Information theoritic analysis of entity dynamics on the linked open data cloud

www.moving-project.eu
TraininG towards a society of data-saVvy inforMation prOfessionals
to enable open leadership INnovation
Chifumi Nishioka and Ansgar Scherp
ZBW -- Leibniz Information Centre for Economics and Kiel University, Germany
Information-theoretic Analysis of Entity
Dynamics on the Linked Open Data cloud

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Motivation
• Understanding the dynamics of the LOD cloud is
important for many applications
• e.g., SPARQL query caching, crawling strategies, term
recommendations
• Related work
• Evolution of LOD documents [Käfer et al. 13]
• Dynamics of LOD sources [Dividino et al. 14]
• Entities on the LOD cloud
• Used by a lot of applications
• Knowledge graph in search engines
• Document modeling [Schuhmacher and Ponzetto 14]
Chifumi Nishioka (chni@informatik.uni-kiel.de)
Come to the presentation of
“TermPicker” by Johann Schaible at
14:30 on 1st June (Wednesday)
We conduct an analysis focusing on entities

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Research Goals
• Measure the changes in entities between two points in time
• Represent the temporal dynamics of entities as time-series
• Time-series clustering
• Periodicity detection
• Evaluate four different features of entities
Goal 1: Represent the temporal dynamics of entities
Goal 2: Find out the representative temporal patterns of
entity dynamics
Goal 3: Find out which features of entity more likely
define temporal dynamics of entities

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Formalization
• 𝑋𝑡: snapshot of LOD documents at point in time 𝑡
• Snapshot is a collection of triples 𝑥
• 𝑥: triple
• 𝑥 = 𝑠, 𝑝, 𝑜 : subject, predicate, and object

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Entity and Entity Representations
• Entities are represented by a set of triples
• Entity Representation: Out
• Set of triples with common subject URI
• e.g., db:John_Brown is defined by two triples
• Entity Representation: InOut
• Set of triples with common subject URI or object URI
• e.g., db:John_Brown is defined by three triples
db:Anne_Smith db:spouseOf db:John_Brown
db:John_Brown db:birthplace db:Los_Angels
db:John_Brown db:works db:Green_University

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Triple Weighting
• example: Barack Obama
• <Barack_Obama, dbp:vicePresident , Joe_Biden> is more
important than <Barack_Obama, rdf:type , foaf:Person>
• Baseline
• All triples have a same weight
• Combined Information Content (combIC)
[Schuhmacher and Ponzetto 14]
• 𝐼𝐶 𝑣 = −log⁡( 𝑃(𝑣))
• 𝑝𝑟𝑒𝑑 𝑥 , 𝑜𝑏𝑗 𝑥 returns predicate and object of a
triple 𝑥, respectively
𝑤 𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒(𝑥) = 1
Each triple in entities has different importance for entities
𝑤𝑐𝑜𝑚𝑏𝐼𝐶 𝑥 = 𝐼𝐶 𝑝𝑟𝑒𝑑 𝑥 + 𝐼𝐶(𝑜𝑏𝑗(𝑥))

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Measuring Entity Dynamics
• Cosine distance
• Euclidean distance
Goal 1: Represent the temporal dynamics of entities
𝛿 𝑐𝑜𝑠𝑑 𝐸𝑡1
, 𝐸𝑡2
= 1 −
𝐸𝑡1
∙ 𝐸𝑡2
||𝐸𝑡1
|| ∙ | 𝐸𝑡2
|
1. Measure the amount of changes in entities between two
successive snapshots by one of two distance measures
𝛿 𝑒𝑢𝑐 𝐸𝑡1
, 𝐸𝑡2
= (𝐸𝑡1,𝑖 − 𝐸𝑡2,𝑖)2
𝑖=1

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Vector Representation of Entities
• Represent an entity 𝐸 by one-hot encoding
• Extract all unique triples from different snapshots
• Fix order of triples
• e.g., db:Anne_Smith at 𝑡1 is (1,1,1,0,0) and at 𝑡2 is
(1,0,1,1,1)
• Cosine distance: 𝛿 𝑐𝑜𝑠𝑑 𝐸𝑡1
, 𝐸𝑡2
= 1 −
2
3∙ 4
= 0.42
• Euclidean distance: 𝛿 𝑒𝑢𝑐 𝐸𝑡1
, 𝐸𝑡2
= 3
𝑡1
1 db:Anne_Smith db:birthplace db:New_York
2 db:Anne_Smith db:works db:Green_University
3 db:Anne_Smith db:spouseOf db:John_Brown
𝑡2
1 db:Anne_Smith db:birthplace db:New_York
4 db:Anne_Smith db:works db:Royal_University
3 db:Anne_Smith db:spouseOf db:John_Brown
5 db:Anne_Smith db:degree db:Master_of_Science

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Temporal Dynamics of Entities
• Temporal Dynamics of an entity 𝐸
• 𝑛: the number of snapshots
Δ(𝐸) = (𝛿 𝐸𝑡1
, 𝐸𝑡2
, 𝛿 𝐸𝑡2
, 𝐸𝑡3
, ⋯ 𝛿(𝐸𝑡 𝑛−1
, 𝐸𝑡 𝑛
))
2. Represent temporal dynamics of entities by a time-series of the
amount of changes in an entity between two successive
snapshots
Subsequently, we mine the resulted time-series to find out
patterns of temporal dynamics of entities

