Original article Biomath 1 (2012), 1211117, 1–6
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h t t p : / / w w w . b i o m a t h f o r u m . o r g / b i o m a t h / i n d e x . p h p / b i o m a t h / Biomath Forum
Predicting and Scoring Links in Anatomical
Ontology Mapping
Peter Petrov∗, Milko Krachounov∗, Ognyan Kulev∗, Maria Nisheva∗, Dimitar Vassilev†
∗Faculty of Mathematics and Informatics, Sofia University St. Kliment Ohridski
5 James Bourchier Blvd., 1164 Sofia, Bulgaria
†Bioinformatics group, AgroBioInstitute
8 Dragan Tsankov Blvd., 1164 Sofia, Bulgaria
Email: jim6329@gmail.com
Received: 12 July 2012, accepted: 11 November 2012, published: 22 December 2012
Abstract—The paper presents a work performed in the
area of automatic and semi-automatic ontology mapping. A
method for inferring additional cross-ontology links while
mapping anatomical ontologies is described and the results
of some experiments performed with various external
knowledge sources and scoring schemes are discussed as
well.
Keywords-ontology; graph; directed acyclic graph; on-
tology mediation; ontology mapping; ontology merging;
scoring scheme; probability; knowledge sharing; knowl-
edge reuse; interoperability
I. INTRODUCTION
The term ontology comes from Philosophy and
has been applied in Information Systems, Information
Retrieval etc. to represent the formalization of a body
of knowledge describing a given domain. Ontologies
have become increasingly popular because they help
to realize many of the most challenging problems in
the IT field like interoperability, information/knowledge
sharing and knowledge reuse.
Information sources (and ontologies in particular),
even from the same problem domain, are usually hetero-
geneous. In order to enable interoperation between such
information sources (ontologies) and to integrate the
information/knowledge from multiple sources, one needs
to build mappings between ontologies. These mappings
establish the semantic correspondence between concepts
and relations in different ontologies. As we have noted in
[10] there are some terminological differences pertaining
to the integration of ontologies within the ontology map-
ping/merging/matching (OM) community. Those termi-
nological differences are mostly between the terminology
adopted in [1] on one side, and in [11] on the other. In
our works, we adopt the terminology of [1]. In the sense
of [1], ontology mapping is the process of taking two
input ontologies and generating semantic links between
their concepts/terms. The generated links are not part of
the two input ontologies; they are stored separately from
them. Two other terms are related to ontology mapping:
ontology aligning and ontology merging. Ontology align-
ing [1] can be viewed as an automatic or semi-automatic
ontology mapping; it denotes the process of discovery
of cross-ontology links by a computer program. Again,
these links are stored separately from the two input on-
tologies. Ontology merging [1] is the ultimate goal when
integrating/mediating two input ontologies; it comes
down to taking two input ontologies and generating an
output ontology that unifies the knowledge contained in
them. It is usually a process which follows the processes
of mapping/aligning and which utilizes the intermediate
results produced by them; during this process, some pairs
of terms (one from each of the two input ontologies)
are merged into single nodes of the output ontology,
while other input terms are not paired but are just copied
unchanged to the output ontology.
This paper discusses some issues in automatic map-
Citation: P Petrov, M Krachounov, O Kulev, M Nisheva, D Vassilev, Predicting and Scoring Links in
Anatomical Ontology Mapping, Biomath 1 (2012), 1211117, http://dx.doi.org/10.11145/j.biomath.2012.11.117
Page 1 of 6
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P Petrov at al., Predicting and Scoring Links in Anatomical Ontology Mapping
ping or aligning of species-specific anatomical ontolo-
gies by utilization of various knowledge sources.
II. PROBLEM FORMULATION
Given the anatomical ontologies of two different
species (model organisms) e.g. mouse and zebrafish, our
goal is to establish semantic links between the terms of
the two ontologies such that: (i) these links are of one of
the following types: R1 = synonymy, R2 = hypernymy,
R3 = hyponymy, R4 = holonymy, R5 = meronymy,
and (ii) each of these links has some degree of certainty
or degree of confidence or confidence score which is a
real number in the interval [0, 1]. The semantic relation
types Rk that we refer to here are well-known and are
widely utilized in the areas of linguistics, knowledge
representation and ontology engineering. That is why we
don’t provide any formal or informal definitions for them
here.
The two input ontologies are represented in the form
of OBO files. OBO stands for “Open Biomedical Ontol-
ogy“ and denotes an ontology language and an ontology
file format [2] for defining ontologies. It has been used
mostly for defining ontologies in the biomedical domain.
