
TDB (min_sup=2)
Item Value
a 40
f 30
g 20
d 10
b 0
h -10
c -20
e -30

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Handling Multiple Constraints
 Different constraints may require different or even
conflicting item-ordering
 If there exists an order R s.t. both C1 and C2 are
convertible w.r.t. R, then there is no conflict between
the two convertible constraints
 If there exists conflict on order of items
 Try to satisfy one constraint first
 Then using the order for the other constraint to
mine frequent itemsets in the corresponding
projected database

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What Constraints Are Convertible?
Constraint
Convertible anti-
monotone
Convertible
monotone
Strongly
convertible
avg(S)  ,  v Yes Yes Yes
median(S)  ,  v Yes Yes Yes
sum(S)  v (items could be of any value,
v  0)
Yes No No
sum(S)  v (items could be of any value,
v  0)
No Yes No
sum(S)  v (items could be of any value,
v  0)
No Yes No
sum(S)  v (items could be of any value,
v  0)
Yes No No
……

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Constraint-Based Mining — A General Picture
Constraint Anti-monotone Monotone Succinct
v  S no yes yes
S  V no yes yes
S  V yes no yes
min(S)  v no yes yes
min(S)  v yes no yes
max(S)  v yes no yes
max(S)  v no yes yes
count(S)  v yes no weakly
count(S)  v no yes weakly
sum(S)  v ( a  S, a  0 ) yes no no
sum(S)  v ( a  S, a  0 ) no yes no
range(S)  v yes no no
range(S)  v no yes no
avg(S)  v,   { , ,  } convertible convertible no
support(S)   yes no no
support(S)   no yes no

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 Summary

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Mining Colossal Frequent Patterns
 F. Zhu, X. Yan, J. Han, P. S. Yu, and H. Cheng, “Mining Colossal
Frequent Patterns by Core Pattern Fusion”, ICDE'07.
 We have many algorithms, but can we mine large (i.e., colossal)
patterns? ― such as just size around 50 to 100? Unfortunately, not!
 Why not? ― the curse of “downward closure” of frequent patterns
 The “downward closure” property
 Any sub-pattern of a frequent pattern is frequent.
 Example. If (a1, a2, …, a100) is frequent, then a1, a2, …, a100, (a1,
a2), (a1, a3), …, (a1, a100), (a1, a2, a3), … are all frequent! There
are about 2100 such frequent itemsets!
 No matter using breadth-first search (e.g., Apriori) or depth-first
search (FPgrowth), we have to examine so many patterns
 Thus the downward closure property leads to explosion!

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Closed/maximal patterns may
partially alleviate the problem but not
really solve it: We often need to mine
scattered large patterns!
Let the minimum support threshold
σ= 20
There are frequent patterns of
size 20
Each is closed and maximal
# patterns =
The size of the answer set is
exponential to n
Colossal Patterns: A Motivating Example
T1 = 1 2 3 4 ….. 39 40
T2 = 1 2 3 4 ….. 39 40
: .
: .
: .
: .
T40=1 2 3 4 ….. 39 40








20
40
T1 = 2 3 4 ….. 39 40
T2 = 1 3 4 ….. 39 40
: .
: .
: .
: .
T40=1 2 3 4 …… 39
n
n
n n
2
/
2
2
/










Then delete the items on the diagonal
Let’s make a set of 40 transactions

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Colossal Pattern Set: Small but Interesting
 It is often the case that
only a small number of
patterns are colossal,
i.e., of large size
 Colossal patterns are
usually attached with
greater importance than
those of small pattern
sizes

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Mining Colossal Patterns: Motivation and
Philosophy
 Motivation: Many real-world tasks need mining colossal patterns
 Micro-array analysis in bioinformatics (when support is low)
 Biological sequence patterns
 Biological/sociological/information graph pattern mining
 No hope for completeness
 If the mining of mid-sized patterns is explosive in size, there is no
hope to find colossal patterns efficiently by insisting “complete set”
mining philosophy
 Jumping out of the swamp of the mid-sized results
 What we may develop is a philosophy that may jump out of the
swamp of mid-sized results that are explosive in size and jump to
reach colossal patterns
 Striving for mining almost complete colossal patterns
 The key is to develop a mechanism that may quickly reach colossal
patterns and discover most of them

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Let the min-support threshold σ= 20
Then there are closed/maximal
frequent patterns of size 20
However, there is only one with size
greater than 20, (i.e., colossal):
α= {41,42,…,79} of size 39
Alas, A Show of Colossal Pattern Mining!








