A Bayesian Approach for Weighted Ontologies and Semantic Search

Anna Formica

, Michele Missikoff

, Elaheh Pourabbas

and Francesco Taglino

National Research Council, Istituto di Analisi dei Sistemi ed Informatica ”Antonio Ruberti”,

Via dei Taurini 19 - 00185, Rome, Italy

National Research Council, Istituto di Scienze e Tecnologie della Cognizione,

Via S. Martino della Battaglia, 44 - 00185, Rome, Italy

Keywords:

Semantic Search, Similarity Reasoning, Weighted Reference Ontology, Bayesian Network.

Abstract:

Semantic similarity search is one of the most promising methods for improving the performance of retrieval

systems. This paper presents a new probabilistic method for ontology weighting based on a Bayesian approach.

In particular, this work addresses the semantic search method SemSim for evaluating the similarity among

a user request and semantically annotated resources. Each resource is annotated with a vector of features

(annotation vector), i.e., a set of concepts deﬁned in a reference ontology. Analogously, a user request is

represented by a collection of desired features. The paper shows, on the bases of a comparative study, that the

adoption of the Bayesian weighting method improves the performance of the SemSim method.

1 INTRODUCTION

A weighted ontology is obtained by associating

a weight with each concept. The adoption of

such weights has proved to be beneﬁcial in several

ontology-based applications and services that range

from ontology mapping to ontology-based decision

making, to semantic search. Our main research ob-

jectives lay in the area of Semantic Similarity Rea-

soning for advanced search, where weighted ontolo-

gies represent a primary base for our search engine,

called SemSim (Formica et al., 2013). There are var-

ious methods for weighting ontology concepts (see

Related Work Section) and this great variety also de-

pends on the meaning that such weights assume. In

SemSim the concept weight is used to derive the in-

formation content (IC) of a concept in a hierarchy ac-

cording to (Resnik, 1995), that represents the basis for

computing the concept similarity.

According to the semantics adopted in SemSim,

given a Universe of Digital Resources (UDR, i.e., the

search space) the IC of a concept is directly related to

its selectiveness and inversely related to the probabil-

ity that, randomly selecting an instance in the UDR,

such an instance belongs to the extension of the con-

cept (i.e., the set of its instances). In a retrieval per-

spective, a concept with higher IC is expected to be

more selective than a concept with lower IC, since

the former has a lower probability than the latter.

Furthermore, in an ontology, the concept weight de-

creases downward along the specialization hierarchy,

proceeding from the root (the most general concept,

e.g., Thing) towards the leaves, the most speciﬁc con-

cepts. This is because the extension of a more speciﬁc

concept is contained in the extension of a more gen-

eral concept, and consequently, the likelihood of the

former is lower than the likelihood of the latter. Sym-

metrically, the IC will progressively increase while

we move downward along the hierarchy. For exam-

ple, given a tourism domain, assuming that Farm-

house is a more speciﬁc concept of Accommodation,

the latter has a lower information content than the for-

mer. Accordingly, at ontology level, the weight of

concepts needs to be consistent with the set inclusion

semantics of the ISA hierarchy, as described above.

The main focus of this paper concerns a method

for assigning the weights to the concepts in the ontol-

ogy, used to compute their IC. It may seem a marginal

problem, but it is not, since a correct weighting strat-

egy can signiﬁcantly improve the performance of the

semantic services based on weighted ontologies. In

the literature there are several proposals, as reported

in the Related Work Section.

In a previous work (Formica et al., 2013), we ex-

perimented two methods of concept weighting, both

following the IC approach. The two methods, called

frequency-based and probabilistic-based, differ for

the way the likelihood of a concept c is computed.

The frequency-based method is the most straightfor-

ward, it consists in counting the instances of each

Formica, A., Missikoff, M., Pourabbas, E. and Taglino, F.

A Bayesian Approach for Weighted Ontologies and Semantic Search.

