Similarity Features, and their Role in Concept Alignment Learning
Shenghui Wang, Gwenn Englebienney, Christophe Gue´ret, Stefan Schlobach, Antoine Isaac, Martijn Schut
Department of Computer Science, Vrije Universiteit Amsterdam, The Netherlands
yInformatics Institute, Universiteit van Amsterdam, The Netherlands
Email:fswang,cgueret,schlobac,aisaacg@few.vu.nl, schut@cs.vu.nl, G.Englebienne@uva.nl
Abstract—Finding mappings between compatible ontologies
is an important and difficult open problem. Instance-based
methods for solving this problem have the advantage of fo-
cussing on the most active parts of the ontologies and reflect the
semantics of the ontologies as they are used in the real world.
We evaluate how the feature representation of the instances is
representative of the corresponding concepts, investigate how
this corresponds with the domain characteristics of the data
and which role it plays in the task of instance-based ontology
mapping. We use two different competitive classifiers and a
standard feature selection to identify important features, and
study the effect of those different classifiers in the concept
alignment context.
Keywords-Instance-based Ontology Matching, Semantic In-
teroperability, Machine Learning
I. INTRODUCTION
Motivation: The problem of semantic heterogeneity
and the resulting problems of interoperability and informa-
tion integration have been studied for well over 40 years
now. It is at present an important hurdle to the realisation of
the Semantic Web. Solving matching problems is one step to
the solution of the interoperability problem. Semantic Web
community has invested significant efforts over the past few
years [1].
Solving the matching problem requires to assess the
conceptual similarity between elements of two separate
ontologies in order to determine relationships (mappings)
such as equivalence or subsumption between them. One way
of judging whether two concepts from different ontologies
are semantically equivalent is to observe their extensional
information, that is, the instance data they classify [2], [3],
[4]. However, it is not always easy to identify identical
instances in many applications. Therefore, a robust instance-
based mapping technique should cope with the case when
there are no explicitly common instances.
Problem Description: This paper focus on instance-
based mapping technique only. In [5], we formulated the
matching problem as a classification problem, where a
mapping can be predicted from the similarity between the
extensional information of two concepts.
As in many other application contexts, the instances
are described and can be compared according to many
dimensions (features). Knowing which of these features play
the most important role during the classification is important
as to optimise the quality of meta-data. Important features
would be taken more care of. It is thus interesting to look for
a way of assessing the relative importance of the features. In
this paper, we use two different automated methods, namely
Markov Random Field (MRF) and Evolution Strategy (ES)
to investigate this importance. Concept mapping can be seen
as a side effect of these methods, and the quality of the
method can be assessed by the quality of the concept map-
ping it produces. We therefore also compare the concept-
mapping performance of our methods to a state-of-the-art,
off-the-shelf classifier: the Support Vector Machine (SVM).
Research Questions: Our aim is to answer the follow-
ing research questions:
 What are the benefits of using a machine learning
algorithm to determine the importance of features?
 Are there regularities wrt. the relative importance given
to specific features for similarity computation? Are
these weights related to application data characteristics?
 How do different classifiers perform on this instance-
based mapping task?
Findings: The two classifiers provide largely consis-
tent, sensible and valuable insight in the importance of the
instance features. As evaluated against a human golden stan-
dard, they also outperform the SVM on the concept mapping
task, thereby indicating that the highlighted features are
indeed important.
II. PROBLEM STATEMENT
Our task is to match two thesauri, GTT and Brinkman,
which are used to annotate different book collections at
the National Library of the Netherlands (Koninklijke Bib-
liotheek or KB). In order to improve the interoperability
between these collections, for example, using GTT concepts
to search books annotated only with Brinkman concepts, we
need to find mappings between these two thesauri.
As investigated in [3], books annotated by a concept
can be treated as instances of this concept. Using shared
book instances has already provided interesting mappings.
However, many books are not used, because they are not
dually annotated. In this paper, we further our investigation
in [5], focus on finding mappings directly using book meta-
data, no matter the books are dually annotated or not.
Books are described by their title, author, abstract, etc.
These features together represent an individual book in-
stance. For each concept, all its instances are grouped into an

