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Association Rule Mining
ARM
http://www.cs.ndsu.nodak.edu/~rahal/765/lectures/
Lecture Outline
Data Mining and Knowledge Discovery
Market Basket Research Models
Association Rule Mining
Apriori
Rule Generation
Methods To Improve Apriori’s Efficiency
Vertical Data Representation
What is Data Mining
Data mining is the exploration and analysis of
large quantities of data in order to discover valid,
novel, potentially useful, and ultimately
understandable patterns and knowledge in
data.
Valid: The patterns hold in general.
Novel: We did not know the pattern beforehand.
Fargo is in Minnesota !
(live in Fargo) (live in ND)
Useful: We can devise actions from the patterns
(actionable)
Understandable: We can interpret and comprehend
the patterns.
What Motivated Data Mining?
As an evolution in the path of IT
1-Data Collection and Database Creation
Primitive File Processing
1960s and earlier
2-Database Management Systems:
Hierarchical/Network/Relational database
system
ERDs
SQL
Recovery and concurrency control in DBMSs
OLTP
1970s-early 1980s
3.1-Advanced Database Systems
Object-oriented/object-relational databases
Application-oriented databases
Spatial, multimedia, scientific, etc …
Mid-1980s-present
3.2-Web-based Database Systems
XML-based databases systems
Web analysis and mining
Semantic Web (the whole web as a single XML
database)
Mid-1990s-present
3.3-Data Warehousing and Data Mining
Multi-dimensional Data warehouse and
OLAP technology
Data Mining and Knowledge Discovery
tools to assist people in their decision-making
processes
Late 1980s-present
Why Use Data Mining Today?
Market Competition Pressure!
“The secret of success is to know something that
nobody else knows.” Aristotle
Wal-Mart VS K-Mart
Right products, right place, right time, and right quantities
Personalization, CRM
Security, homeland defense
Analysis of important application data
Bioinformatics
Stock market data
Human analysis skills are inadequate:
Volume and dimensionality of the data
High data growth rate
Storage
Computational power
Off-the-shelf software
Other factors
Where Could All Of This Data
Be Coming From?
Supermarket scanners
Preferred customer cards
Sunmart’s MoreCards
Credit card transactions
Call center records
ATM machines
Demographic data
Sensor networks
Cameras
Web server logs
Customer web site trails
Biological data (e.g. MicroArray Experiments for
expression levels)
Image data
Types Of Data/Information
Repositories For Data Mining
By definition, data mining should be
applicable to any kind of information
repository
Flat files
Relational databases
data warehouses
transactional databases
Advanced database systems
object-oriented
Object-relational
Application-oriented databases
Multimedia
Text
Image
Video
Audio
Heterogeneous databases
Appear as centralized
Independent components managing different
parts of the data
How Could We Describe Data
Numerical : Domain is ordered and can be
represented on the continuous real line (e.g.
age, income)
Continuous?
Nominal or categorical : Domain is a finite
set without any natural ordering (e.g.
occupation, marital status, race)
Ordinal : Domain is finite and ordered,
(e.g.: grade scale, months in a year)
The Knowledge Discovery
Process
Broader than Data Mining
Steps:
Identify the problem
Data mining
Action
Evaluation and measurement
Deployment and integration into real-life
processes and/or applications
The Data Mining Step in More
Detail
Cleaning and integration of various data sources
Remove noise and outliers
Missing Values (e.g. null values)
Noisy data (errors)
Inconsistent Data (integration)
Selection and transformation of relevant data into appropriate
forms
Focus on fields of interest
Education on salary
Create common units
FirstName and F_Name
Height in cm and inches
Generate new fields
Discovery of interesting patterns from the data
Pattern evaluation to identify the interesting patterns based on
some predefined measures
Knowledge presentation to communicate the mined knowledge and
information to the user mostly through visualization techniques to
provide a better view
This process can be repeated as needed
Data mining systems are expected to handle
large amounts of data
Analysis of small datasets is sometimes called
machine learning
SDA – Statistical data analysis.