DOI: 10.5220/0006073301710178

In Proceedings of the 8th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2016) - Volume 2: KEOD, pages 171-178

ISBN: 978-989-758-203-5

171

concept and then normalizing such a number over

the total number of instances of concepts. The

probabilistic-based method depends, in general, on

the characteristics of the application domain and the

structure of the taxonomy. Both approaches exhibit

pros and cons. The frequency-based method depends

on the number of UDR resources, and the more this

number increases the more the concept weights are

expected to be trustworthy. However, this method

can be expensive, since it is necessary to maintain

a count of the extensions of each concept in the on-

tology. This is only feasible in the Closed World

Assumption and in the presence of a relatively sta-

ble UDR, otherwise for each update it is necessary

to recompute a (more or less extensive) part of on-

tology weights. Conversely, the probabilistic-based

approach is valid for both Closed and Open World As-

sumptions and, with large UDR, tends to be more sta-

ble. In fact, UDR updates usually evolve according to

a given probability distribution (e.g., in a University,

the ratio of students to professors tend to be stable,

despite a signiﬁcant number of new enrollments ev-

ery year). Here, the problem is to be able to guess

what are the more appropriate probabilities to be as-

sociated with each concept. In the perspective of ad-

dressing large application domains, in this paper we

adopt the probabilistic approach.

The SemSim similarity reasoning method is based

on semantic annotations in the form of Ontology-

based Feature Vectors (OFV), where each component

is a concept in a reference ontology (referred to as

feature when used for annotation). Each resource in

the UDR is associated with an annotation vector (re-

ferred to as AV) while the user request is represented

by a request vector (RV). The SemSim search engine

then computes the semantic similarity by contrasting

the RV against each AV, producing a ranked list of re-

sources.

In this paper, we present a new probabilistic

method for ontology weighting based on a Bayesian

Network (BN). The importance of integrating BN

into ontologies is discussed in (Grubisic et al., 2013),

where they are considered a valid support to experts

in the modeling of a speciﬁc problem domain. The

new Bayesian weighting method deﬁned here can be

considered as an extension of the previous method

deﬁned in (Formica et al., 2013), i.e., it starts with

the same probability assignments (w

) given in the

mentioned paper, used here as a priori probabilities.

Then, such probabilities are reﬁned taking into con-

sideration the subsumption relations and the inherent

dependencies among concepts. To this end, we build

a BN isomorphic to the ISA hierarchy of the ontology

referred to as Onto-Bayesian Network (OBN). It is

constructed as follows: each concept in the ontology

corresponds to a node in OBN and each subsumption

relation corresponds to a probabilistic dependency.

Considering the above example, we assume that the

probabilistic weight of Farmhouse depends on the

weight of its subsumer Accommodation. The method,

referred to as SemSim-b, is illustrated in Section 3,

while Section 4 shows its validation, by examining the

correlation, precision, and recall and comparing them

with the experiment given in (Formica et al., 2013).

The results demonstrate that SemSim-b outperforms

the previous SemSim method. Finally, Section 5 con-

cludes the paper.

2 WEIGHTED ONTOLOGIES

In this section, we recall the probabilistic approach

deﬁned in (Formica et al., 2010), (Formica et al.,

2013) in order to assign weights to a given ontology.

The UDR is the set of digital resources that are

semantically annotated with a reference ontology (an

ontology is a formal, explicit speciﬁcation of a shared

conceptualization (Gruber, 1993)). In our work we

address a simpliﬁed notion of ontology, Ont, consist-

ing of a set of concepts organized according to a spe-

cialization hierarchy. In particular, Ont is a taxonomy

deﬁned by the pair:

Ont =< C, ISA >

where C = {c

} is a set of concepts and ISA is the

set of pairs of concepts in C that are in subsumption

(subs) relation:

ISA = {(c

, c

) ∈ C ×C|subs(c

, c

)}

Given two concepts c

, c

∈ C, their least upper bound,

lub(c

, c

), is always uniquely deﬁned in C (we as-

sume the hierarchy is a tree). It represents the least

abstract concept of the ontology that subsumes both

and c

Each resource in the UDR is annotated with an

OFV

, which is a vector that gathers a set of concepts

of the ontology Ont, aimed at capturing its semantic

content. The same also holds for a user request. It is

represented as follows:

ofv = (c

,...,c

), where c

∈ C, i = 1,...,n

Note that, when an OFV is used to represent the

semantics of a user request, it is referred to as seman-

tic Request Vector (RV) whereas, if it is used to rep-

resent the semantics of a resource, it is referred to as

The proposed OFV approach is based on the Term Vec-

tor (or Vector Space) Model approach, where terms are sub-

stituted by concepts (Salton et al., 1975).

KEOD 2016 - 8th International Conference on Knowledge Engineering and Ontology Development

172

semantic Annotation Vector (AV). They are denoted

as follows, respectively:

rv = {r

, . . . , r

av = {a

, . . . , a

where {r

, . . . , r

} ∪ {a

, . . . , a

} ⊆ C.

