Prediction of Prediction of Class and Property Assertions Class - - PowerPoint PPT Presentation

Prediction of Prediction of Class and Property Assertions Class and Property Assertions

• n OWL Ontologies through
• n OWL Ontologies through

Evidence Combination Evidence Combination

Giuseppe Giuseppe Rizzo Rizzo Nicola Nicola Fanizzi 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 Proposed Appr Approach

• ach

In particular: task of In particular: task of prediction prediction of assertions

• f assertions

 class-membership

class-membership

 object and data-type props filler

• bject 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

Knowledge Base Knowledge Base K

K = < = <T T , , A A> >

 TBox

TBox T

T : set of axioms

: set of axioms defining defining concepts 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

• pen-world semantics

Dissimilarity Measures/1 Dissimilarity Measures/1

 Given a

Given a context context of concepts

• f concepts

C C = { = { C C1

1,

, C C2

2, …,

, …, C Cm

m }

}

 Projection

Projection function: function:

 Discernibility

Discernibility function for function for C Ci

i :

:

Dissimilarity Measures/2 Dissimilarity Measures/2

 Given a context

Given a context C C , p , p ∈ ∈R R and and w w ∈ ∈R Rn

n

family of family of dissimilarity dissimilarity measures: measures:

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 Basic belief assignment Basic belief assignment (BBA) (BBA) m m : 2 : 2Ω

Ω [0,1]

→ [0,1] →

 ∑

∑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 m1

1 and

and m m2

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 = contrast attributed to the case A = Ω 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

• f labeled individuals

TrSet TrSet = {( = {(x x1

1,

, v v1

1), …, (

), …, (x xM

M,

, v vM

M)}

)} ⊆ ⊆ Ind Ind( (A

A)

) x x V V

 a

a query individual query individual x xq

q

 Select the set of

Select the set of k k nearest neighbors nearest neighbors N Nk

k(

(x xq

q)

) according to a (dis)similarity measure according to a (dis)similarity measure

Evidential Nearest-Neighbors Evidential Nearest-Neighbors

 Each (

Each (x xi

i,

, v vi

i) in

) in N Nk

k(

(x xq

q) induces a BBA

) induces a BBA m mi

i

regarding the value to be predicted for regarding the value to be predicted for x xq

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 VQ

Q = {-1,+1}

= {-1,+1}

• r
• r

V VQ

Q = {-1,0,+1}

= {-1,0,+1}

 Object property

Object property R R filler: filler: V VR

R =

= Ind Ind( (A

A)

)

 Datatype property

Datatype property P P value: value: V VP

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 ALC ops

• ps

 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

 Evidential NN

Evidential NN procedure procedure based on based on

 DST

DST

 Dissim. measure

• Dissim. measure

 Prediction of

Prediction of

 class-membership

class-membership

 (functional) role

(functional) role fillers fillers

Outlook Outlook

 Tackle prediction of

Tackle prediction of non-functional non-functional properties vals properties vals

 Regression/Ranking

Regression/Ranking

 based on non-

based on non- explicit criteria explicit criteria

 Integration with

Integration with Rough DL Rough DL

The End The End

Thank you Thank you

Questions ? Questions ?

Offline Offline Find us at: Find us at: http://lacam.di.uniba.it:8000/ http://lacam.di.uniba.it:8000/