Download Distributed Higher Order Association Rule Mining

國立雲林科技大學
National Yunlin University of Science and Technology
Distributed Higher Order Association
Rule Mining Using Information
Extracted from Textual Data
From: Shenzhi Li, Tianhao Wu,William M. Pottenger,
SIGKDD Explorations.Vol. 7, Issue 1, pp. 26-35.
Presenter : Wei-Shen Tai
Advisor : Professor Chung-Chian Hsu
2005/8/3
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Outline
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Introduction
Related work
D-HOTM framework
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Entity extraction
Distributed High-Order ARM
A example for application
Metrics for evaluation
Conclusion and future work
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Information extraction and mining
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Why we need them?
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The burgeoning amount of textual data in distributed
sources combined with the obstacles involved in
creating and maintaining central repositories.
“System of Systems”
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The United States Department of Homeland Security
(DHS) recognizes that the proliferation of databases
and schemas involving fragmented data poses a
challenge to information sharing.
In response, the DHS is promulgating a approach that
acknowledges the infeasibility of creating a single
massive centralized database.
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DHS’s problems
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Overlap between tiers
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A three-tier structure with some local databases, state databases
and federal databases.
Constraints on system interoperability and legal
restrictions on data sharing,
More centralized the database, the less information that is
shared.
A “System of Systems” approach
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A standards for interoperability and communication in areas.
Indeed, efforts are underway to establish standards in database
schema integration(e.g., OWL, GJXDM, etc.)..
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Mining distributed data
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Current algorithms for mining distributed data
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Information extracted from distributed textual data
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Only when the global schema across all databases is known.
No preexisting global schema (i.e., dictionary of terms) is available.
This is due to the fact that the entities extracted may differ between
textual documents at the same or different locations.
Schemas of textual entities are highly fluid in nature.
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As a result, a fixed global schema cannot be assumed and current
algorithms that rely on the existence of such a schema cannot be
employed.
Distributed Association Rule Mining
(ARM)
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Distributed Association Rule Mining (ARM) algorithms
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Mine association rules from data in horizontally or vertically
fragmented databases.
Useful rules can be mined from diverse databases with different
local schemas as long as records can be linked via.
Higher-order
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Implies that rules may be inferred between items that do not occur
in the same local database schema.
In other words, rules can be inferred based on items (entities) that
may never occur together in any record in any of the distributed
databases being mined.
Distributed higher-order text mining
(D-HOTM)
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Advantage
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Requires neither the knowledge of the global schema
nor schema integration as a precursor to mining rules.
Extracts entities and discovers rules based on higherorder associations between entities in records linked by
a common key.
Major components:
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Entity extraction
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Based on information extraction rules learned using a semisupervised active learning algorithm.
Distributed association rule mining
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About ARM
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Association rule mining (ARM)
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Discovers associations between items. Given two
distinct sets of items, X and Y, we say Y is associated
with X if the appearance of X implies the appearance of
Y in the same context.
ARM outputs a list of association rules of the format
XY, where X  Y has a predetermined support and
confidence.
Many ARM algorithms are based on the well-known
Apriori algorithm.
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Parallelism in ARM (1/2)
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Data parallelism
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Logically partitions the database among processors.
Each processor works on its local partition using the same
computational model.
Count distribution (CD) is a simple data-parallelism algorithm.
Each processor generates the local candidate itemsets
independently based on the local partition.
Then the global counts are computed by sharing (or broadcasting)
the local counts, and the global frequent candidate itemsets are
generated.
Data-parallelism exchanges only the counts among processors,
which minimizes the communication cost. As a result, it seems
ideal for use in a distributed environment.
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Parallelism in ARM (2/2)
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Task parallelism
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Each processor performs different computations
independently, yet all have access to the entire dataset.
For example, the computation of candidate itemsets of
different sizes might be distributed among processors in
a parallel loop across itemsets.
In this case, each processor generates global counts
independently.
In a distributed environment, this can be accomplished
by performing an initial ‘copy-in’ operation of the
dataset, albeit often at great cost.
Fast Distributed Mining v.s.
Optimized Distributed Association Mining
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Fast Distributed Mining (FDM)
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Based on count distribution.
The advantage of FDM over CD is that it reduces the communication cost
by sending the local frequent candidate itemsets to a polling site instead of
broadcasting.
Optimized Distributed Association Mining (ODAM) algorithm
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Both reduces the size of the average transaction and reduces the number of
message exchanges in order to achieve better performance.
The transactions are reduced by deleting the non-frequent items from the
itemsets and merging several transactions with the same itemsets into one
record.
As for the message exchange, instead of using broadcast as with CD or
polling sites like FDM, ODAM just sends all local information to one site,
called the receiver.