Nowadays OBO is adopted by the GO project [2], [3],
the OBO Foundry initiative [4], and other communities.
III. FORMALIZATION OF THE PROBLEM
In mathematical terms, each of the two input anatom-
ical ontologies can be considered as a directed acyclic
graph together with a function colouring the graph’s
edges. The colours model the relations defined within the
input ontologies (like is a and part of ) which we call
inner-ontology relations. Typically, there are other inner-
ontology relations except those two. These additional
relations usually pertain to the development of the par-
ticular organism and not just to its adult/gross anatomy.
Such relations are for example start stage, end stage,
develops from but practically we don’t deal with them as
we are mainly concerned with the organism’s adult/gross
anatomy, not with the organism’s growth and develop-
ment. We shall use further the following notation:
O1 = OM : DAG1 = (V1,E1),
F1 : E1 →C = {c1,c2, ...,cn};
O2 = OZ : DAG2 = (V2,E2),
F2 : E2 →C = {c1,c2, ...,cn}.
Here O1 and O2 are the two input anatomical ontolo-
gies; DAG1, DAG2 are their corresponding directed
acyclic graphs; V1 and V2 are the sets of terms of the
two input ontologies (each term has an identifier and a
name); E1 and E2 are the relations defined within the
two input ontologies; F1 and F2 are the edge-colouring
functions. Two terms u1 and u2 are connected with an
edge e if and only if the pair of terms (u1,u2) belongs
to the relation represented by e.
The relations is a (specialization/generalization) and
part of (membership/aggregation) are the two typical
examples of inner-ontology relations defined within the
ontologies O1 and O2. In our notation, we map relations
to colours (through F1 and F2), and we deal only with
two relations (is a, part of). So it can be assumed
that n = 2, c1 = is a, c2 = part of . Thus, if for
example, u1 =“brain”, u2 =“central nervous system”,
u1,u2∈V1, then there usually exists an edge e between
u1 and u2 such that F1(e) = part of (because the
brain is part of the central nervous system and anatomical
ontologies of most organisms usually declare this fact
explicitly).
Also given are several (typically large) external knowl-
edge sources which might be either biomedical ones
or general-purpose ones. They contain anatomical terms
and relations (is a, part of , others) between their own
terms. Three concrete external knowledge sources have
been used for the purposes of this work. These are
T1 = UMLS, T2 = FMA, T3 = WordNet. UMLS [5],
[14] and FMA [6], [15] are biomedical knowledge
sources, and WordNet [7], [8], [16] is a general purpose
knowledge source. Formally stated, each of these knowl-
edge sources Ts, s = 1, 2, 3, contains the following
information:
• Terms. Ms = {ts1,ts2, ...,tsms} is the set of
terms in the knowledge source Ts. Here tsk =
(idsk;namesk); idsk is the identifier within Ts
of the term tsk; namesk is the textual name within
Ts of the term tsk; ms (usually 106 ≤ ms ≤ 107)
is the number of terms in the knowledge source Ts.
• Relations. These are the is a and part of relations
defined within the external knowledge source Ts:
R
′
Ts
= Ris aTs ⊆Ms ×Ms,
R
′′
Ts
= R
part of
Ts
⊆Ms ×Ms.
Typically other relations are also defined within the
external knowledge source Ts but only these two
are relevant to our work.
Each knowledge source src = Ts, s = 1, 2, 3, is
up-front assigned a score f(src) which is based on
its preciseness in predicting synonymy and parent-child
(is a, part of ) relations between terms of the two in-
put ontologies. Details on this evaluation (of the three
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P Petrov at al., Predicting and Scoring Links in Anatomical Ontology Mapping
knowledge sources that we use) can be found in [9].
Having the notation introduced above, we now seek
to find a set of predictions (a set of 4-tuples):
D = {(v1k,v2k,rk,sk) |k = 1,2, ..., |D|},
such that v1k∈V1, v2k∈V2, rk∈{R1,R2,R3,R4,R5}
and sk∈(0,1]. Here, for each k, v1k is a term from the
input ontology O1, v2k is a term from the input ontology
O2, rk are automatically (i.e. in silico) predicted cross-
ontology links from one of the five types defined in the
previous section, and sk is a real number denoting the
confidence score of the prediction that the terms v1k
and v2k are related/linked by a cross-ontology link of
the type rk. Requiring that sk ∈ (0,1], we basically
imply that the set D which we seek, is in fact a set of
cross-ontology predictions or a set of predicted cross-
ontology links between O1 and O2 where each score
is probabilistic-based (modeling, given the information
we have in the input ontologies and also in the available
knowledge sources, the probability that the correspond-
ing prediction is actually true).