In other words, data mining must be scalable
to large data sets
Scalability and efficiency
Data Mining
Knowledge
Patterns
Target
Data
Preprocessed
Data
Pattern
evaluation
Knowledge
presentation
Discovery
Original Data
Selection
and transformation
Cleaning
and integration
Data Mining Tasks
Characterization
the process of summarizing the general
characteristics and features of a specific class of
data (usually referred to as the target class)
Characterizing the items in a store whose sales
have decreased by 50% over a certain period of
time.
There maybe some common characteristics to all those
items which we would like to uncover.
Produced by a no-longer trusted producer
Discrimination
Discrimination is very similar to characterization in
that it reveals the characteristics of a target class
in comparison to those characteristics
pertaining to one or more other classes.
The target and contrasting classes are specified by
user and their data is retrieved from the database
before the discrimination process starts.
As an example, a user might want to discriminate
between the characteristics of the items in a store
whose
sales have increased by 10% over a certain period of
time this year
sales have increased by 10% over the same period of
time last year.
Association Rule Mining
The process of discovering association rules
among attribute values that exist in a given set of
data.
Market basket research (MBR) where users are
usually interested in mining associations between
items in a store by using daily transactions.
An example of a rule might be diapersbeer meaning
that customers buying diapers are very likely to buy beer.
This will give us a good pointer to place diapers next to
beer so as to increase sales
sometimes people wonder about the strange placement of
products in large stores
Maternity to infant
Classification
The process of using a set of training data with known class
labels to come up with a model (or function) that predicts
the unknown class label of new samples.
An example of classification can be found in the banking
industry
customer characteristics like age, annual income, marital
status, etc are used to predict the possibility of approving loan
applications (the loan status is the class label).
In an initial step, a dataset containing a certain number of
customers with known class labels is used to create a classifier
which can then be used to predict the class label of a new
application
ANN
Classification is very similar to regression except that the
later is applicable to numerical data while the former is
applicable to categorical and numerical data.
Clustering
The is process of grouping data objects into
clusters such that
intra-cluster similarity is maximized
inter-cluster similarity is minimized.
In other words, objects within the same clusters
are very similar and objects in different clusters
are not.
E.g. studying collective properties of people at
different income levels
Cluster people based on incomes
Study common properties within clusters
Lower income related to lower education
Outlier detection
Through clustering, we can find groups of objects
that behave similarly
sometimes, we are only interested in those objects
that lie scattered around without behaving
similarly to any pattern existing in the data.
Those objects are known as outliers as they do
not adhere to the patterns defined by the rest of
the objects in the dataset.
Outlier detection is usually desired in applications
where abnormal behavior is
of interest such as intrusion detection in networks or
terrorist detection in ports of entry
not of interest, such as when we clean a dataset from
noise
Outlier
Border
Core
Eps = 1cm
MinPts = 5
Similarity searches
given a database of objects, and a “query”
object,
find all similar objects (neighbours)
Google search
Given a query which a small document
Find all similar documents
Ranked order them
Final Notes on Data Mining
Forms the center of a set of research
fields and applications dealing with data
analysis:
databases, statistics, machine learning,
artificial intelligence, information
sciences/technology and the like
at the same time introduces a lot of new
features rendering itself as a separate
science.
scalability to large datasets
Not all types of patterns mined by data
mining systems are interesting.
Subjective and objective interesting
measures.
Market Basket Research
We will mainly use the Market Basket
Research (MBR) application in our ARM
description
A large set of items, e.g. products sold in a
supermarket.
A large set of transactions or baskets, each of
which contains a small set of the items (called
an itemset) bought by a customer during a
single visit to a store.
The Set Model
Data is organized as a "TRANSACTION
TABLE" with 2 attributes: TT(Tid, Itemset)
A transaction is a customer transaction at a
cash register.
Each customer is given an identifier, Tid,
for every transaction made
Itemset is the set of items in the
customer's "basket".