Finally, a Weighted Reference Ontology (WRO) is

deﬁned as follows:

WRO =< Ont, w >

where w, the concept weighting function, is a proba-

bility distribution deﬁned on C, such that given c ∈ C,

w(c) is a decimal number in the interval [0. . .1].

Figure 1 shows the WRO drawn upon the tourism

domain that will be used in the running example. In

this ﬁgure, the weights w

have been assigned ac-

cording to the probabilistic-based approach deﬁned in

(Formica et al., 2013). In particular, the weight of

the root of the hierarchy, referred to as Thing is equal

to 1, and the weights of the concepts of the hierar-

chy are assigned according to a top-down approach,

as follows. Given a concept c, let c

be the parent of

c, w

, divided by

number of the children of c

)

|children(c

For instance, let us consider the concept

Salon. The associated w

is 0.05 because

(Attraction) = 0.2 and Attraction has four

children.

Below, the semantics of a feature vector OFV is

presented, by extending its ﬁrst formulation given in

(Formica et al., 2008). When a concept is used in an

OFV to annotate a resource or to represent a RV , it is

referred to as a feature.

Consider an ontology Ont, a set of features F, F ⊆

C, let SPEC be the reﬂexive and transitive closure of

ISA. Then, the semantics of a feature a ∈ F is deﬁned

as follows:

Γ(a) = {res ∈ UDR | feat(b, res), (b,a) ∈ SPEC}

where feat(b, res) means that the resource res ∈ UDR

is annotated by the feature b ∈ F. The semantics of

an ofv, say:

ofv = {a

,..., a

}

is therefore deﬁned according to the Γ function as fol-

lows:

Γ(ofv) =

Γ(a

)

Overall, we emphasize the difference between the

concept semantics and feature semantics. A concept

denotes the set of the instances whose type is such a

concept; while, if a concept is used as a feature, it

denotes all the resources in the UDR annotated with

such a feature.

3 BAYESIAN NETWORKS FOR

WEIGHTED ONTOLOGIES

The core of the proposed solution is the adoption of a

Bayesian approach for ontology weighting.

Bayesian Networks (BN), also known as belief

networks, are probabilistic graphical models based

on DAGs. They have been deﬁned in the late 1970s

within cognitive science and artiﬁcial intelligence as

the method of choice for uncertain reasoning (Pearl

and Russell, 2001). A BN is therefore a graphical

structure that allows us to represent and reason about

an uncertain domain. In particular, each node in the

graph represents a random variable, that can take dif-

ferent values associated with probabilities, while the

edges represent probabilistic dependencies of the cor-

responding random variables. In particular, an edge

from a node X

(parent node) to a node X

(child node)

indicates that a value taken by the variable X

de-

pends on the value taken by the variable X

or, roughly

speaking, the variable X

“inﬂuences” X

. Note that

nodes without parents (roots) are not inﬂuenced by

any node, nodes without children (leaves) do not in-

ﬂuence any node, while any node affects its children.

Therefore, nodes that are not directly connected in the

BN represent variables that are conditionally indepen-

dent of each other. According to the global semantics

of BN, the full joint distribution is:

P(x

, ...,x

) =

∏

P(x

|pa

)

where x

is a value of the variable X

, pa

is a set of

values for the parents of X

, and P(x

|pa

) denotes the

conditional probability distribution of x

given pa

Therefore, in a BN, each node is associated with

a probability function that takes, as input, a particular

set of values for the node’s parent variables, and gives

(as output) the probability of the variable represented

by the node. These probability functions are speciﬁed

by means of (conditional) probability tables

, one for

each node of the graph.

In our approach, as mentioned in the Introduction,

we build a BN isomorphic to the ISA hierarchy, re-

ferred to as Onto-Bayesian Network (OBN). In the

OBN, according to the BN approach, the concepts are

boolean variables and the Bayesian weight associated

with a concept c, indicated as w

, is the probability P

that the concept c is True (T ), i.e.:

As mentioned in the Introduction, in order to compute

the weights w

, conditional probability tables are de-

A (conditional) probability table is deﬁned for a set

of (non-independent) random variables to represent the

marginal probability of a single variable w.r.t. the others.

A Bayesian Approach for Weighted Ontologies and Semantic Search

173

Thing

Accommodation

Transportation

Attraction

Gastronomy

Shopping

AlternativeAcc.