20
40
T1 = 2 3 4 ….. 39 40
T2 = 1 3 4 ….. 39 40
: .
: .
: .
: .
T40=1 2 3 4 …… 39
T41= 41 42 43 ….. 79
T42= 41 42 43 ….. 79
: .
: .
T60= 41 42 43 … 79
The existing fastest mining algorithms
(e.g., FPClose, LCM) fail to complete
running
Our algorithm outputs this colossal
pattern in seconds

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Methodology of Pattern-Fusion Strategy
 Pattern-Fusion traverses the tree in a bounded-breadth way
 Always pushes down a frontier of a bounded-size candidate
pool
 Only a fixed number of patterns in the current candidate pool
will be used as the starting nodes to go down in the pattern tree
― thus avoids the exponential search space
 Pattern-Fusion identifies “shortcuts” whenever possible
 Pattern growth is not performed by single-item addition but by
leaps and bounded: agglomeration of multiple patterns in the
pool
 These shortcuts will direct the search down the tree much more
rapidly towards the colossal patterns

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Observation: Colossal Patterns and Core Patterns
A colossal pattern α
D
Dα
α1
Transaction Database D
Dα1
Dα2
α2
α
αk
Dαk
Subpatterns α1 to αk cluster tightly around the colossal pattern α by
sharing a similar support. We call such subpatterns core patterns of α

47
Robustness of Colossal Patterns
 Core Patterns
Intuitively, for a frequent pattern α, a subpattern β is a τ-core
pattern of α if β shares a similar support set with α, i.e.,
where τ is called the core ratio
 Robustness of Colossal Patterns
A colossal pattern is robust in the sense that it tends to have much
more core patterns than small patterns




|
|
|
|
D
D
1
0 


48
Example: Core Patterns
 A colossal pattern has far more core patterns than a small-sized pattern
 A colossal pattern has far more core descendants of a smaller size c
 A random draw from a complete set of pattern of size c would more
likely to pick a core descendant of a colossal pattern
 A colossal pattern can be generated by merging a set of core patterns
Transaction (# of Ts) Core Patterns (τ = 0.5)
(abe) (100) (abe), (ab), (be), (ae), (e)
(bcf) (100) (bcf), (bc), (bf)
(acf) (100) (acf), (ac), (af)
(abcef) (100) (ab), (ac), (af), (ae), (bc), (bf), (be) (ce), (fe), (e),
(abc), (abf), (abe), (ace), (acf), (afe), (bcf), (bce),
(bfe), (cfe), (abcf), (abce), (bcfe), (acfe), (abfe), (abcef)

50
Colossal Patterns Correspond to Dense Balls
 Due to their robustness,
colossal patterns correspond to
dense balls
 Ω( 2^d) in population
 A random draw in the pattern
space will hit somewhere in the
ball with high probability

51
Idea of Pattern-Fusion Algorithm
 Generate a complete set of frequent patterns up to a
small size
 Randomly pick a pattern β, and β has a high probability to
be a core-descendant of some colossal pattern α
 Identify all α’s descendants in this complete set, and
merge all of them ― This would generate a much larger
core-descendant of α
 In the same fashion, we select K patterns. This set of
larger core-descendants will be the candidate pool for the
next iteration

