GRAPH KERNELS FOR RDF DATA KNOWLEDGE MANAGEMENT GROUP INSTITUTE OF - - PowerPoint PPT Presentation

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 3 31.05.12

… property value prediction, …

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

The Learning Tasks (I)

„Machine Learning“ topic110 person100 person200

skos:prefLabel foaf:knows foaf:name

„Jane Doe“ „female“

foaf:gender foaf:topic_interest foaf:gender

?

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 4 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Graph Kernels for RDF Data

The Learning Tasks (II) … link prediction, …

„Machine Learning“ topic110 person100 person200

skos:prefLabel foaf:knows foaf:name

„Jane Doe“ „female“

foaf:gender foaf:topic_interest foaf:topic_interest

?

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 5 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Graph Kernels for RDF Data

The Learning Tasks (III)

?

„Machine Learning“ topic110 person100 person200

skos:prefLabel foaf:knows foaf:name

„Jane Doe“ „female“

foaf:gender foaf:topic_interest

… clustering,…

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 6 31.05.12

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.

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 7 31.05.12

RELATED WORK

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

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

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

κ(x, y) =< φ(x), φ(y) >

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 9 31.05.12

The Gap

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

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

• ntologies

kernel methods for general graphs

RDF Graph Kernels too specific too general

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 10 31.05.12

The Goal Define kernel functions, which can be used with ANY kernel machine, can handle ANY RDF graph, exploit the specifics of RDF.

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

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

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 12 31.05.12

Intersection Graph

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

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 13 31.05.12

Instance graph

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

Instance graph: k-hop-neighbourhood of entity e

• Explore graph starting from entity e up to a depth k

„Machine Learning“ topic110 person100 person200

skos:prefLabel foaf:knows foaf:name

„Jane Doe“ „female“

foaf:gender foaf:topic_interest

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 14 31.05.12

„Machine Learning“ topic110 person100 person200

skos:prefLabel foaf:knows foaf:name

„Jane Doe“ „female“

foaf:gender foaf:topic_interest

„Machine Learning“ topic110 person100 person200

skos:prefLabel foaf:knows foaf:name

„Jane Doe“ „female“

foaf:gender foaf:topic_interest

Instance graph - Example

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

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:name

„Jane Doe“ „female“

foaf:topic_interest foaf:gender

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 15 31.05.12

Intersection Graph

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

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 16 31.05.12

„Machine Learning“ topic110 person100 person200

skos:prefLabel foaf:knows foaf:name

„Jane Doe“ „female“

foaf:gender foaf:topic_interest

Intersection graph

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

• 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) ∈ E1 ∧ (v1, p, v2) ∈ E2}

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 17 31.05.12

Intersection Graph

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

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 18 31.05.12

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

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

E0 ⊆ E V 0 = {v | ∃u, p : (u, p, v) ∈ E0 ∨ (v, p, u) ∈ E0}

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 19 31.05.12

Intersection Trees

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

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

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

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 21 31.05.12

Property Value Prediction

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

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 22 31.05.12

Property Value Prediction Results

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

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

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

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 24 31.05.12

Classification model

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

) , ( ) , ( )) , ( ), , ((

2 1 2 1 2 2 1 1

• s

s

• s
• s
• s

βκ ακ κ + =

s1

• 1

s2

• 2

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 25 31.05.12

Link Prediction Results

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

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 26 31.05.12

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.

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

Knowledge Management Group Institute of Applied Informatics and Formal Description Methods (AIFB) 27 31.05.12

Future Work Test with other kernel machines Investigate dependence of graph characteristics

• n performance of various graph kernels

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

Thanks!