RegularAcc.

CozyAcc.

Campsite

FarmHouse

InternationalHotel

PrivateHouse

Pension

SeasideCottage

CountryResort

Flight

Train

Ship

CarRental

Bus

Exhibition

Museum

Salon

ArcheologicalSite

Concert

Theatre

Cinema

ClassicalConcert

RockConcert

PictureGallery

ArtGallery

LightMeal

EthnicMeal

RegularMeal

VegetarianMeal

MediterraneanMeal

ThaiMeal

IndianMeal

MexicanMeal

InternationalMeal

FrenchMeal

ShoppingCenter

Bazaar

= 0.20; w

= 0.20

= 0.07; w

= 0.014

= 0.03; w

= 0.042

= 0.03; w

= 0.00042

= 0.03; w

= 0.00042

= 0.02; w

= 0.00028

= 0.02; w

= 0.00028

= 0.02; w

= 0.00028

= 0.01; w

= 0.00001

= 0.01; w

= 0.00001

= 0.02; w

= 0.0002

= 0.03; w

= 0.0002

= 0.02; w

= 0.0002

= 0.07; w

= 0.014

= 0.07; w

= 0.014

= 0.04; w

= 0.008

= 0.04; w

= 0.008

= 0.04; w

= 0.008

= 0.04; w

= 0.008

= 0.04; w

= 0.008

= 0.05; w

= 0.010

= 0.05; w

= 0.010

= 0.05; w

= 0.010

= 0.05; w

= 0.010

= 0.03; w

= 0.0003

= 0.03; w

= 0.0003

= 0.07; w

= 0.014

= 0.03; w

= 0.00042

= 0.03; w

= 0.00042

= 0.07; w

= 0.014

= 0.07; w

= 0.014

= 0.02; w

= 0.00028

= 0.02; w

= 0.00028

= 0.02; w

= 0.00028

= 0.03; w

= 0.00042

= 0.03; w

= 0.00042

= 0.10; w

= 0.020

= 0.10; w

= 0.020

= 0.20; w

= 0.20

= 0.20; w

= 0.20

= 0.20; w

= 0.20

= 0.20; w

= 0.20

= 0.03; w

= 0.042

= 1; w

= 1

Figure 1: The WRO of our running example with the w

and w

concept weights.

KEOD 2016 - 8th International Conference on Knowledge Engineering and Ontology Development

174

Table 1: Probability table of Gastronomy.

Gastronomy

T F

0.20 0.80

Table 2: Conditional probability table of LightMeal.

LightMeal

Gastronomy T F

T 0.07 0.93

F 0 1

ﬁned by using w

proposed according to the proba-

bilistic approach recalled in the previous section as a

priori weights. In particular, given two concepts c

, we assume that:

P(c

=T |c

=T )=w

)

where c

is the parent of c

according to the ISA rela-

tion.

For instance, consider the concepts Gastronomy,

LightMeal, and VegetarianMeal of the ontology given

in Figure 1. Gastronomy (G for short) has as

parent T hing, which is always True (w

(T hing) =

(T hing) = 1), therefore the weight w

coincides

with the weight w

, i.e., w

(G) = w

(G), where

(G) = P(G=T |T hing=T ) = P(G=T) = 0.2, as

shown in Table 1. Consider now LightMeal (L). In

this case the conditional probability, which is given

in Table 2, depends on the True/False (T/F) values

of its father Gastronomy, and in particular w

(L) =

P(L=T |G=T ) = 0.07 (therefore P(L=F|G = T ) =

0.93). Then, the weight w

associated with L, w

(L)

= P(L=T ), is computed starting from the probability

of its parent Gastronomy as follows:

P(L=T ) =

∑

v∈{T,F}

P(L=T, G = v)

= P(L=T, G=T ) + P(L=T, G=F)

= P(L=T |G=T )P(G=T )

+ P(L=T |G=F)P(G=F)

= 0.07 × 0.2 + 0 × 0.8 = 0.014

taking into account the Kolmogorov deﬁnition for two

given variables A and B:

P(A, B) = P(A|B)P(B).

Therefore, the Bayesian weight w

(L) = P(L=T ) =

0.014, as shown in Table 4. Analogously, in Table 5

the probability of VegetarianMeal (V ) is given. The

weight w

(V ) has been computed by using the con-

ditional probabilities given in Table 3, and by taking

into account the weight w

(L) computed above (see

Table 4).