52
Pattern-Fusion: The Algorithm
 Initialization (Initial pool): Use an existing algorithm to
mine all frequent patterns up to a small size, e.g., 3
 Iteration (Iterative Pattern Fusion):
 At each iteration, k seed patterns are randomly picked
from the current pattern pool
 For each seed pattern thus picked, we find all the
patterns within a bounding ball centered at the seed
pattern
 All these patterns found are fused together to generate
a set of super-patterns. All the super-patterns thus
generated form a new pool for the next iteration
 Termination: when the current pool contains no more
than K patterns at the beginning of an iteration

53
Why Is Pattern-Fusion Efficient?
 A bounded-breadth pattern
tree traversal
 It avoids explosion in
mining mid-sized ones
 Randomness comes to help
to stay on the right path
 Ability to identify “short-cuts”
and take “leaps”
 fuse small patterns
together in one step to
generate new patterns of
significant sizes
 Efficiency

54
Pattern-Fusion Leads to Good Approximation
 Gearing toward colossal patterns
 The larger the pattern, the greater the chance it will
be generated
 Catching outliers
 The more distinct the pattern, the greater the chance
it will be generated

55
Experimental Setting
 Synthetic data set
 Diagn an n x (n-1) table where ith row has integers from 1 to n
except i. Each row is taken as an itemset. min_support is n/2.
 Real data set
 Replace: A program trace data set collected from the “replace”
program, widely used in software engineering research
 ALL: A popular gene expression data set, a clinical data on ALL-AML
leukemia (www.broad.mit.edu/tools/data.html).
 Each item is a column, representing the activitiy level of
gene/protein in the same
 Frequent pattern would reveal important correlation between
gene expression patterns and disease outcomes

56
Experiment Results on Diagn
 LCM run time increases
exponentially with pattern
size n
 Pattern-Fusion finishes
efficiently
 The approximation error of
Pattern-Fusion (with min-sup
20) in comparison with the
complete set) is rather close
to uniform sampling (which
randomly picks K patterns
from the complete answer
set)

57
Experimental Results on ALL
 ALL: A popular gene expression data set with 38
transactions, each with 866 columns
 There are 1736 items in total
 The table shows a high frequency threshold of 30

58
Experimental Results on REPLACE
 REPLACE
 A program trace data set, recording 4395 calls
and transitions
 The data set contains 4395 transactions with
57 items in total
 With support threshold of 0.03, the largest
patterns are of size 44
 They are all discovered by Pattern-Fusion with
different settings of K and τ, when started with
an initial pool of 20948 patterns of size <=3

59
Experimental Results on REPLACE
 Approximation error when
compared with the complete
mining result
 Example. Out of the total 98
patterns of size >=42, when
K=100, Pattern-Fusion returns
80 of them
 A good approximation to the
colossal patterns in the sense
that any pattern in the
complete set is on average at
most 0.17 items away from one
of these 80 patterns

60
 Summary

61
Mining Compressed Patterns: δ-clustering
 Why compressed patterns?
 too many, but less meaningful
 Pattern distance measure
 δ-clustering: For each pattern P,
find all patterns which can be
expressed by P and their distance
to P are within δ (δ-cover)
 All patterns in the cluster can be
represented by P
 Xin et al., “Mining Compressed
Frequent-Pattern Sets”, VLDB’05
ID Item-Sets Support
P1 {38,16,18,12} 205227
P2 {38,16,18,12,17} 205211
P3 {39,38,16,18,12,17} 101758
P4 {39,16,18,12,17} 161563
P5 {39,16,18,12} 161576
 Closed frequent pattern
 Report P1, P2, P3, P4, P5
 Emphasize too much on
support
 no compression
 Max-pattern, P3: info loss
 A desirable output: P2, P3, P4

62
Redundancy-Award Top-k Patterns
 Why redundancy-aware top-k patterns?
 Desired patterns: high
significance & low
redundancy
 Propose the MMS
(Maximal Marginal
Significance) for
measuring the
combined significance
of a pattern set
 Xin et al., Extracting
Redundancy-Aware
Top-K Patterns, KDD’06

63
 Summary

 Do they all make sense?
 What do they mean?
 How are they useful?
diaper beer
female sterile (2) tekele
Annotate patterns with semantic information
morphological info. and simple statistics
Semantic Information
Not all frequent patterns are useful, only meaningful ones …
How to Understand and Interpret Patterns?