IV. ALGORITHMIC PROCEDURES
Three algorithmic procedures are applied to the graph
structures that were described formally in the previous
section. Each of them adds more links to the set D that
is being sought. These three procedures are detailed in
[12], here we mention them only briefly.
Within the first procedure, the two input ontologies
are scanned for identity matches between the names
of their terms. If t1 ∈ V1 and t2 ∈ V2 have the
same names, they are marked as synonyms predicted
by what we call the direct matching (DM) procedure.
The cross-ontology links discovered/predicted this way
are assigned the highest possible scores of 1.0 as these
predictions come from information contained entirely in
the two input ontologies.
During the second procedure, using the information
(the terms and the relations) in the external knowledge
sources, and identity matches between term names of the
two input ontologies and term names of the three external
knowledge sources, we build a graph model/structure
which aligns each of the two input ontologies to each
of the three external knowledge sources. This model
contains a set of semantic links (of the types Rk,
k = 1, 2, ..., 5, that were defined above) between the
two input ontologies on the one side, and the three
external knowledge sources on the other side. Then a set
of logical rules is applied, and conclusions are drawn for
the semantic relations that exist between terms t1 ∈V1
and t2 ∈V2 of the two input ontologies. The following
rules are applied at this stage:
• Rule (A). If two terms t1 ∈V1 and t2 ∈V2 have
been detected as synonyms of the same term
t∈Ts, then t1 and t2 are marked as predicted
cross-ontology synonyms of each other;
• Rule (B). If tj∈Vj has been detected as a synonym
of t∈Ts (s=1, 2, 3), and if the term t3−j∈V3−j
has been detected as an (is a/part of)
child/parent of t, then tj is marked as predicted
cross-ontology (is a/part of) parent/child of
t3−j (here j =1 or j =2).
The application of these rules is what we call the
source matching predictions (SMP) procedure. Rule
(A), when applied, finds the synonymy relations (i.e. the
relations of type R1) between terms from the two input
ontologies. Rule (B) is a composite (generalized) version
of four separate rules (two options for is a/part of by
two options for child/parent makes four options in total).
These four rules which originate from rule (B), when
applied, find the hypernymy, hyponymy, holonymy and
meronymy relations (i.e. the relations of types R2, R3,
R4, R5) between terms of the two input ontologies. All
links predicted through SMP are given the score f(src),
where src is the knowledge source confirming/implying
these predictions.
Finally, we run a procedure that we denote as the child
matching predictions (CMP) procedure. This one tries
to find R1, R2, R3, R4 and R5 links between terms of
the two input ontologies, t1∈V1 and t2∈V2, for which
no links have been predicted either by DM or by SMP.
The approach CMP takes is to consider patterns of cross-
ontology connectivity (found by DM and SMP) between
t1 ∈V1 (parent term 1), t2 ∈V2 (parent term 2), and
the child terms of the two parent terms t1 and t2. Three
separate patterns of connectivity are considered by CMP:
(i) t1∈V1←−tch1∈V1←→tch2∈V2−→t2∈V2
(we call this an U Pattern);
(ii) t1∈V1←−tch2∈V2←→tch1∈V1−→t2∈V2
(we call this an X Pattern);
(iii) t1 ∈V1 ←− tch1 ∈V1 −→ t2 ∈V2 or
t1 ∈V1 ←− tch2 ∈V2 −→ t2 ∈V2
(we call these two patterns V Patterns).
In this notation, the −→ and ←− arrows denote sets
of non-CMP parent-child links (the arrows always point
from child to parent). These are asymmetrical links. The
←→ arrows denote sets of non-CMP synonymy links
These are symmetrical links. The tch1 and tch2 are child
terms from the two input ontologies. Each occurrence of
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P Petrov at al., Predicting and Scoring Links in Anatomical Ontology Mapping
any of these patterns between t1 and t2 (the two parent
terms) we call a pattern instance. All arrows within one
pattern instance represent either is a or part of links
(we don’t allow mixing these two within a single pattern
instance).
Based on these patterns of connectivity, new cross-
ontology links (CMP links) are introduced (one CMP
link per pattern instance) between t1 and t2. We call
these links individual CMP links. To assign scores to the
individual CMP links, the concepts score of a set of non-
CMP links between two terms and score of a pattern
instance (or score of an individual CMP link) are
defined below. Also, we introduce two functions, Conj
and Disj, with N ≥ 2 parameters each, which, provided
that the probabilities p1,p2, ...,pN of N events are
given, define the probabilities of (i) all these events
occurring at the same time (Conj), and (ii) at least one of
these events occurring (Disj). We call the Conj and Disj
functions accumulation functions as they accumulate
scores of non-CMP links to produce a score of an
individual CMP link. Finally, all individual CMP links
between t1 and t2 are aggregated through what we call
an aggregation function (which can be e.g. the max
of N ≥ 1 numbers). Next, we define in some more
detail the concepts which we just introduced in relation
to CMP.