Table 3: Conditional probability table of VegetarianMeal.

VegetarianMeal

LightMeal T F

T 0.03 0.97

F 0 1

Table 4: Probability table of LightMeal.

LightMeal

T F

0.014 0.986

4 SemSim AND VALIDATION

The SemSim method has been conceived to search for

the resources in the UDR that best match the RV, by

contrasting it with the various AV, associated with the

searchable digital resources. This is achieved by ap-

plying the semsim function, which has been deﬁned

to compute the semantic similarity between OFV.

In SemSim, the weights are used to derive the IC

of the concepts that, according to (Lin, 1998), repre-

sents the basis for computing the concept similarity.

In particular, according to the information theory, the

IC of a concept c, is deﬁned as:

IC = −log(w(c))

The semsim function is based on the notion of sim-

ilarity between concepts (features), referred to as con-

sim. Given two concepts c

, c

, it is deﬁned as follows:

consim(c

, c

) =

2×IC(lub(c

))

IC(c

)+IC(c

)

where the lub represents the least abstract concept of

the ontology that subsumes both c

and c

. Given an

instance of RV and an instance of AV , say rv and av re-

spectively, the semsim function computes the consim

for each pair of concepts belonging to the set formed

by the Cartesian product of the rv, and av.

However, we focus on the pairs that exhibit high

afﬁnity. In particular, we adopt the exclusive match

philosophy, where the elements of each pair of con-

cepts do not participate in any other pair. The method

aims to identify the set of pairs of concepts of the rv

Table 5: Probability table of VegetarianMeal.

VegetarianMeal

T F

0.00042 0.99958

A Bayesian Approach for Weighted Ontologies and Semantic Search

175

and av that maximizes the sum of the consim similar-

ity values (maximum weighted matching problem in

bipartite graphs (Dulmage and Mendelsohn, 1958)).

In particular, given:

rv = {r

,..., r

}

av = {a

,..., a

}

as deﬁned in Section 2, let S be the Cartesian Product

of rv and av:

S = rv × av

then, P (rv, av) is deﬁned as follows:

P (rv, av) = {P ⊂ S | ∀ (r

, a

), (r

, a

) ∈ P,

6= r

, a

6= a

, |P| = min{n, m}}.

Therefore, on the basis of the maximum weighted

matching problem in bipartite graphs, semsim(rv,av)

is given below:

semsim(rv, av) =

max

P∈P (rv,av)



∑

)∈P

consim(r

)



max{n,m}

In (Formica et al., 2013), we deﬁned semsim-p in

which the weights w

of the concepts in the WRO are

computed by using the probabilistic approach. Anal-

ogously, in this paper we introduce semsim-b where

the weights, w

, are deﬁned by using a Bayesian Net-

work, as described in Section 3.

4.1 Validation

In order to validate semsim-b, we refer to the ex-

periment proposed in (Formica et al., 2013). In

that experiment, we considered four request vectors,

namely rv

, i = 1, ...4, which are recalled below:

= {Campsite, EthnicMeal, RockConcert, Bus}

= {InternationalHotel, InternationalMeal,

ArtGallery, Flight}

= {Pension, MediterraneanMeal,Cinema,

ShoppingCenter}

= {CountryResort, LightMeal, ArcheologicalSite,

Museum, Train}

and 22 annotated resources, represented by their

annotation vectors, namely av

, av

, ..., av

. Below,

only 10 of them are recalled for lack of space:

= {InternationalHotel, FrenchMeal,Cinema,

Flight}

= {Pension,VegetarianMeal, ArtGallery,

ShoppingCenter}

= {CountryResort, MediterraneanMeal, Bus}

= {CozyAccommodation,VegetarianMeal,

Museum, Train}

= {InternationalHotel, ThaiMeal, IndianMeal,

Concert, Bus}

= {SeasideCottage, LightMeal, ArcheologicalSite,

Flight, ShoppingCenter}

= {RegularAccommodation, RegularMeal,

Salon, Flight}

= {InternationalHotel,VegetarianMeal, Ship}

= {FarmHouse, MediterraneanMeal,

CarRental}

= {RegularAccommodation, EthnicMeal,

Museum}

...