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Time-series Clustering
• Clustering algorithm: k-means++ [Arthur and
Vassilvitskii 07]
• Introduce an improved initial seeding into k-means
• Distance measure: Euclidean distance
• The most efficient measure for distance between
time-series with a reasonably high accuracy [Wang et
al. 13]
• Optimization of the number of clusters :
Average Silhouette
Goal 2: Find out the representative temporal patterns of
entity dynamics

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Periodicity Detection
• Periodicity Detection
• A task of detecting periodicity from time-series
• Example 1: (1, 3, 2, 1, 3, 2) -> periodicity of three
• Example 2: (1, 2, 1, 2, 1, 2) -> periodicity of two
• Employ a convolution-based algorithm [Elfeky et al.
05]
We assume that the amount of changes of entities have
some periodicity
We see the centroids of the resulted clusters as patterns of
entity dynamics

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Dataset
• Dynamic Linked Data Observatory (DyLDO)
dataset [Käfer et al. 12]
• Weekly snapshots of the fixed set of LOD documents
• 165 snapshots over three years (05/2012 to 07/2015)
• Entities in the DyLDO dataset
• Almost 75% of entities appear only at one snapshot
• Focus on entities that appear at >70% of snapshots
Entity
representation
# of unique
entities in 165
snapshots
# of entities that
appear at >70% of
snapshots
Out 27,788,902 2,909,700
InOut 29,097,929 2,950,533

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Patterns of Entity Dynamics (1/3)
• Analysis with respect to eight conditions
• Conditions are made by two entity representations,
two distance measures, two triple weighting methods
• Result of clustering
• # of clusters are smaller when using combIC

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Out Cosine Baseline Out Cosine CombIC
Out Euclidean CombIC
Out Euclidean Baseline

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InOut Cosine Baseline InOut Cosine CombIC
InOut Euclidean Baseline InOut Euclidean CombIC

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Periodicity of Entity Dynamics
We observe periodicities in temporal dynamics of entities
• e.g., “Periodicity of 56” indicates that the amount of
entity changes vary along with one-year cycle
• Different patterns have different periodicities

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Features for Entity Dynamics (1/2)
• Four features of entities
• RDF Type (𝑓1)
• Property (𝑓2)
• Union of RDF types and properties (𝑓3)
• Pay level domain (PLD) of entity URI (𝑓4)
• e.g., http://dbpedia.org/resource/The_Beatles -> dbpedia.org
• Evaluate four features by RandIndex
• RandIndex: a metric of clustering
• Measure the difference of clustering by a feature and
by entity dynamics (i.e., time-series vectors)

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Features for Entity Dynamics (2/2)
• Entities that share a common PLD are more likely
to have similar temporal dynamics of entities
when employing baseline for triple weighting
• When using combIC, entities that have a common
RDF type or ECS more likely to belong a same
cluster

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Thank you for your
attention!
Project consortium and funding agency
MOVING is funded by the EU Horizon 2020 Programme under the project number INSO-4-2015: 693092

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Conclusion
• Temporal dynamics of entities on the LOD cloud
• Represent the temporal dynamics of entities as time-
series
• Find out the representative temporal patterns of
entity dynamics
• Find out which features of entity
• Future work
• e.g., SPARQL query caching

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Appendix

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Reference
• [Arthur and Vassilvitskii 07] D. Arthur and S. Vassilvitskii. k-means++: The advantages of
careful seeding. SODA, 2007.
• [Elfeky et al. 05] M.G. Elfeky, W.G. Aref, and A.K. Elmagarmid. Periodicity detection in
time series databases. IEEE TKDE, 2005.
• [Käfer et al. 12] T. Käfer, J. Umbrich, A. Hogan, and A. Polleres. Towards a dynamic
linked data observatory. LDOW, 2012.
• [Käfer et al. 13] T. Käfer, A. Abdelrahman, J. Umbrich, P. O’Byrne, and A. Hogan.
Observing linked data dynamics. ESWC, 2013.
• [Neumann and Moerkotte 11] T. Neumann and G. Moerkotte. Characteristic sets:
Accurate cardinality estimation for RDF queries with multiple joins. ICDE, 2011.
• [Schuhmacher and Ponzetto 14] M. Schuhmacher and S.P. Ponzetto. Knowledge-based
graph document modeling. WSDM, 2014.
• [Wang et al. 13] X. Wang, A. Mueen, H. Ding, G. Trajcevski, P. Scheuermann, and E.
Keogh. Experimental comparison of representation methods and distance measures for
time series data. Data Mining and Knowledge Discovery, 2013.
• [Yang and Leskovec 11] J. Yang and J. Leskovec. Patterns of temporal variation in online
media. WSDM, 2011.

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Entities in the DyLDO dataset
• Distribution of # of times of appearances of
entities in 165 snapshots
Entity representation Out Entity representation InOut

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Resulted Temporal Patterns (1/4)
Out Cosine Baseline Out Cosine CombIC

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Out Euclidean Baseline Out Euclidean CombIC

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InOut Cosine Baseline InOut Cosine CombIC

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InOut Euclidean Baseline InOut Euclidean CombIC

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Information theoritic analysis of entity dynamics on the linked open data cloud

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