Definition 1 (Conj): Conj is a function which takes N
arguments (each of them in [0, 1]) and returns a result
in [0, 1]. We discuss a possible implementation for it
below.
Definition 2 (Disj): Disj is a function which takes N
arguments (each of them in [0, 1]) and returns a result in
[0, 1]. We discuss possible implementations for it below.
Definition 3 (score of a non-CMP link): The score of
a non-CMP link between any two terms (which could be
from the same ontology or not) is defined as follows:
score(sij)=
I if sij is an IO link,
D if sij is a DM link,
f(src) if sij is an SMP link which
came from the source src ∈
{UMLS, FMA, WordNet}.
Here IO stands for inner-ontology, DM stands for
direct matching and SMP stands for source matching
predictions; sij is one single non-CMP link (i.e. one
single evidence); the I and D are constants (typically
having the values of 1.0).
Definition 4 (score of a set of non-CMP links): The
score of a set of non-CMP links (score of an evidence
set) is defined as follows:
score(Si) = Disjmk=1(score(sik)),
where Disj is the function from Definition 2, sik are
non-CMP (i.e. either IO or DM or SMP) links, and the
Disj is taken over all non-CMP links taking part in the
evidence set Si.
Definition 5 (score of an individual CMP link): The
score of an individual CMP link e is defined as:
score(e) = p · Conjni=1(score(Si)),
where p ∈ [0, 1] is a CMP penalty constant, Conj is the
function from Definition 1, and the Conj is taken over
all evidence sets Si that take part in the pattern instance,
which the link e originates from (note that n = 2 for
the V patterns and n = 3 for the X and U patterns).
Definition 6 (aggregation function): Let K be the
number of all individual CMP links drawn between
t1 ∈ V1 and t2 ∈ V2. An aggregation function is a
known function Fagg which takes the scores of all these
K individual CMP links and produces a single number
PCMP (t1,t2) ∈ [0,1], which we call score of the
aggregated (final) CMP link drawn between t1 and t2.
As a final result from the CMP procedure, this aggre-
gated CMP link is drawn between any two terms t1 and
t2 for which at least one pattern (of any of the three types
X, U, V) is found. The score of this link is calculated in
the way shown above.
V. COMPARISON OF ALTERNATIVE SCORING
SCHEMES
We have produced several distinct scoring
schemes by varying the functions Conj, Disj and Fagg
which were defined above.
• Scheme #1:
(1a) Conj(s1,s2) = s1s2;
Conj(s1,s2,...,sN)=Conj(Conj(s1,s2,...,sN−1),sN)
(1b) Disj(s1,s2) = s1 + s2 −s1s2;
Disj(s1,s2,...,sN)=Disj(Disj(s1,s2,...,sN−1),sN)
(1c)Fagg(s1,s2, ...,sN) = max(s1,s2, ...,sN)
• Scheme #2:
(2a) Conj(s1,s2) = s1s2;
Conj(s1,s2,...,sN)=Conj(Conj(s1,s2,...,sN−1),sN)
(2b) Disj(s1,s2) = s1 + s2 −s1s2;
Disj(s1,s2,...,sN)=Disj(Disj(s1,s2,...,sN−1),sN)
(2c)Fagg(s1,s2, ...,sN) = Disj(s1,s2, ...,sN)
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• Scheme #3:
(3a) Conj(s1,s2) = s1s2;
Conj(s1,s2,...,sN)=Conj(Conj(s1,s2,...,sN−1),sN)
(3b)Disj(s1,s2)=α(s1+s2−s1s2)+(1−α)max(s1,s2);
Disj(s1,s2,...,sN)=Disj(Disj(s1,s2,...,sN−1),sN)
(3c)Fagg(s1,s2, ...,sN) = Disj(s1,s2, ...,sN)
The Disj functions from schemes #1 and #2 are
identical to the formula for calculating the probability
of the union of two (and respectively N) independent
events.
Fagg from scoring scheme #1 corresponds to the
probability of the union of two events such that one is
completely dependent on the other. Fagg from scoring
scheme #2 coincides with Disj from the same scoring
scheme, which equals the probability of the union of
two independent events.
Therefore in a probabilistic model the expression
s1 +s2−s1s2 is a good choice for combining two in-
dependent scores, while max(s1,s2) is a good choice
for combining scores when one score is completely
dependent on the other.