For each request vector, we computed the sem-

sim value against the 22 annotation vectors, and then,

we calculated the Pearson correlation index (Corr)

against human judgment (HJ) scores. While the

original experiment demonstrated that SemSim out-

performs some of the most representative similarity

methods deﬁned in the literature (i.e., Dice, Jaccard,

Cosine, and Weighted Sum (Formica et al., 2013)), in

this work, we show in Tables 6 and 7 that semsim-b

(SS-b) achieves a higher correlation with HJ with re-

spect to semsim-p (SS-p).

Furthermore, Table 8 reports the values of the Pre-

cision and Recall measures obtained by a threshold

ﬁxed to 0.60. As we observe, the Precision achieved

by applying semsim-b is equal to 1 for all the four RV ,

and for three of them, namely rv

, rv

, and rv

, it is

higher with respect to the Precision obtained by ap-

plying semsim-p. We also observe that both semsim-b

and semsim-p achieve the same Recall (equal to 1) for

three out of four RV , while the Recall for the remain-

ing RV (i.e. rv

) by semsim-b is lower than the one by

semsim-p.

5 RELATED WORK

In this section, we ﬁrst recall some of the existing pro-

posals concerning the weighting of the concepts of an

ontology. Successively, a second line of research is

recalled regarding the integration of BN and Ontolo-

gies.

5.1 Ontology Weighting Methods

In (Gao et al., 2015) an approach based on edge-

counting and information content theory for measur-

ing semantic similarities has been presented. In par-

ticular, different ways of weighting the shortest path

length are proposed, although they are essentially

based on WordNet frequencies. As also mentioned

in (Formica et al., 2008), we do not adopt the Word-

Net frequencies for several reasons. Firstly, because

KEOD 2016 - 8th International Conference on Knowledge Engineering and Ontology Development

176

Table 6: Correlation about rv

and rv

HJ SS-p SS-b HJ SS-p SS-b

0.10 0.54 0.20 0.72 0.80 0.68

0.10 0.34 0.12 0.21 0.55 0.43

0.25 0.50 0.37 0.16 0.35 0.18

0.18 0.49 0.22 0.10 0.49 0.26

0.51 0.64 0.37 0.10 0.47 0.34

0.14 0.40 0.18 0.20 0.49 0.34

0.16 0.51 0.24 0.71 0.90 0.77

0.10 0.37 0.20 0.10 0.49 0.38

0.10 0.46 0.29 0.10 0.35 0.18

0.21 0.49 0.32 0.40 0.46 0.30

0.15 0.45 0.16 0.10 0.44 0.28

0.10 0.25 0.12 0.10 0.23 0.10

0.89 0.71 0.67 0.10 0.34 0.16

0.10 0.38 0.16 0.44 0.55 0.41

0.10 0.33 0.13 0.86 0.70 0.64

0.10 0.39 0.18 0.25 0.54 0.40

0.93 0.87 0.77 0.10 0.48 0.21

0.26 0.46 0.17 0.10 0.39 0.21

0.50 0.73 0.37 0.10 0.46 0.23

0.34 0.51 0.32 0.10 0.41 0.21

0.77 0.85 0.52 0.10 0.48 0.26

0.46 0.72 0.56 0.10 0.46 0.20

Corr 1.00 0.90 0.93 1.00 0.83 0.88

we deal with specialized domains (e.g., tourism), re-

quiring specialized domain ontologies and WordNet

is a generic lexical ontology. Secondly, there are con-

cepts in WordNet for which the frequency is not given

(e.g., accommodation), or is irrelevant, as in the case

of meal (the frequency is 20).

In (Rusu et al., 2014), the importance of measur-

ing semantic similarity between concepts of an ontol-

ogy is emphasized. In particular, the authors show

that their proposal improves the basic distance met-

ric, although the information content approach is not

addressed in the experiment.

The method proposed in (Seco et al., 2004) is

based on the assumption that the more descendants

a concept has the less information it expresses. Con-

cepts that are leaf nodes are the most speciﬁc in the

taxonomy and their information content is maximal.

Analogously to our proposal, in this method the infor-

mation content is computed by using only the struc-

ture of the specialization hierarchy. However, it forces

all the leaves to have the same IC, independently of

their depth in the hierarchy.

