This document presents an algorithm for matching properties between linked databases using Kullback-Leibler divergence (KL-Divergence). It first creates documents representing the distributions of objects linked to properties in each database. It then computes the normalized KL-Divergence between all document pairs to identify the most similar properties. The property with the lowest KL-Divergence score to a given property is returned as its match. Experimental results on real linked datasets found the algorithm could accurately match properties over 90% of the time.

1. Property Matching and Query Expansion on
Linked Data Using Kullback-Leibler Divergence
Sean Golliher, Nathan Fortier, Logan Perreault
December 12, 2013
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2. Property Matching Problem
Databases with different properties:
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3. def: Query Expansion
Query expansion (QE) is the process of reformulating a seed
query to improve retrieval performance in information retrieval
operations.
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4. Societal Cloud
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5. Cloud Diagram (TRIZ Problem Solving)
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6. Cloud Diagram Broken
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7. Property Matching Problem
How do we find all actors in both databases?
Don’t want to manually inspect all databases
Can we use SPARQL query language to infer across all datasets?
SELECT ?p
WHERE { s ?p o }
Can only match total sizes of returned triple sets
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8. Original Bayesian Approach
Problems with Bayesian Approach
Had to create, and track, a large vocabulary for training
Smoothing issues with very sparse text
Underflow issues – small confidence values
Complexity of likelihood was growing:
n different features in feature set X and c classes + tunable parameters.
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9. KL-Divergence
Original paper from 1951 entitled “On Information and Sufficiency”
Also referred to as“relative entropy”
A system gains entropy when it moves to a state with more possible
arrangements. For example, a liquid to a gas.
Used in paper from 2003 for text categorization:
”Using KL-Distance for Text Categorization
Elegant and efficient method for plagiarism detection
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10. KL-Divergence
Measure of divergence of information between two distributions:
D(P
Q) =
P(x) log
x∈X
P(x)
Q(x)
Not symmetric
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11. KL-Divergence Example
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12. KL-Divergence Example
Table : Generic Vocabularies Generated by Fixing on Predicates
d1
d2
d3
subject1
object1
object2
subject2
object3
object3
subject3
object4
subject1
object1
object2
subject4
object3
subject2
object3
ex: D(d1 d2 ) = 1 log 1/5 + 1 log 1/5 + ........ + 2 log 2/5
5
0
5
0
5
1/4
tf( subject1 ) is 1/5 in d1 and 0 in d2 – using value for now
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13. Algorithm Description
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14. Formal Problem Statement
Given:
Two databases DB1 and DB2
A predicate p1 ∈ DB1
An object type S1 where some triple “s p1 o exists in D1
where s ∈ S1
Find predicate p2 in DB2 where p2 is equivilant to p1
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15. High Level Description
Create a document d1 containing labels of all objects linked
by p1
Find an object type S2 ∈ d2 where S1 is equivilant to S2
For each predicate p2 used by S2 create a document d2
containing labels of all objects linked by p2
Remove stop words and language tags from d1 and d2
For each document compute the normalized KL-Divergence,
KLD ∗ (d1 , d2 )
Return predicate corresponding to the document with the
lowest KL-Divergence
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16. Algorithm 1 FindPredicate(DB1 , DB2 , p1 , S1 )
Create document d1 containing labels of all objects linked by p1
Find an object type S2 ∈ d2 where S1 is equivilant to S2
for each predicate p2 used by S2 do
Create document d2 containing labels of all objects linked by p2
end for
Remove stop words and language tags from d1 and d2
min ← 1
for each predicate pi used by S2 do
k ← KLD ∗ (d1 , di )
if k < min then
min ← k
pmap ← pi
end if
end for
return pmap
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17. Computing KL-Divergence
KL-Divergence is computed as
(P(tk , di ) − P(tk , dj )) × log
KLD(di , dj ) =
k∈V
Where
P(tk , di ) =
tf (tk , di )
x∈di tf (tx , dj )
P(tk , di )
(1)
P(tk , dj )
(2)
If tk does not occur in di then P(tk , di ) ←
KL-Divergence is then normalized as follows:
KLD ∗ (di , dj ) =
KLD(di , dj )
KLD(di , 0)
(3)
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18. Algorithm 2 tf (tk , di )
tf ← 0
for each term tx in di do
if sim(tk , tx ) > τ then
tf ← tf + 1
end if
end for
return tf
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19. Experimental Results
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20. Experimental Results
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21. Experimental Results
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22. Experimental Results
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23. Experimental Results
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24. Experimental Results
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25. Questions?
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