In scoring scheme #3 we design a scoring function
whose values are between the values of the first two
scoring functions (#3 is a linear combination of #1 and
#2). The main objective behind the use of this third scor-
ing function is to account for the dependencies between
the knowledge sources (UMLS, FMA, WordNet) without
completely ignoring the fact that, if more than one of
them confirm certain prediction, that usually improves
the odds that this prediction is correct. In scheme #3,
α ∈ [0, 1] is a parameter of the linear combination
defined in (3b). It varies depending on the knowledge
source or the combination of knowledge sources, which
confirm the predictions whose scores we accumulate in
(3b). The α parameter acts as a buffer to prevent the
score from growing too fast when adding up cumulative
predictions (i.e. when the predictions being accumulated
are confirmed by several knowledge sources): when α
equals 0.0, the value is growing the quickest (as it should
for independent scores); when α equals 1.0, the value
is limited by the maximum score of the scores being
accumulated.
To experimentally show that the choice of Disj from
(3b) is a reasonable one, we have generated a set of
observations on two dependent random variables x1, x2
with Boolean (1/0 i.e. true/false) truth values, and we
have confirmed that if we substitute the scores s1 and s2
in (3b) with the probabilities P(xi = true) (i = 1, 2),
and α with the modulus of the correlation coefficient
between the two random variables, we get a very good
approximation for the probability P(z = true) of their
Boolean disjunction z = (x1 or x2).
VI. RESULTS AND DISCUSSION
Let us consider the following two figures which il-
lustrate how the scores generated by the three scoring
schemes are related to each other and demonstrate the
advantages of scheme #3.
Figure 1. Scatter plot: scheme #1 vs schemes #2 and #3
Figure 2. Scatter plot: scheme #3 vs schemes #1 and #2
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It can be seen on Fig.1 that the data in scheme
#1 appear clustered around the configured values for
knowledge source scores (and combinations of these),
because there isn’t anything to account for the amount
of available evidence gathered from each source (e.g. the
number of patterns confirming a prediction). Compared
to scheme #1, both schemes #2 and #3 scatter the clusters
because the Fagg values are growing when more patterns
are confirming a given prediction. As Fagg in scheme
#3 is limited through the α parameter, it causes a more
moderate scattering as seen on Fig. 1, while scheme #2
causes a very rapid increase.
The main advantage of scheme #3 is that it allows us
to control the speed at which additional patterns increase
the score, while scheme #2 gives control only over the
initial value of that score. Within scheme #2, when
having one pattern confirming the prediction, the scores
start somewhere around the configured CMP score value
(defined by the penalty constant), and grow with the
same speed up to 1.0. Within scheme #3 this growth can
be slowed down and controlled through the α parameter.
The difference between the schemes #2 and #3 can be
seen on Fig. 2 in red, and it clearly shows how easily
some scores approach the value 1.0 when scheme #2 is
used. The Disj function from Scheme #3 also causes a
softening effect on the score when there are multiple
knowledge sources and algorithmic procedures (DM,
SMP, CMP) confirming the prediction, because it allows
us to control the speed at which the score grows and
even to use the actual correlation coefficient between the
distinct knowledge sources. This is not directly visible on
the figures at this scale, because it largely produces local
shifts in the position of the clusters and has the biggest
effect on data predicted by the knowledge sources (SMP)
which constitute the cluster around score=1.0.
VII. CONCLUSION
We presented in this paper an original algorithmic
approach to inferring (predicting and scoring) cross-
ontology links within automatic mapping of distinct
species-specific anatomical ontologies. The full mapping
procedure assumes that the auto-generated set of predic-
tions will be carefully checked by a curator (a human,
an anatomy expert) and his/her input will be utilized to
accurately calculate the correlation coefficients between
certain pairs of knowledge sources. These correlation
coefficients could be used as values for the α parameters
of the scoring scheme. The procedures described briefly
here and detailed in [12], and the scoring schemes
introduced here, are utilized in the software program
AnatOM [10], [13] developed as part of our work
on semi-automatic mapping and merging of anatomical
ontologies.
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http://dx.doi.org/10.1038/nbt1346
http://dx.doi.org/10.1093/nar/gkh061
http://dx.doi.org/10.1016/j.jbi.2003.11.007
http://dx.doi.org/10.1145/219717.219748
http://dx.doi.org/10.11145/j.biomath.2012.11.117
Introduction
Problem formulation
Formalization of the problem
Algorithmic procedures
Comparison of alternative scoring schemes
Results and discussion
Conclusion
References