The document proposes a graph traversal approach called Dedalo to explain patterns in Linked Data using background knowledge from the graph. Dedalo uses an A* search algorithm to iteratively build a graph by dereferencing URIs, find explanation paths between initial nodes and entities in the graph, and build explanations by evaluating paths and final nodes. It finds the highest quality explanations for patterns like countries where men are more educated than women. Future work aims to improve Dedalo by addressing biases from incomplete data and combining multiple explanations.

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Walking Linked Data:
a graph traversal approach to explain clusters
Ilaria Tiddi, Mathieu d’Aquin, Enrico Motta
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Problem: explaining patterns
Data: women/men literacy rate from UNESCO [1]
In which countries are men more educated than women?
ThHeo ywe ldloow y coouu knntroiews? ( )
Education : Men Women Equal

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Problem: explaining behaviors
We explain thanks to our own (background) knowledge.
Can we do the same with the knowledge from Linked Data?

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Linked Data contain explanations
:Somalia db:Somalia
but where?
:Ethiopia
:India
:UK
:US
db:Ethiopia
db:India
db:UK
db:US
sameAs
sameAs
sameAs
sameAs
sameAs

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Linked Data contain explanations
:Somalia db:Somalia
but where?
:Ethiopia
:India
:UK
:US
db:Ethiopia
db:India
db:UK
db:US
…
…
…
sameAs
dc:subject
dc:subject
dc:subject
sameAs
sameAs
sameAs
sameAs
dc:subject
dc:subject

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Linked Data contain explanations
:Somalia db:Somalia
but where?
:Ethiopia
:India
:UK
:US
db:Ethiopia
db:India
db:UK
db:US
…
…
…
db:Category:Least
DevelopedCountries
db:Category:
LiberalCountries
sameAs
dc:subject
dc:subject
dc:subject
sameAs
sameAs
sameAs
sameAs
dc:subject
dc:subject
skos:relatedMatch
skos:relatedMatch
skos:relatedMatch

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Linked Data contain explanations
:Somalia db:Somalia
1,200/pp
but where?
:Ethiopia
:India
:UK
:US
db:Ethiopia
db:India
db:UK
db:US
600/pp
3,800/pp
36,000/pp
dbp:gdp
49,000/pp
sameAs dbp:gdp
sameAs
sameAs
sameAs
sameAs
dbp:gdp
dbp:gdp
dbp:gdp

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Linked Data contain explanations
:Somalia db:Somalia
1,200/pp
dbp:gdp
dbp:gdp
dbp:gdp
but where?
:Ethiopia
:India
:UK
:US
db:Ethiopia
db:India
db:UK
db:US
600/pp
3,800/pp
36,000/pp
3,800/pp
36,000/pp
≤
≤
≤
≥
49,000/pp ≥
sameAs
sameAs
sameAs
sameAs
sameAs
dbp:gdp
dbp:gdp

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Looking for explanations in graph
:Somalia
:Ethiopia
:India
dbp:gdp
sameAs 4,000/pp
cat:LeastDeveloped
Countries
sameAs
sameAs
…
…
…
dbp:gdp
 Given a graph of Linked Data where
 URI are nodes
 RDF properties are edges
…
…
…
…
…
dc:subject
dc:subject
dbp:gdp
dc:subject
skos:related
skos:related
≤
≤
≤

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Looking for explanations in graph
:Somalia
:Ethiopia
:India
dbp:gdp
sameAs 4,000/pp
cat:LeastDeveloped
Countries
sameAs
sameAs
…
…
…
…
…
…
…
dc:subject
dc:subject
dbp:gdp
dbp:gdp
dc:subject
skos:related
skos:related
≤
≤
≤
…
 Find
 the ending value most pointed by entities in the cluster
 the best path in order to further expand the graph

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A* algorithm for Linked Data
 Best-first search algorithm
 Given an initial node and a final node
 find the least expensive path between them
 Path cost function f(path) = actual cost g(path)+ future cost h(path)
 Without knowledge of the graph
 Search in the graph for the best path and explanation
 The graph is iteratively build by URI dereferencing
 No need to know the Linked Data graph a priori

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Dedalo: an A* process for Linked Data
Building graph
(URI dereferencing)
Choosing the
best path
Finding the
best explanation
 Iteratively building a Linked Data graph and looking for an
explanation of the pattern

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Dedalo: an A* process for Linked Data
Dereference URIs through HTTP GET
 take an entity
db:Ethiopia
 read its properties and values
db:Ethiopia
 add them to the graph
db:Category:AfricanCountries
dc:subject
dbp:gdp 1,200
:
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db:Ethiopia
dc:subject db:Category:AfricanCountries
dbp:gdp 1,200
owl:sameAs
…
…
…
…
…
…

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Dedalo: an A* process for Linked Data
Collect new paths (sequences of edges)
 add the new property to the previous path
owl:sameAsdc:subject
owl:sameAsdbp:gdp
 evaluate new paths with Entropy1
ent(owl:sameAsdc:subject)
ent(owl:sameAsdbp:gdp)
 add to the pile of paths (the first one is chosen)
owl:sameAsdc:subject
owl:sameAsdbp:gdp
owl:sameAs
[1] Tiddi et al., ESWC 2014
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Dedalo: an A* process for Linked Data
Build explanations (path + final nodes)
 Each of the values the new path points to
 e1= owl:sameAsdc:subject
 e2= owl:sameAsdc:subject
db:Category:AfricanCountries
db:Category:SouthAsianCountries
 Compare numerical value if the property is a datatype
 e2= owl:sameAsdc:gdp ≥
1,200
 e3= owl:sameAsdc:gdp ≤ 1,200
 Rank explanations according to the
F-Measure
initial URIs
(countries)
URIs pointing to
URIs
in
1,200

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Dedalo: experiments
Countries where men are more educated than women
skos:exactMatchdbp:hdiRank ≥ 126 87.8% 197”
skos:exactMatchdc:subject
db:Category:Least_Developed_Countries
74.7% 524’’
skos:exactMatchdbp:gdpPPPPerCapitaRank ≥ 89 68.3% 269”
Countries where women are more educated than men
skos:exactMatchdbp:hdiRank ≤ 119 63.4% 198”
skos:exactMatchdbp:gdpPPPPerCapitaRank ≤ 56 62.3% 236’’
Countries where education is equal
skos:exactMatchdbp:gdpPPPRank ≥ 64 62.0% 234”
skos:exactMatchdbp:gdpPPPPerCapitaRank ≥ 29 61.0% 268’’

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Conclusions and future work
 Dedalo, A* process to search explanation within Linked Data
 From a pattern to explain
 Finds the path to the best explanation
 Using Entropy and F-Measure
 Focusing on the bias introduced by incomplete data2
 Combining atomic explanations3
 Evaluating Dedalo on a large use case: Google Trends
[2, 3] Tiddi et al., EKAW 2014

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Thanks! Questions?
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