Distributed mining of vertically
fragmented data
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A privacy preserving association rule mining algorithm for vertically
distributed data.
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The authors use a vector to represent each (vertically fragmented) record
in which the attributes in the schema are distributed amongst the different
local sites.
It is a method for mining association rules when the (global) schema is
distributed amongst multiple sites.
This approach requires a priori knowledge of the complete (global)
schema by all sites, and is thus unsuitable for mining rules from
distributed data for which local schemas differ and the global schema is
unknown.
Three assumptions:
(1) the databases are vertically fragmented;
(2) there is a global key to unambiguously link subsets of items, and no
additional techniques are needed to identify which subsets should be
linked;
(3) the global database schema is known.
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Entity Extraction
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reduced regular expression (RRE)
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Discovers sequences of words and/or part-of-speech
tags that, for a given entity, have high frequency in the
labeled instances of the training data (true set) and low
frequency in the unlabeled instances (false set).
First discovers the most common element1 of an RRE,
termed the root of the RRE. The algorithm then extends
the RRE in “AND”, “GAP”, and “Start/End” learning
phases.
In each iteration, a single RRE is generated. This RRE
is considered a sub-rule of the current entity.
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RRE Discovery Process
Discover the
Root
“AND”
Learning Process
“GAP”
Learning Process
RRE Start and End
Learning Process
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Definition in D-HOTM
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Object
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In a given local database apply a row to
represent it. For example a particular individual
mentioned in an investigative report.
Item (or items)
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Identifying the object such as a person’s name
or SSN, each row also contains other items
known to exist in the source document.
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Fragmentation types
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Horizontally fragmented
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There is no guarantee that every site will include the same set of
items,
And in the case where an object is not a document or report but a
person, different distributed sites may also refer to the same object
multiple times (e.g., investigative reports about different crimes
committed by the same individual).
Vertically fragmented
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There is no one-to-one mapping connecting records in the
distributed databases.
In addition, the (local) ‘schema’ for each individual document
varies, and no clean division of all objects’ items into identical sets.
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Skeleton of D-HO ARM
(1) Select linkage items
(2) Assign a globally unique ID to each record/object
(3) Identify linkable records using Apriori on global
IDs
(4) Exchange information about linkable records
(5) For each site
(6) Apply the Apriori algorithm locally
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Select linkage items
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Items used for linking records
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One requirement for this set is that the item (or combination of
items) must uniquely identify objects.
In police investigative reports, SSN (suspect No.) might be
selected as the subset used for linkage because such reports are
written about individuals, and individuals are uniquely identified
by SSN.
SSN uniquely represents person objects.
object vs. record
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the items in the subset used for linkage refer to objects, while a
record consists of the collection of items (i.e., entities) extracted
from a given document (e.g., a police report).
Naturally this implies that one or more of the items in a given
record uniquely represent the object used for record linkage.
Discovers linkable records using
the item(s)
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For example
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If a given suspect appears in a burglary record in
Detroit, and the same suspect also appears in a mugging
case in Philadelphia, and the SSN is chosen as the
linking item, then those two distributed records are
considered linkable.
Application
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In a practical sense, linking these two records might
reveal new information to the investigating police
officer.
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Identifiers problem
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Ideally assumption
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The item (or combination of items) should be globally unique and
consistent.
Unique means different objects have different identifiers while
consistent implies that the records about the same object have the
same identifiers.
Problems
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Two databases will have the same object (a reference to a scholarly
research article) with different items.
{ID, title, year, citenum} and {ID, title, year, code}
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The 2-itemset {code citenum} can then be calculated using the global
ID to match records in the two different databases – a higher-order
association between code and citenum via the global ID.
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Detection of Linkable Records
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If each local record corresponds to a single document
object.
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The combination of the title and author attributes serve both to link
records from different sites and to uniquely identify objects.
Record identifiers (such as DOIs for investigative reports)
differ from the object identifiers used for linking.
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For example, suppose records are comprised of the entities
extracted from reports that contain criminal suspect information
such as SSN and modus operandi. Higher-order associations can be
discovered by linking two such records through the SSN item.
In this case, the linking item, SSN, uniquely identifies individuals,
not records.
A single investigative report record may contain multiple SSNs.
Theory for the Detection of
Linkable Records (1/3)
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Definition 1: Given two records Ri and Rj,
let T= Ri  Rj, and T. For any item aT,
we say Ri and Rj are 2nd-order linkable
through a, or a2-linkable, denoted as Ri ~a Rj.
Theorem 1: The relation between records
that are a2-linkable is reflexive, symmetric
and transitive.