Note that tuples in TT are not "flat" (each
itemset is a "set")
i.e. not relational (why?)
a transformation can be made to equivalent but
normalized models
TID
1
2
3
4
5
6
7
8
9
10
Atts
abc
abd
abe
acd
ace
ade
bcd
bce
bde
cde
TID IID
The Normalized Set Model
Data is organized as a
“NORMALIZED TRANSACTION
TABLE" with 2 attributes:
NTT(Tid,Iid)
An itemset is the group of items
belonging to the same transaction
The TT(Tid, ItemSet) can be
"transformed" to NTT(Tid, Iid) and
vice versa
Could be stored in a database
Very deep (10 to 30 tuples)
1
a
6
a
1
b
6 d
1
c
6
2
a
7 b
2
b
7
2
d
7 d
3
a
8 b
3
b
8
c
3
e
8
e
4
a
9 b
4
c
9 d
4
d
9
5
a
10 c
5
c
10 d
5
e
10 e
e
c
e
The Boolean Model: "Boolean
Transaction Table“:
BTT(Tid, Item-1, Item-2,... Item-n)
Tid is a transaction identifier
Each column is a particular Item (1
column for each item)
a 1 if item is in the basket
a 0 if item is not in the basket
TT, NTT and BTT are equivalent
This is the model mostly chosen for
ARM
TID
1
2
3
4
5
6
7
8
9
10
a b c d e
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
Association Rule Mining
Association Rule Mining (ARM) finds
interesting associations and/or correlation
relationships among large sets of data items.
Association rules provide information in the
form of "if-then" statements.
These rules are
computed from the data
unlike the if-then rules of logic, association rules
are probabilistic in nature
strength could be measured
An association rule defines a relationship
of the form:
AC
(if A then C)
Read as A implies C, where A and C are
sets of items in a data set.
A called antecedent and C the consequent
Given DB, ARM finds all the ARs
D = A data set comprising n records
I = The set of m attributes, {i1,i2, …
Itemset = Some subset of I. Each
(transactions) and m Boolean valued
attributes (BTT model)
,im}, represented in D.
record in D is an itemset
For all rules AC: AI, CI, and
AC= (A and C are disjoint).
An Example DB
Items = 5
I = {a,b,c,d,e}
Transactions = 10
D = {{a,b,c}, {a,b,d},
{a,b,e}, {a,c,d}, {a,c,e},
{a,d,e}, {b,c,d}, {b,c,e},
{b,d,e}, {c,d,e}}
TID
1
2
3
4
5
6
7
8
9
10
Atts
abc
abd
abe
acd
ace
ade
bcd
bce
bde
cde
Support of an Itemset
Support of an itemset IS is the number
of transactions in D containing all items
in IS (support of IS={ab} is 3?)
Given a support threshold s, sets of
items that appear in > s transactions
are called frequent itemsets
The process is called frequent itemset
mining
Items={m=milk, c=cheese, p=pepsi,
b=bread, j=juice}.
Support threshold = 3 transactions.
T1
T3
T5
T7
=
=
=
=
{m, c, b}
{m, b}
{m, p, b}
{c, b, j}
T2
T4
T6
T8
=
=
=
=
{m, p, j}
{c, j}
{m, c, b, j}
{b, c}
Frequent itemsets: {m}, {c}, {b}, {j},
{m, b}, {c, b}, {j, c}.
Support and Confidence of a
Rule AC
Support of an itemset IS is the number of
transactions containing all items in IS
Itemsets are used to derive rules
Support of a rule R: AC is the number of
transactions in D containing all items in A U C.
Frequent rule
Significance of a rule
Confidence of a rule is Support(R)/ Support(A)
Confident rule
Strength of a rule
Out of those containing A, how many also contain C
Frequent + Confident Strong
Example
B1
B3
B5
B7
{m, c, b}
{m, b}
{m, p, b}
{c, b, j}
B2
B4
B6
B8
=
=
=
=
{m, p, j}
{c, j}
{m, c, b, j}
{b, c}
An association rule: {m, b} c.
What is the confidence?
=
=
=
=
support(m, b, c) = 2
Support(m, b) = 4
Confidence = 2/4 = 50%.
