Prediction of Prediction of Class and Property Assertions Class and Property Assertions on OWL Ontologies through on OWL Ontologies through Evidence Combination Evidence Combination Giuseppe Rizzo Giuseppe Rizzo Nicola Fanizzi Nicola Fanizzi Claudia Claudia d’Amato d’Amato Floriana Floriana Esposito Esposito LACAM - Computer Science Dept. LACAM - Computer Science Dept. University of Bari, Italy University of Bari, Italy WIMS'11 WIMS'11
Motivation Motivation Semantic Web knowledge bases characterized by Semantic Web knowledge bases characterized by uncertainty uncertainty incompleteness / inconsistency incompleteness / inconsistency Purely dedutcive methods may fall short Purely dedutcive methods may fall short Exploiting alternative (approximate / inductive) Exploiting alternative (approximate / inductive) approaches to perform data mining tasks approaches to perform data mining tasks
Proposed Appr Approach oach Proposed In particular: task of In particular: task of prediction prediction of assertions of assertions class-membership class-membership object and data-type props filler object and data-type props filler Proposal Proposal Nearest Neighbors approach Nearest Neighbors approach Dempster-Shafer Dempster-Shafer Evidence Theory (DST) Evidence Theory (DST) BBA, Belief, Plausibility, Confirmation BBA, Belief, Plausibility, Confirmation Evidence Evidence combination combination DS, Yager, other combination rules DS, Yager, other combination rules
DL Knowledge Bases DL Knowledge Bases K = < = < T T , , A A > > Knowledge Base K Knowledge Base TBox TBox T T : set of axioms : set of axioms defining concepts defining concepts and and properties properties ABox ABox A A : set of assertions : set of assertions concerning the world-state concerning the world-state Facts that involve the individuals (resources) Facts that involve the individuals (resources) using concepts and properties using concepts and properties Reasoning services Reasoning services open-world semantics open-world semantics
Dissimilarity Measures/1 Dissimilarity Measures/1 Given a Given a context context of concepts of concepts = { C C 1 , C C 2 , …, C C m } C C = { 1 , 2 , …, } m Projection Projection function: function: Discernibility Discernibility function for function for C C i : : i
Dissimilarity Measures/2 Dissimilarity Measures/2 Given a context , p ∈ ∈ R w ∈ ∈ R Given a context C C , p R and and w R n n family of dissimilarity dissimilarity measures: measures: family of
Evidence Theory Evidence Theory Frame of discernment Frame of discernment Ω Ω set of hypotheses for a certain domain set of hypotheses for a certain domain : 2 Ω Ω [0,1] Basic belief assignment (BBA) (BBA) m m : 2 [0,1] → → Basic belief assignment ∑ ∑ A A m m ( ( A A ) = 1 ) = 1 m m ( ( A A ) belief committed ) belief committed exactly exactly to to A A no additional claims about its subsets no additional claims about its subsets m m ( ( A A ) > 0 => ) > 0 => A A is a is a focal focal element element
Belief and Plausibility Belief and Plausibility Belief Belief function: function: Plausibility Plausibility function: function:
Rules of Combination Rules of Combination Given BBAs Given BBAs m m 1 1 and and m m 2 2 DS rule DS rule normalized version: normalized version: 1 - 1 - c c hides the hides the contrast contrast between the BBAs between the BBAs
Rules of Combination/2 Rules of Combination/2 Yager's rule Yager's rule more more epistemologically epistemologically sound: sound: contrast attributed to the case A = Ω contrast attributed to the case A = Ω (total ignorance) total ignorance) ( Other rules used in the experiments: Other rules used in the experiments: Dubois-Pradé, Mixing Dubois-Pradé, Mixing
Evidential Nearest-Neighbors Evidential Nearest-Neighbors Given Given A A set of values set of values V V ( to be predicted) to be predicted) ( a a training set training set of labeled individuals of labeled individuals ⊆ )} ⊆ TrSet = {( = {( x x 1 1 , , v v 1 1 ), …, ( ), …, ( x x M M , , v v M M )} Ind Ind ( ( A A ) ) x x V V TrSet a a query individual query individual x x q q Select the set of Select the set of k k nearest neighbors nearest neighbors N N k k ( ( x x q q ) ) according to a (dis)similarity measure according to a (dis)similarity measure
Evidential Nearest-Neighbors Evidential Nearest-Neighbors Each ( Each ( x x i i , , v v i i ) in ) in N N k k ( ( x x q q ) induces a BBA ) induces a BBA m m i i regarding the value to be predicted for x regarding the value to be predicted for x q q Combine the induced BBAs: Combine the induced BBAs:
Evidential Nearest-Neighbors Evidential Nearest-Neighbors Predict based on belief / plausibility values: Predict based on belief / plausibility values:
Evidential Nearest-Neighbors Evidential Nearest-Neighbors Alternatively, use a Alternatively, use a confirmation confirmation function function then: then:
Prediction Tasks Prediction Tasks Class-membership w.r.t. Class-membership w.r.t. Q Q : : V Q = {-1,+1} or V Q = {-1,0,+1} V Q = {-1,+1} or V Q = {-1,0,+1} Object property Object property R R filler: filler: V V R R = = Ind Ind ( ( A A ) ) Datatype property Datatype property P P value: value: | ∃ ∃ ) ∈ ∈ V V P P = { = { v v | P P ( ( a a , , v v ) A A } }
Experiments Experiments Ontologies from standard repositories Ontologies from standard repositories 10 fold cross validation 10 fold cross validation k k = log|TSet| = log|TSet| 4 combination rules 4 combination rules Random classes created with Random classes created with ALC ops ALC ops 5 built-in 5 built-in functional functional properties properties
Indices Indices Using a reasoner to decide the ground truth: Using a reasoner to decide the ground truth: Match Match rate rate (M%) (M%) Omission Omission error rate error rate (O%) (O%) Commission Commission error rate error rate (C%) (C%) Induction Induction rate rate (I%) (I%)
Outcomes Outcomes Class Membership Class Membership
Outcomes Outcomes Object Property Values Object Property Values
Outcomes Outcomes Data Property Values Data Property Values
Conclusions Conclusions Contribution Contribution Outlook Outlook Evidential NN Tackle prediction of Evidential NN Tackle prediction of procedure procedure non-functional non-functional based on properties vals based on properties vals Regression/Ranking DST DST Regression/Ranking Dissim. measure Dissim. measure based on non- based on non- Prediction of explicit criteria explicit criteria Prediction of Integration with Integration with class-membership class-membership Rough DL Rough DL (functional) role (functional) role fillers fillers
The End The End Thank you Thank you Questions ? Questions ? Offline Offline Find us at: http://lacam.di.uniba.it:8000/ Find us at: http://lacam.di.uniba.it:8000/
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