Theory for the Detection of
Linkable Records (2/3)
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Definition 2: Given n distinct records R1, R2, …, Ri, …, Rn
and Ti= Ri  Ri+1 with Ti, let L be a list of items L = (a1,
a2, …, ai,…, an-1) such that aiTi. Then we say records R1
and Rn are (k+1)th-order linkable through L, where k is the
number of distinct items in L. The (k+1)th-order link is
denoted R1 ~a1 R2 ~a2 R3 ~a3 R4 … Ri-1 ~a(i-1) Ri … Rn-1 ~a(n1) R , or in short, R ~L R . We term L a viable path.
n
1
n
Theorem 2: For any higher-order link between two
records, there must exist at least one link which does not
have repeated items in the viable path, or repeated records
in the link.
Theory for the Detection of
Linkable Records (3/3)
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Definition 3: The length of a higher-order link cluster is defined as the number
of groups in the cluster. The distance between two groups is defined as the
shortest of all possible higher-order links.
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For example, given the following two higher-order link clusters:
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Ra ~a Rab ~b Rbc ~c Rc
Ra ~a Rac ~c Rc
The length of the first cluster is four while the length of the second is three.
Suppose these two link clusters contain the only links between Ra and Rc, then from
the link cluster Ra ~a Rac ~c Rc. we see that the distance between Ra and Rc is three.
Theorem 4: Given a frequent k-itemset X generated by Apriori for k2, for
any pair of items which are members of X, the distance between the groups on
those items is at most three.
Theorem 5: Given a frequent k-itemset A and j-itemset B (j,k2) for which A
is not a subset of B and B is not a subset of A, suppose there exists at least one
item which is a member of A and B. Furthermore, suppose there are items aA
and bB, then the distance between groups Ra and Rb is at most four.
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An Example Application
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Link results
1. The distance between RJack and RDiana is three, and the groups are higherorder linked as follows: RJack-Jack,Diana ~Jack RJack,Diana ~Diana RDiana-Jack,Diana.
2. Using the GIDLists to represent the groups on the items, we have
{2,6,8}-{6} ~Jack {6} ~Diana {4,6}-{6}, or {2,8}~Jack {6} ~Diana {4}.
Merged records based on the
higher-order links discovered
 The Apriori algorithm is applied again, this time to each local database.
Since higher-order associations have been implicitly included in the new,
merged records, both higher-order and the usual first-order associations will
be included in the resulting rules generated by Apriori.
For example, “Gun Þ Robbery” and “Diana Þ Robbery” are rules generated
based on higher-order associations discovered by the D-HO ARM algorithm.
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Metrics for evaluation
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Support value
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One of the most important metrics used in ARM, which is defined
as the frequency of an itemset divided by the total number of
instances.
In distributed databases, the total number of instances can be
calculated by counting the number of unique global object IDs.
Problems
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Different objects (and subsequently records) can be incorrectly
mapped to the same global ID
Records that should be mapped to a single global ID can be
mapped to different IDs.
The error rate of the mapping function will thus influence both the
support and confidence metrics.
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An example of mapping
Modeled data
{1,3} {2,4}
Ground truth
P
{1,2} {3,4}
{5,6}
Mapping
function
G
{5,6}
Human
Expert
1,2,3,4,5,6
Sample data
1. The ground truth data set is obtained through experts’ identification.
2. The modeled data set is obtained through the mapping function.
3. The sample data set is R={1,2,3,4,5,6}, where records 1 and 2
represent the same object (e.g., have the same primary key), records 3
and 4 represent another object, and records 5 and 6 represent a third
object.
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Error rate and difference degree
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Observed error rate f is:
f  1
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GP
n
nG  nG  P

nG
We also define the observed difference degree t’
as:
n'
t'  , t'  0
n
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where n’ is the size of the modeled data set and n
is the size of the ground truth.
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Conclusions
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Heterogeneous distributed databases can be easily
centralized.
Distributed higher-order rules can be mined from
multiple diverse databases without knowledge of
the global schema.
Propose a support metric in the context of
distributed higher-order ARM.
Mining higher-order rules from distributed textual
data in a hybrid fragmented form independent of
the knowledge of the global schema.
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Future work
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ID identification automatically
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Distributed ARM deals with the efficiency of computation
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Make workload balancing as well as optimization of both computation and
communication.
Opposite direction mining
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This process could be partially automated given semantic mappings such
as those supported by the recently released Web Ontology Language.
Be used to mine association rules from the results returned from a search
(as opposed to mining rules from entire databases).
For example, a user may wish to find strong associations between
Axiom’s classification codes and the number of citations on Citeseer for a
particular set of documents returned by queries.
Multilevel parallelism
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Can be introduced to improve runtime performance: e.g., at each
distributed database, a parallel ARM algorithm can be executed.