Word: “pattern” – from Merriam-Webster
A Dictionary Analogy
Non-semantic info.
Examples of Usage
Definitions indicating
semantics
Synonyms
Related Words

Semantic Analysis with Context Models
 Task1: Model the context of a frequent pattern
Based on the Context Model…
 Task2: Extract strongest context indicators
 Task3: Extract representative transactions
 Task4: Extract semantically similar patterns

Annotating DBLP Co-authorship & Title Pattern
Substructure Similarity Search
in Graph Databases
X.Yan, P. Yu, J. Han
…
…
…
…
Database:
Title
Authors
Frequent Patterns
P1: { x_yan, j_han }
Frequent Itemset
P2: “substructure search”
Pattern { x_yan, j_han}
Non Sup = …
CI {p_yu}, graph pattern, …
Trans. gSpan: graph-base……
SSPs { j_wang }, {j_han, p_yu}, …
Semantic Annotations
Context Units
< { p_yu, j_han}, { d_xin }, … , “graph pattern”,
… “substructure similarity”, … >
Pattern = {xifeng_yan, jiawei_han} Annotation Results:
Context Indicator (CI) graph; {philip_yu}; mine close; graph pattern; sequential pattern; …
Representative
Transactions (Trans)
> gSpan: graph-base substructure pattern mining;
> mining close relational graph connect constraint; …
Semantically Similar
Patterns (SSP)
{jiawei_han, philip_yu}; {jian_pei, jiawei_han}; {jiong_yang, philip_yu,
wei_wang}; …

68
 Summary

69
Summary
 Roadmap: Many aspects & extensions on pattern mining
 Mining patterns in multi-level, multi dimensional space
 Mining rare and negative patterns
 Constraint-based pattern mining
 Specialized methods for mining high-dimensional data
and colossal patterns
 Mining compressed or approximate patterns
 Pattern exploration and understanding: Semantic
annotation of frequent patterns

70
Ref: Mining Multi-Level and Quantitative Rules
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71
Ref: Mining Other Kinds of Rules
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Functional and Approximate Dependencies Using Partitions. ICDE’98.
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associations in a large database of customer transactions. ICDE'98.
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72
Ref: Constraint-Based Pattern Mining
 R. Srikant, Q. Vu, and R. Agrawal. Mining association rules with item
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Large Databases, CIKM'02
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Framework for Graph Pattern Mining”, PAKDD'07

73
Ref: Mining Sequential Patterns
 X. Ji, J. Bailey, and G. Dong. Mining minimal distinguishing subsequence patterns with
gap constraints. ICDM'05
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sequences. DAMI:97.
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Patterns Efficiently by Prefix-Projected Pattern Growth. ICDE'01.
 R. Srikant and R. Agrawal. Mining sequential patterns: Generalizations and
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Datasets. SDM'03.
 M. Zaki. SPADE: An Efficient Algorithm for Mining Frequent Sequences. Machine
Learning:01.

Mining Graph and Structured Patterns
 A. Inokuchi, T. Washio, and H. Motoda. An apriori-based algorithm for
mining frequent substructures from graph data. PKDD'00
 M. Kuramochi and G. Karypis. Frequent Subgraph Discovery. ICDM'01.
 X. Yan and J. Han. gSpan: Graph-based substructure pattern mining.
ICDM'02
 X. Yan and J. Han. CloseGraph: Mining Closed Frequent Graph Patterns.
KDD'03
 X. Yan, P. S. Yu, and J. Han. Graph indexing based on discriminative frequent
structure analysis. ACM TODS, 30:960–993, 2005
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search. ACM Trans. Database Systems, 31:1418–1453, 2006
74