5.2 Ontology and Bayesian Networks

In (Rajput and Haider, 2011) a framework, called

BNOSA, has been proposed that uses an ontology to

conceptualize a problem domain. In this framework, a

BN has been adopted to predict missing values and/or

Table 7: Correlation about rv

and rv

HJ SS-p SS-b HJ SS-p SS-b

0.10 0.55 0.43 0.10 0.39 0.21

0.62 0.80 0.68 0.10 0.36 0.23

0.29 0.36 0.30 0.45 0.48 0.41

0.10 0.44 0.26 0.88 0.75 0.68

0.10 0.38 0.25 0.10 0.38 0.21

0.31 0.56 0.43 0.50 0.66 0.58

0.10 0.45 0.29 0.10 0.43 0.27

0.10 0.38 0.26 0.10 0.37 0.25

0.12 0.36 0.30 0.10 0.37 0.25

0.18 0.45 0.29 0.14 0.42 0.33

0.78 0.85 0.70 0.14 0.40 0.30

0.38 0.52 0.33 0.16 0.34 0.25

0.10 0.39 0.16 0.18 0.48 0.29

0.42 0.63 0.40 0.20 0.42 0.33

0.10 0.28 0.17 0.10 0.29 0.16

0.31 0.47 0.39 0.31 0.59 0.51

0.10 0.51 0.24 0.10 0.49 0.32

0.18 0.43 0.30 0.84 0.86 0.75

0.10 0.49 0.32 0.32 0.57 0.46

0.22 0.40 0.30 0.36 0.71 0.55

0.10 0.53 0.37 0.21 0.50 0.37

0.10 0.50 0.23 0.29 0.58 0.44

Corr 1.00 0.81 0.86 1.00 0.88 0.93

to resolve conﬂicts of multiple values. In contrast, in

our approach the BN has been used to assign weights

to concepts of the reference ontology.

(Clark and Radivojac, 2013) applies BN for com-

puting the information content of concepts in a tax-

onomy and, more in general, of a sub-graph, by sum-

ming the information content of each concept in the

sub-graph. However, with respect to our work, it does

not focus on any speciﬁc way for building the con-

ditional probability tables of the BN, and such tables

are assumed to be given.

In (Yazid et al., 2014), a similarity measure for the

retrieval of medical cases has been proposed. This ap-

proach is based on a BN, where the a priori probabil-

ities are given by experts on the basis of cause-effect

conditional dependencies. As already mentioned, in

our approach the a priori probabilities are not given by

experts and rely on the probabilistic-based approach.

In (Jung et al., 2010), an ontology mapping-based

search methodology (OntSE) is proposed in order to

Table 8: Precision and Recall about the four request vectors.

Precision Recall

SS-b SS-p SS-b SS-p

1.00 0.50 0.67 1.00

1.00 1.00 1.00 1.00

1.00 0.67 1.00 1.00

1.00 0.50 1.00 1.00

A Bayesian Approach for Weighted Ontologies and Semantic Search

177

evaluate the semantic similarity between user key-

words and terms (concepts) stored in the ontology,

using a BN. Furthermore, in (Grubisic et al., 2013),

the authors emphasize the need of having a non-

empirical mathematical method for computing con-

ditional probabilities in order to integrate a BN in an

ontology. In particular, in the proposed approach the

conditional probabilities depend only on the structure

of the domain ontology. However, in the last two

mentioned papers, the conditional probability tables

for non-root nodes are computed starting from a ﬁxed

value, namely 0.9.

In line with (Grubisic et al., 2013), we also pro-

vide a non-empirical mathematical method for com-

puting conditional probabilities, but our approach

does not depend on a ﬁxed value as initial assumption.

In fact, in SemSim-b the conditional probabilities are

computed on the basis of the weight w

, which de-

pends only on the structure of the domain ontology,

i.e., the probability of the parent node divided by the

number of sibling nodes.

6 CONCLUSION

In this paper we presented a new approach to seman-

tic similarity reasoning based on the integration of

Bayesian Networks and Weighted Ontologies. Such

a solution improves the performance of the Sem-

Sim method proposed in (Formica et al., 2013). In

essence, the proposed approach is based on the con-

struction of a Bayesian Network, isomorphic to a

given ontology, referred to as OBN (Onto Bayesian

Network). Then, the OBN is used to compute the in-

formation content of each concept in the ontology. We

have shown that the SemSim method achieves better

performances by using the weights obtained from the

OBN rather than the ones achieved according to the

probabilistic-based approach. The SemSim method

has been conceived assuming that the ontology is or-

ganized as a tree-shaped taxonomy. In a future work,

we will focus on ontologies organized as DAG, there-

fore we will extend these results to ISA hierarchies

with multiple inheritance.

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