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

Uta Lösch - Stephan Bloehdorn - Achim Rettinger* GRAPH KERNELS FOR RDF DATA KNOWLEDGE MANAGEMENT GROUP INSTITUTE OF APPLIED INFORMATICS AND FORMAL DESCRIPTION METHODS (AIFB) KIT – University of the State of Baden-Wuerttemberg and www.kit.edu National Research Center of the Helmholtz Association

The Vision Given any data in RDF format… skos:prefLabel „Machine topic110 person100 Learning“ foaf:knows foaf:gender foaf:topic_interest „Jane Doe“ person200 „female“ foaf:name …solve any standard statistical relational learning task, like… Knowledge Management Group 2 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

The Learning Tasks (I) skos:prefLabel „Machine topic110 person100 Learning“ foaf:knows foaf:gender foaf:topic_interest ? „Jane Doe“ person200 „female“ foaf:name foaf:gender … property value prediction, … Knowledge Management Group 3 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

The Learning Tasks (II) ? skos:prefLabel „Machine foaf:topic_interest topic110 person100 Learning“ foaf:knows foaf:gender foaf:topic_interest „Jane Doe“ person200 „female“ foaf:name … link prediction, … Knowledge Management Group 4 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

The Learning Tasks (III) skos:prefLabel „Machine topic110 person100 Learning“ foaf:knows ? foaf:gender foaf:topic_interest „Jane Doe“ person200 „female“ foaf:name … clustering,… … or class-membership prediction, entity resolution, ... Knowledge Management Group 5 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

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. Knowledge Management Group 6 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

RELATED WORK Knowledge Management Group 7 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

The (good old) Kernel Trick Any RDF graph Define Kernel Solve any Task (Classify / κ ( x, y ) = < φ ( x ) , φ ( y ) > Predict / Cluster) Any Kernel Machine (SVM / SVR / Kernel k-means) Knowledge Management Group 8 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

The Gap Instance types Walks (Bloehdorn & Sure, (Gärtner et al., 2007) 2003) Relations on Shortest Paths kernel kernel instances (Fanizzi (Borgwardt and et al., 2008) Kriegel, 2005) methods methods for for Complex concept general ontologies Cycles (Horváth et descriptions al., 2004) graphs (Fanizzi et al., 2008) Trees Tripel-Patterns (Shervashidze et (Bicer et al., 2011) al, 2009) too specific too general RDF Graph Kernels Knowledge Management Group 9 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

The Goal Define kernel functions, which � can be used with ANY kernel machine, � can handle ANY RDF graph, � exploit the specifics of RDF. Knowledge Management Group 10 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Overview Motivation Related Work Proposed family of RDF kernel functions based on Intersection Graphs � Intersection Trees � Empirical evaluation on � Property Value Prediction � Link Prediction Knowledge Management Group 11 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Intersection Graph Input Instance graph Instance Entity e 1 RDF extraction data G(e 1 ) G(e 2 ) graph Entity e 2 Inter- section Output Intersection graph Feature count Kernel value G(e 1 ) ∩ G(e 2 ) k(e 1 ,e 2 ) Knowledge Management Group 12 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Instance graph skos:prefLabel „Machine topic110 person100 Learning“ foaf:knows foaf:gender foaf:topic_interest „Jane Doe“ person200 „female“ foaf:name � Instance graph: k- hop-neighbourhood of entity e Explore graph starting from entity e up to a depth k � Knowledge Management Group 13 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Instance graph - Example Instance graph of depth 2 for person200 skos:prefLabel skos:prefLabel „Machine „Machine topic110 topic110 person100 Learning“ Learning“ foaf:knows foaf:gender foaf:topic_interest foaf:topic_interest „Jane Doe“ person200 „Jane Doe“ person200 „female“ foaf:name foaf:name Instance graph of depth 2 for person200 skos:prefLabel „Machine topic110 person100 topic110 person100 Learning“ foaf:knows foaf:knows foaf:gender foaf:gender foaf:topic_interest foaf:topic_interest „Jane Doe“ person200 „female“ „Jane Doe“ person200 „female“ foaf:name foaf:name Knowledge Management Group 14 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Intersection Graph Input Instance graph Instance Entity e 1 RDF extraction data G(e 1 ) G(e 2 ) graph Entity e 2 Inter- section Output Intersection graph Feature count Kernel value G(e 1 ) ∩ G(e 2 ) k(e 1 ,e 2 ) Knowledge Management Group 15 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Intersection graph Intersection graph of graphs G(e 1 ) and G(e 2 ): � V ( G 1 ∩ G 2 ) = V 1 ∩ V 2 E ( G 1 ∩ G 2 ) = { ( v 1 , p, v 2 ) | ( v 1 , p, v 2 ) ∈ E 1 ∧ ( v 1 , p, v 2 ) ∈ E 2 } Intersection of depth 2 for person100 and person200 skos:prefLabel „Machine topic110 topic110 person100 Learning“ foaf:knows foaf:gender foaf:topic_interest foaf:topic_interest „Jane Doe“ „Jane Doe“ person200 person200 „female“ foaf:name foaf:name Knowledge Management Group 16 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Intersection Graph Input Instance graph Instance Entity e 1 RDF extraction data G(e 1 ) G(e 2 ) graph Entity e 2 Inter- section Output Intersection graph Feature count Kernel value G(e 1 ) ∩ G(e 2 ) k(e 1 ,e 2 ) Knowledge Management Group 17 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Feature count � Kernel function: Count specific substructures of the intersection graph. � Any set of edge-induced subgraphs… E 0 ⊆ E { v | ∃ u, p : ( u, p, v ) ∈ E 0 ∨ ( v, p, u ) ∈ E 0 } V 0 = � …qualifies as a candidate feature set Edges � Walks/Paths up to a length of an arbitrary l � Connected edge-induced subgraphs � Knowledge Management Group 18 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

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 Knowledge Management Group 19 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data

Overview Motivation Related Work Proposed family of RDF kernel functions based on Intersection Graphs � Intersection Trees � Empirical evaluation on � Property Value Prediction � Link Prediction Knowledge Management Group 20 31.05.12 Uta Lösch, Stephan Bloehdorn, Achim Rettinger Institute of Applied Informatics and Formal Description Methods (AIFB) Graph Kernels for RDF Data