75
Ref: Mining Spatial, Spatiotemporal, Multimedia Data
 H. Cao, N. Mamoulis, and D. W. Cheung. Mining frequent spatiotemporal
sequential patterns. ICDM'05
 D. Gunopulos and I. Tsoukatos. Efficient Mining of Spatiotemporal Patterns.
SSTD'01
 K. Koperski and J. Han, Discovery of Spatial Association Rules in Geographic
Information Databases, SSD’95
 H. Xiong, S. Shekhar, Y. Huang, V. Kumar, X. Ma, and J. S. Yoo. A framework
for discovering co-location patterns in data sets with extended spatial
objects. SDM'04
 J. Yuan, Y. Wu, and M. Yang. Discovery of collocation patterns: From visual
words to visual phrases. CVPR'07
 O. R. Zaiane, J. Han, and H. Zhu, Mining Recurrent Items in Multimedia with
Progressive Resolution Refinement. ICDE'00

76
Ref: Mining Frequent Patterns in Time-Series Data
 B. Ozden, S. Ramaswamy, and A. Silberschatz. Cyclic association rules. ICDE'98.
 J. Han, G. Dong and Y. Yin, Efficient Mining of Partial Periodic Patterns in Time Series
Database, ICDE'99.
 J. Shieh and E. Keogh. iSAX: Indexing and mining terabyte sized time series. KDD'08
 B.-K. Yi, N. Sidiropoulos, T. Johnson, H. V. Jagadish, C. Faloutsos, and A. Biliris. Online
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Attributes. ICDE’01.
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TKDE’03
 L. Ye and E. Keogh. Time series shapelets: A new primitive for data mining. KDD'09

77
Ref: FP for Classification and Clustering
 G. Dong and J. Li. Efficient mining of emerging patterns: Discovering
trends and differences. KDD'99.
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Analysis for Effective Classification”, ICDE'07

78
Ref: Privacy-Preserving FP Mining
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Vertically Partitioned Data. KDD’02

Mining Compressed Patterns
 D. Xin, H. Cheng, X. Yan, and J. Han. Extracting redundancy-
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 D. Xin, J. Han, X. Yan, and H. Cheng. Mining compressed
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patterns: A profile-based approach. KDD'05
79

Mining Colossal Patterns
 F. Zhu, X. Yan, J. Han, P. S. Yu, and H. Cheng. Mining colossal
frequent patterns by core pattern fusion. ICDE'07
 F. Zhu, Q. Qu, D. Lo, X. Yan, J. Han. P. S. Yu, Mining Top-K Large
Structural Patterns in a Massive Network. VLDB’11
80

81
Ref: FP Mining from Data Streams
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82
Ref: Freq. Pattern Mining Applications
 T. Dasu, T. Johnson, S. Muthukrishnan, and V. Shkapenyuk. Mining Database Structure; or
How to Build a Data Quality Browser. SIGMOD'02
 M. Khan, H. Le, H. Ahmadi, T. Abdelzaher, and J. Han. DustMiner: Troubleshooting
interactive complexity bugs in sensor networks., SenSys'08
 Z. Li, S. Lu, S. Myagmar, and Y. Zhou. CP-Miner: A tool for finding copy-paste and related
bugs in operating system code. In Proc. 2004 Symp. Operating Systems Design and
Implementation (OSDI'04)
 Z. Li and Y. Zhou. PR-Miner: Automatically extracting implicit programming rules and
detecting violations in large software code. FSE'05
 D. Lo, H. Cheng, J. Han, S. Khoo, and C. Sun. Classification of software behaviors for failure
detection: A discriminative pattern mining approach. KDD'09
 Q. Mei, D. Xin, H. Cheng, J. Han, and C. Zhai. Semantic annotation of frequent patterns.
ACM TKDD, 2007.
 K. Wang, S. Zhou, J. Han. Profit Mining: From Patterns to Actions. EDBT’02.

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