And so what does that mean?
50% that contain {m, b} also contain c
More On The Problem Definition
ARM is a two-step process:
Find all frequent itemsets: By definition, each
of these itemsets will occur at least as frequently
as a pre-determined minimum support threshold
Generate strong association rules from the
frequent itemsets: By definition, these rules
must satisfy the minimum support and minimum
confidence thresholds
A typical question: “find all strong association
rules with support > s and confidence > c.”
Given a database D
Find all frequent itemsets (F) using s
Produce all strong association rules using c
Finding F is the most
computationally expensive part,
once we have the frequent sets
generating ARs is straight forward
The Anti-Monotonicity (downwardclosure) of Support
Naïve: generate all subset itemsets of I and test each
The number of potential subset itemsets 2m
If m=5, #potential itemsets = 32
If m=20, #potential itemsets 1,048,576
Imagine what would supermarkets have? m = 10,000?
Conclusion?
Breakthrough: If an itemset A has support greater than s
then all its subsets must also be have support greater than s
Naïve approach is infeasible
example
Alternatively if an itemset A is not frequent then none of its
supersets will be supported.
Proposed by Agrawal 1993 from IBM Almaden Research
Center…its started ARM and the field of data mining
Apriori
Proposed by Agrawal
Apriori
Uses the downward-closure of support to
reduce the number of itemsets that need
to be counted (called candidate frequent
itemsets C)
Works on a level-by-level basis (i.e. uses
frequent itemsets L from the previous to
generate frequent itemsets at this level)
Ck and Lk
At every level k generates Ck from Lk-1and
counts their frequency in the database
Two steps are performed to generate Ck
Join Step: Ck is generated by joining Lk-1with itself
Prune Step: all itemsets in Ck whose k-1 subsets are
not ALL frequent (i.e. present in Lk-1) are removed
How many subsets does an itemset of size k have?
k
2
E.g. k=3
How many subsets of size k-1 does an itemset of size
k have?
k
The Apriori Algorithm
Pseudo-code:
Ck: Candidate frequent 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;
Remove any itemset from Ck+1 that has at least
one infrequent k subset
for each transaction t in database do
increment the counts of all candidates in Ck+1
that are contained in t (count the frequency
of each itemset in Ck+1)
Lk+1 = candidates in Ck+1 with min_support
end
return k Lk;
Example of Generating
Candidates
Suppose the items in all itemsets are listed in some order
L3={abc, abd, acd, ace, bcd}
Self-joining: L3*L3
Combine any two itemsets in Lk if they only differ by the last item
abcd from abc and abd
acde from acd and ace
C4 = {abcd , acde}
Pruning:
abcd: abc, abd, acd, bcd
acde: acd, ace, ade, cde
C4={abcd}
How To Generate Candidates?
Lk Ck+1
Step 1: self-joining Lk
insert into Ck+1
select p.item1, p.item2, …, p.itemk, q.itemk
from Lk p, Lk q
where p.item1=q.item1, …, p.itemk-1=q.itemk-1, p.itemk <
q.itemk
Step 2: pruning
forall itemsets c in Ck+1 do
forall k-subsets s of c do
if (s is not in Lk) then delete c from Ck+1
An Example – Support 2
Database D
TID
100
200
300
400
itemset sup.
C1 {1}
2
{2}
3
Scan D
{3}
3
{4}
1
{5}
3
Items
134
235
1235
25
C2
L2 itemset sup
{1 3}
{2 3}
{2 5}
{3 5}
2
2
3
2
C3 itemset
{2 3 5}
L1 itemset sup.
{1}
{2}
{3}
{5}
C2
itemset sup
{1 2}
1
{1 3}
2
{1 5}
1
Scan D
{2 3}
2
{2 5}
3
{3 5}
2
Scan D
L3 itemset sup
{2 3 5} 2
2
3
3
3
itemset
{1 2}
{1 3}
{1 5}
{2 3}
{2 5}
{3 5}
Generation of Association
Rules
Given all frequent itemsets
Every frequent itemset I of size > 2 is divided
into a candidate head Y and a body X
such that X intersection Y = {}.