integrated representation of this concept, feature by feature.
For example, all titles of these books are put together as a
“bag of words.” Term frequencies are measured within bags,
so that a concept is represented by a high dimensional vector
where each element represents the frequency of a term. The
similarity between two concepts is calculated with respect
to each feature, using the cosine similarity between the term
frequencies in these bags.
The similarity between the two elements of a pair of
concepts i is therefore measured and represented by a high
dimensional vector Fi. The similarity between feature j of
the concepts is indicated by Fij . These similarity vectors
can be treated as points in a space. In this “similarity
space,” each dimension corresponds to the similarity in
terms of one feature. As we know, some points (i.e., some
pairs of concepts) are real mappings but some are not. Our
hypothesis is that the label of a point — whether it represents
a mapping or not — is correlated with the position of this
point in this space.
Given some existing mappings, e.g., from a manual effort,
our goal is to learn this correlation. Therefore the mapping
problem is transformed into a classification problem. With
already labelled points and the actual similarity values of
concepts involved, it is possible to classify a point — i.e.,
to decide whether the pair represents a mapping — based
on its location in the similarity space. One baseline method
is to apply a standard support vector machine (SVM) to find
a hyperplane which separates classes with different labels.
Another option is to look for a direct correlation between
labels and similarities. Here we adopt two classifiers: one
based on a graphical Markov Random Field [6] and the other
using multi-objective evolution strategy [7].
III. METHODS
All three methods assume that mappings are independent.
This is a simplifying assumption (since if a term A maps to
B, the probability that A maps to any C 6= B clearly de-
creases), but it is necessary because explicitly modelling the
dependencies between all possible mappings is intractable.
A. Markov Random Field (MRF)
Let T = f (Fi; Li) gNi=1 be the training set of mappings,
with, for each given pair of concepts i, a feature vector
Fi 2 RK , where K is the number of features, and an
associated label Li.
We consider a simple graphical model, consisting of
an observed multivariate input F and a latent variable L
which represents the label. We assume that the mappings
are identically distributed conditionally on the observations,
and model the conditional probability of a mapping given
the input, p(LijFi), using a probability distribution from the
exponential family. That is:
p(LijFi) =
1
Z(Fi)
exp

KX
j=1
jfj(Li; Fi)


; (1)
where  = fj gKj=1 are the weights associated to the
potential function and Z(Fi), called the partition function, is
a normalisation constant ensuring that the probabilities sum
to 1. It is given by
Z(Fi) =
X
L2f0;1g
exp

KX
j=1
jfj(L;Fi)


: (2)
Because of our assumption that mappings are independent,
the likelihood of the data set for given model parameters
p(T j) is given by:
p(T j) =
NY
i=1
p(LijFi) (3)
During learning, our objective is to find the most likely
values for . We assume a prior probability distribution on 
which favours small values, assigning a normal distribution
with zero mean and covariance 2 for each i. The posterior
probability of  is then given by
p(jT ) = p(T j)p()

p(T ); (4)
where p(T ) is a normalisation term which does not depend
on  and can therefore be ignored during optimisation.
Moreover, since the logarithm is a monotonically increasing
function, we can optimise log p(jT ) rather than p(jT );
this turns out to be easier. Ignoring constants, the function
we optimise is thus:
`() =
NX
i=1
2
4
KX
j=1
jfj(Li; Fi) logZ(Fi)
3
5
KX
j=1
2j
22
:
(5)
This is equivalent with logistic regression, where we assume
a linear function for the discriminant and introduce regu-
larisation on the model parameters. The result is a convex
function which can easily be optimised using any variation
of gradient ascent. We used the L-BFGS [8] for the results
presented here. The first derivative of `() is given by
NX
i=1
"
fj(Li; Fi)
X
L2f0;1g
fj(L;Fi)p(LjFi;)
#

j
2
(6)
The variance of the prior, , is a parameter that has to be
set by hand and can be seen as a regularisation parameter
which prevents overfitting of the training data. The decision
criterion for assigning a label to a new pair of concepts is
then given by:
LPi =
(
1 if p(Li = 1jFi) > 0:5
0 otherwise
(7)

