Uta Lösch - Stephan Bloehdorn - Achim Rettinger* GRAPH ......Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 3 31.05.12 … property

KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association

KNOWLEDGE MANAGEMENT GROUP INSTITUTE OF APPLIED INFORMATICS AND FORMAL DESCRIPTION METHODS (AIFB)

www.kit.edu

GRAPH KERNELS FOR RDF DATA Uta Lösch - Stephan Bloehdorn - Achim Rettinger*

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB)

2 31.05.12

The Vision

Given any data in RDF format…

…solve any standard statistical relational learning task,

like…

Uta Lösch, Stephan Bloehdorn, Achim Rettinger Graph Kernels for RDF Data

„Machine Learning“ topic110 person100

person200

skos:prefLabel

foaf:knows

foaf:name „Jane Doe“ „female“

foaf:gender foaf:topic_interest


3 31.05.12

… property value prediction, …


The Learning Tasks (I)


person200

skos:prefLabel

foaf:knows



foaf:gender ?


4 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Graph Kernels for RDF Data

The Learning Tasks (II)

… link prediction, …


person200

skos:prefLabel

foaf:knows



foaf:topic_interest ?


5 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Graph Kernels for RDF Data

The Learning Tasks (III)

?


person200

skos:prefLabel

foaf:knows



… clustering,…

… or class-membership prediction, entity resolution, ...


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The constraints

… while !   using readily available learning algorithms

!   exploiting specifics of RDF graphs

!   relying on the graph structure and labels only

!   avoiding manual effort as much as possible.



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RELATED WORK



8 31.05.12

Any RDF graph

Define Kernel

Any Kernel Machine

(SVM / SVR /Kernel k-means)

Solve any Task (Classify /

Predict / Cluster)

The (good old) Kernel Trick


(x, y) =< �(x), �(y) >


9 31.05.12

The Gap


Instance types (Bloehdorn & Sure,

2007)

Relations on instances (Fanizzi

et al., 2008)

Complex concept

descriptions (Fanizzi et al.,

2008)

Tripel-Patterns (Bicer et al., 2011)

Walks (Gärtner et al.,

2003)

Shortest Paths (Borgwardt and Kriegel, 2005)

Cycles (Horváth et al., 2004)

Trees (Shervashidze et

al, 2009)

kernel methods

for ontologies

kernel methods for general graphs

RDF Graph Kernels too specific too general


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The Goal

Define kernel functions, which !   can be used with ANY kernel machine,

!   can handle ANY RDF graph,

!   exploit the specifics of RDF.



11 31.05.12

Overview

Motivation Related Work Proposed family of RDF kernel functions based on ! Intersection Graphs ! Intersection Trees

Empirical evaluation on !   Property Value Prediction !   Link Prediction



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Intersection Graph


Input

RDF data

graph

Entity e1

Entity e2

Instance extraction

Instance graph G(e1) G(e2)

Intersection graph

G(e1)∩G(e2) Feature count

Output

Kernel value k(e1,e2)

Inter-section


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Instance graph


!   Instance graph: k-hop-neighbourhood of entity e ! Explore graph starting from entity e up to a depth k


person200

skos:prefLabel

foaf:knows




14 31.05.12


person200

skos:prefLabel

foaf:knows




person200

skos:prefLabel

foaf:knows



Instance graph - Example


Instance graph of depth 2 for person200

„Machine Learning“ topic110

person200

skos:prefLabel

foaf:name „Jane Doe“

foaf:topic_interest

Instance graph of depth 2 for person200

topic110 person100

person200

foaf:knows


foaf:topic_interest foaf:gender


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Intersection Graph


Input

RDF data

graph

Entity e1

Entity e2

Instance extraction


Intersection graph


Output


Inter-section


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person200

skos:prefLabel

foaf:knows



Intersection graph


! Intersection graph of graphs G(e1) and G(e2):

Intersection of depth 2 for person100 and person200

topic110

person200 foaf:name „Jane Doe“

foaf:topic_interest

V (G1 \G2) = V1 \ V2

E(G1 \G2) = {(v1, p, v2)|(v1, p, v2) 2 E1 ^ (v1, p, v2) 2 E2}

(2)


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Intersection Graph


Input

RDF data

graph

Entity e1

Entity e2

Instance extraction


Intersection graph


Output


Inter-section


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Feature count

!   Kernel function: Count specific substructures of the intersection graph.

!   Any set of edge-induced subgraphs…

!   …qualifies as a candidate feature set ! Edges ! Walks/Paths up to a length of an arbitrary l ! Connected edge-induced subgraphs


E0 ✓ E

V 0 = {v | 9u, p : (u, p, v) 2 E0 _ (v, p, u) 2 E0}

(2)


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Intersection Trees


!   Problem: ! Intersection graph needs explicit calculation of instance

graphs and the intersection. ! Computationally expensive

! Intersection Tree: !   Alternative representation of common structures !   Can be extracted directly from the RDF graph ! Tree structure

! Synchronized exploration starting from both entities !   Common elements are part of the intersection tree !   e1 and e2 need special treatment


20 31.05.12

Overview

Motivation Related Work Proposed family of RDF kernel functions based on ! Intersection Graphs ! Intersection Trees

Empirical evaluation on !   Property Value Prediction !   Link Prediction



21 31.05.12

Property Value Prediction


!   Multilabel learning problem (SVM) !   Data set: SWRC

! Contains persons, publications, research topics, research groups, and projects.

!   2547 entities, 1058 persons !   Task: Predict if a person is member of a research group

! Classification model: !   1 classifier per class (research group) !   Evaluation measure is averaged over classifiers ! Leave-one-out-Cross-Validation


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Property Value Prediction Results


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

Accuracy F1 measure

Bloehdorn & Sure

Gärtner

Intersection graph based kernels

Intersection tree based kernels


23 31.05.12

Link Prediction

! Predict links between entities (SVM) !   Data set: Friend-of-a-friend (FOAF)

! Gathered from Livejournal.com !   3040 entities, description of 638 persons, 8069 instances of the

foaf:knows relation

!   Task: Predict unknown foaf:knows-relations

! Classification model ! Predict likelihood that the relation foaf:knows exists

between a pair of entities



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Classification model


),(),()),(),,(( 21212211 oossosos os βκακκ +=

s1 o1

s2 o2


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Link Prediction Results


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

NDCG bpref

SUNS-20

Intersection tree based Kernels


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Summary

We introduced two families of kernel functions for RDF graphs, which !   can be used with ANY kernel machine !   and might solve ANY associated learning task.

!   They can be applied to ANY RDF graph !   while exploiting the specifics of RDF.

!   They show comparable performance to more specific and more general approaches.



27 31.05.12

Future Work

!   Test with other kernel machines !   Investigate dependence of graph characteristics

on performance of various graph kernels


Thanks!

Uta Lösch - Stephan Bloehdorn - Achim Rettinger* GRAPH ......Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 3 31.05.12 … property

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