This process starts with Y = {}, resulting in the
rule I {}
always holds with 100% confidence (why?)
After that, the algorithm iteratively generates
candidate heads of size k + 1, starting with k = 0
Is Apriori Fast Enough?
Performance Bottlenecks
The core of the Apriori algorithm:
Uses frequent (k – 1)-itemsets to generate candidate frequent kitemsets
Uses databases scan to collect counts for the candidate itemset – 1 scan
per level
The bottleneck of Apriori: candidate generation
Huge candidate sets:
104 frequent 1-itemset will generate 107 candidate 2-itemsets
To discover a frequent pattern of size 100, e.g., {a1, a2, …, a100}, one
needs to generate 2100 1030 candidates.
Multiple scans of database:
Needs n scans, n is the length of the longest pattern
One scan per level
Improving Apriori
Transaction reduction
Reducing the number of transactions scanned in
future iterations
A transaction that does not contain any frequent
k-itemsets cannot contain any frequent (k+1)itemsets.
E.g. Frequent 1 itemsets {1, 3, 5}
Trans = {2,4}
As a result, we need not consider it further for
subsequent scans of D for l-itemsets where l>k.
Saves on scanning times
Partitioning
Using this approach we only need two database
scans to generate all frequent itemsets
Good when original DB can’t fit in memory
First, we divided D, into n non-overlapping
partitions such that each can easily fits into
memory.
The minimum support threshold (referred to local
support threshold) for itemsets in each partition is
minsuppxN/|D| (where N is the number of
transactions in that partition).
For each partition, all frequent itemsets within that
partition are found. These are called local frequent
itemsets.
For each itemset, we record tids of the
transactions containing the items in the itemset.
As a result, we could find the local frequent
itemsets in just one database scan.
Local frequent itemsets
may not be frequent with respect to the entire
database, D;
however, any frequent itemset in D must occur as a
local frequent itemset in at least one partition
Therefore we could use the local frequent
itemsets as candidates with respect to D.
Second, we scan D to get the support of all
candidate itemsets (which have already been
generated using the partitions).
Partition size and number of partitions are set so
that each partition can fit into main memory and
therefore be read only once in each phase.
Good when original DB can’t fit in memory
Sampling
This is statistical-based approach
the principle that since we can not deal with the
whole population, we can get a representative
sample (usually random) whose size is much
smaller than the population and work with that.
The accuracy of approaches used this idea
depends on how “representative” the chosen
sample is.
In short, we select a sample S form D and
generate all frequent itemsets in S usually using a
lower support threshold than minsupp.
Some approaches that follow this idea claim that
they can mine all rules using samples.
Tries
Another data structure that is commonly used is a
trie (or prefix-tree).
The first approach to ever use tries in ARM is
Frequent Pattern Growth (FPGrowth) by Han et al.
The idea here is to view each transaction as an
ordered string of items.
The idea is compress by maximizing overlap
between transactions
Every k-itemset is attached to its k - 1-prefix.
Every node stores the last item in the itemset it
represents, its support, and its branches
Vertical Data Representation
Each item, I, is represented by a bit
vector, VI
The support of an item is the count of 1s
in its vector
The support of an itemset {a,b} is the
count of 1s in Va & Vb
An Example
TT Layout
TID
100
200
300
400
BTT Layout
Items
134
235
1235
25
TID
100
200
300
400
12345
10110
01101
11101
01001
Binary Vertical (BV) Layout D
TID
100
200
300
400
12345
10110
01101
11101
01001
Database D
TID
12345
100
10110
Support(3) = 3
200
01101
Support (3,5) = 2
300
11101
Support (1,3,5) = 1
400
01001
Just ANDing operations
Could be optimized by compression
through P-trees
Saves time
References - 2000
R. Agarwal, C. Aggarwal, and V. V. V. Prasad. A tree projection algorithm for generation of frequent
itemsets. In Journal of Parallel and Distributed Computing (Special Issue on High Performance Data
Mining), 2000.