B. Multi-Objective Evolution Strategy
The evolutionary computing paradigm consists of a num-
ber of algorithms (genetic algorithms, evolutionary program-
ming, and others) that are based on, among others, natural
selection and genetic inheritance; these algorithms are used
for optimisation, modelling and simulation. For the purpose
of this paper, we decided to use evolutionary strategies (ES).
Evolutionary strategies have two characteristic properties:
firstly, they are used for continuous value optimisation, and,
secondly, they are self-adaptive. The first property is desir-
able for our problem at hand, because we are dealing with
real-valued representations. The second property makes the
search strategy adaptive, i.e., it dynamically changes search
parameters if necessary. Such self-adaptation is shown to
be highly effective in complex search processes where it is
difficult to tune the parameters manually.
As compared with the genotype/phenotype solution en-
coding used in Genetic Algorithm, an ES individual is a
direct model of the searched solution. That is, an individual
is defined by  and some evolution strategy parameters:
h;i $ h1; : : : ; K ; 1; : : : ; Ki (8)
Then, a metric for the quality of individuals — a fitness
function — is established. The fitness function is related to
the decision criterion for the ES, which is sign-based:
LESi =

1 if
PK
j=1 iFij > 0
0 otherwise
(9)
From 9, we can see that maximising the number of positive
results and negative results are two opposite goals. Those
goals can be expressed as a multi-objective fitness function
using a first component f1 for the number of true positives
matches and the other one f2 for the number of true
negatives.
f1( j F;L) = #fFi j
KX
j=1
iFij > 0 ^ Li = 1g(10)
f2( j F;L) = #fFi j
KX
j=1
iFij  0 ^ Li = 0g(11)
Instead of searching for one global optimum, this definition
allows the finding of best compromises between errors made
on positive and negatives matches.
The evolution process itself essentially consists of three
operators: the recombination, mutation and survivor selec-
tion operators.
 Recombination is applied on two parent
individuals h11; : : : ; 
1
K ; 
1
1 ; : : : ; 
1
Ki and
h21; : : : ; 
2
K ; 
2
1 ; : : : ; 
2
Ki. From an arithmetic
recombination weighted by a coefficient
, a first new
individual h01; : : : ; 
0
K ; 
0
1; : : : ; 
0
Ki is created:
0j = (1
j)
1
j +
j
2
j ; j = 1; : : : ;K (12)
0j = (1
j)
1
j +
j
2
j ; j = 1; : : : ;K (13)
similarly, an second child h001 ; : : : ; 
00
K ; 
00
1 ; : : : ; 
00
Ki is
created with 00j =
j
1
j +(1
j)
2
j and 
00
j =
j
1
j +
(1
j)2j . The value of
is drawn from a uniform
distribution on [0; 1].
 Mutation is applied on one parent individual
h1; : : : ; K ; 1; : : : ; Ki. It results in the creation of
one child h01; : : : ; 
0
K ; 
0
1; : : : ; 
0
Ki.
0j = j + 
0
jNj(0; 1); j = 1; : : : ;K (14)
0j = j exp
 0N (0;1)+Nj(0;1); j = 1; : : : ;K(15)
with N (0; 1) being a random number drawn from a
“standard” normal distribution (i.e. with mean equal to
0 and standard deviation of 1). The notation Nj(0; 1)
denotes the use of a different value for every jth strategy
parameter. The two  parameters are used to define a
learning rate. Following conventions, we set them to
be inversely proportional to the square root of problem
size  = 1=
p
2
p
K and  0 = 1=
p
2K.
 Survivor selection is performed using the NSGA2 [9]
strategy. The parent population and the offspring so-
lution are joined into one unique, temporary, popula-
tion. Those individuals are sorted into different fronts
according to Pareto optimality. Starting form the best
non dominated front of solution, each successive front
is made of next non dominated solution that are not yet
in a front. Those fronts are used to generate the new
parent population. When not all the elements in a front
can be picked up, the selection between the individuals
in such a way it preserves diversity.
During one loop of the algorithm, new candidate solutions
are created using recombination and/or mutation until an
oversize criterion is reached. Then, survivor operator is
applied to lower the number of individuals to the original
population size. The final result of the learning process is the
set of best solutions found, according to Pareto optimality.
An expert can use the system, stop it at any time and
pick up a solution among the best ones found so far. In
the absence of an expert, a simple heuristic is used: The
winner is the individual whose positive score is the closest
to the average of positives scores for all the population.
We implemented the ES classifier using OpenBeagle [10],
keeping a population of 30 individuals at each iteration.
C. Support Vector Machine
Support vector machines (SVMs) are a set of machine
learning algorithms classically used for classification and
regression problems [11]. Our work concerns the assess-
ment of a mapping for a given similarity vector. That is,
binary classification. In this context, SVM can be used as
a maximum margin classifier whose task consists in finding
an hyperplane h, with parameters ! 2 RK and b 2 R,
separating the two classes. A sign-based criterion allows the