R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large
databases. SIGMOD'93, 207-216, Washington, D.C.
R. Agrawal and R. Srikant. Fast algorithms for mining association rules. VLDB'94 487-499, Santiago,
Chile.
R. Agrawal and R. Srikant. Mining sequential patterns. ICDE'95, 3-14, Taipei, Taiwan.
R. J. Bayardo. Efficiently mining long patterns from databases. SIGMOD'98, 85-93, Seattle,
Washington.
S. Brin, R. Motwani, and C. Silverstein. Beyond market basket: Generalizing association rules to
correlations. SIGMOD'97, 265-276, Tucson, Arizona.
S. Brin, R. Motwani, J. D. Ullman, and S. Tsur. Dynamic itemset counting and implication rules for
market basket analysis. SIGMOD'97, 255-264, Tucson, Arizona, May 1997.
K. Beyer and R. Ramakrishnan. Bottom-up computation of sparse and iceberg cubes. SIGMOD'99, 359370, Philadelphia, PA, June 1999.
D.W. Cheung, J. Han, V. Ng, and C.Y. Wong. Maintenance of discovered association rules in large
databases: An incremental updating technique. ICDE'96, 106-114, New Orleans, LA.
M. Fang, N. Shivakumar, H. Garcia-Molina, R. Motwani, and J. D. Ullman. Computing iceberg queries
efficiently. VLDB'98, 299-310, New York, NY, Aug. 1998.
References (2)
G. Grahne, L. Lakshmanan, and X. Wang. Efficient mining of constrained correlated sets. ICDE'00, 512521, San Diego, CA, Feb. 2000.
Y. Fu and J. Han. Meta-rule-guided mining of association rules in relational databases. KDOOD'95, 3946, Singapore, Dec. 1995.
T. Fukuda, Y. Morimoto, S. Morishita, and T. Tokuyama. Data mining using two-dimensional optimized
association rules: Scheme, algorithms, and visualization. SIGMOD'96, 13-23, Montreal, Canada.
E.-H. Han, G. Karypis, and V. Kumar. Scalable parallel data mining for association rules. SIGMOD'97,
277-288, Tucson, Arizona.
J. Han, G. Dong, and Y. Yin. Efficient mining of partial periodic patterns in time series database.
ICDE'99, Sydney, Australia.
J. Han and Y. Fu. Discovery of multiple-level association rules from large databases. VLDB'95, 420-431,
Zurich, Switzerland.
J. Han, J. Pei, and Y. Yin. Mining frequent patterns without candidate generation. SIGMOD'00, 1-12,
Dallas, TX, May 2000.
T. Imielinski and H. Mannila. A database perspective on knowledge discovery. Communications of ACM,
39:58-64, 1996.
M. Kamber, J. Han, and J. Y. Chiang. Metarule-guided mining of multi-dimensional association rules
using data cubes. KDD'97, 207-210, Newport Beach, California.
M. Klemettinen, H. Mannila, P. Ronkainen, H. Toivonen, and A.I. Verkamo. Finding interesting rules
from large sets of discovered association rules. CIKM'94, 401-408, Gaithersburg, Maryland.
References (3)
F. Korn, A. Labrinidis, Y. Kotidis, and C. Faloutsos. Ratio rules: A new paradigm for fast, quantifiable
data mining. VLDB'98, 582-593, New York, NY.
B. Lent, A. Swami, and J. Widom. Clustering association rules. ICDE'97, 220-231, Birmingham,
England.
H. Lu, J. Han, and L. Feng. Stock movement and n-dimensional inter-transaction association rules.
SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery (DMKD'98), 12:112:7, Seattle, Washington.
H. Mannila, H. Toivonen, and A. I. Verkamo. Efficient algorithms for discovering association rules.
KDD'94, 181-192, Seattle, WA, July 1994.
H. Mannila, H Toivonen, and A. I. Verkamo. Discovery of frequent episodes in event sequences. Data
Mining and Knowledge Discovery, 1:259-289, 1997.
R. Meo, G. Psaila, and S. Ceri. A new SQL-like operator for mining association rules. VLDB'96, 122133, Bombay, India.
R.J. Miller and Y. Yang. Association rules over interval data. SIGMOD'97, 452-461, Tucson, Arizona.
R. Ng, L. V. S. Lakshmanan, J. Han, and A. Pang. Exploratory mining and pruning optimizations of
constrained associations rules. SIGMOD'98, 13-24, Seattle, Washington.
N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal. Discovering frequent closed itemsets for association
rules. ICDT'99, 398-416, Jerusalem, Israel, Jan. 1999.
References (4)
J.S. Park, M.S. Chen, and P.S. Yu. An effective hash-based algorithm for mining association rules.
SIGMOD'95, 175-186, San Jose, CA, May 1995.
J. Pei, J. Han, and R. Mao. CLOSET: An Efficient Algorithm for Mining Frequent Closed Itemsets.
DMKD'00, Dallas, TX, 11-20, May 2000.
J. Pei and J. Han. Can We Push More Constraints into Frequent Pattern Mining? KDD'00. Boston,
MA. Aug. 2000.
G. Piatetsky-Shapiro. Discovery, analysis, and presentation of strong rules. In G. Piatetsky-Shapiro
and W. J. Frawley, editors, Knowledge Discovery in Databases, 229-238. AAAI/MIT Press, 1991.
B. Ozden, S. Ramaswamy, and A. Silberschatz. Cyclic association rules. ICDE'98, 412-421, Orlando,
FL.
J.S. Park, M.S. Chen, and P.S. Yu. An effective hash-based algorithm for mining association rules.
SIGMOD'95, 175-186, San Jose, CA.
S. Ramaswamy, S. Mahajan, and A. Silberschatz. On the discovery of interesting patterns in
association rules. VLDB'98, 368-379, New York, NY..
S. Sarawagi, S. Thomas, and R. Agrawal. Integrating association rule mining with relational database
systems: Alternatives and implications. SIGMOD'98, 343-354, Seattle, WA.
A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining association rules in
large databases. VLDB'95, 432-443, Zurich, Switzerland.
A. Savasere, E. Omiecinski, and S. Navathe. Mining for strong negative associations in a large
database of customer transactions. ICDE'98, 494-502, Orlando, FL, Feb. 1998.
References (5)
C. Silverstein, S. Brin, R. Motwani, and J. Ullman. Scalable techniques for mining causal
structures. VLDB'98, 594-605, New York, NY.
R. Srikant and R. Agrawal. Mining generalized association rules. VLDB'95, 407-419, Zurich,
Switzerland, Sept. 1995.
R. Srikant and R. Agrawal. Mining quantitative association rules in large relational tables.
SIGMOD'96, 1-12, Montreal, Canada.
R. Srikant, Q. Vu, and R. Agrawal. Mining association rules with item constraints. KDD'97, 67-73,
Newport Beach, California.
H. Toivonen. Sampling large databases for association rules. VLDB'96, 134-145, Bombay, India,
Sept. 1996.
D. Tsur, J. D. Ullman, S. Abitboul, C. Clifton, R. Motwani, and S. Nestorov. Query flocks: A
generalization of association-rule mining. SIGMOD'98, 1-12, Seattle, Washington.
K. Yoda, T. Fukuda, Y. Morimoto, S. Morishita, and T. Tokuyama. Computing optimized rectilinear
regions for association rules. KDD'97, 96-103, Newport Beach, CA, Aug. 1997.
M. J. Zaki, S. Parthasarathy, M. Ogihara, and W. Li. Parallel algorithm for discovery of association
rules. Data Mining and Knowledge Discovery, 1:343-374, 1997.
M. Zaki. Generating Non-Redundant Association Rules. KDD'00. Boston, MA. Aug. 2000.
O. R. Zaiane, J. Han, and H. Zhu. Mining Recurrent Items in Multimedia with Progressive
Resolution Refinement. ICDE'00, 461-470, San Diego, CA, Feb. 2000.
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