attribution of a class ci 2 f 1;+1g to a data vector i.
ci =

+1 if h!
Fii+ b > 0
1 if h!
Fii+ b  0
(16)
The objective is to maximise the margin separating the two
classes whilst minimizing classification error risk. Classifica-
tion is expressed as a constraint. The decision rule from the
equation 16 can be changed into the constraint in equation 17
(where N is the number of elements in the training dataset).
ci(h!
Fii+ b)  1; i = 1; : : : ; N (17)
The margin to maximize separates each class set of points
closest to the hyperplane. Those support vectors satisfy the
condition jj h!
Fii + b jj2 = 1. It can be shown that
maximizing this margin is equivalent to minimizing the
quantity 12 h!
!i.
We now have an objective to minimize and some con-
straints. Next step of SVM formulation is to take the
Lagrangian L(!; ; b) of this optimisation problem. This
notation introduces a set of Lagrange coefficients i 2 R+.
L(!; ; b) =
1
2
h!
!i
NX
i=1
i[ci(h!
Fii+ b) 1] (18)
This formulation is only able to deal with data that is
strictly linearly separable. In order to deal with non linearly
separable datasets, the scalar product hFi
Fji is replaced
by a kernel function K(Fi; Fj). The expected outcome of
this so called “kernel trick” is to map the data from RK
to a higher dimension space were they will be linearly
separable. Moreover, a tolerance for error is added by setting
a maximum boundary C for the i. The final optimization
problem is:
Max:
PN
i=1 i
1
2
PN
i;j=1 ijcicjK(Fi; Fj)
with
PN
i=1 ici = 0
and 0  i  C; i = 1; : : : ; N
(19)
And the final decision criterion for the SVM is:
LSVMi =

1 if
PN
l=1 lclK(Fl; Fi) + b  0
0 otherwise
(20)
The choice of the kernel function has a sensitive impact
on the performance of the classifier. Practically, it dictates
the shape of the surface that will surround the two classes.
We decided to use the commonly used Radial Basis Func-
tion (RBF) to get “potato-shaped” classes. This kernel is
expressed as
K(Fi; Fj) = exp (
jjFi Fj jj2): (21)
We used the implementation of libSVM for the results
reported here, with
= 0:5 and C = 8.
j Feature
1 Lexical
2 Jaccard
3 Date
4 ISBN
5 NBN
6 PPN
7 SelSleutel
8 abstract
9 alternative
10 annotation
j Feature
11 author
12 contributor
13 creator
14 dateCopyrighted
15 description
16 extent
17 hasFormat
18 hasPart
19 identifier
20 isVersionOf
j Feature
21 issued
22 language
23 mods:edition
24 publisher
25 refNBN
26 relation
27 spatial
28 subject
29 temporal
30 title
Table I
LIST OF THE FEATURES
IV. EXPERIMENTS
We match the GTT and Brinkman thesauri, which con-
tain 35K and 5K concepts respectively. They are used to
annotate two book collections of the KB, containing 2M
books of which nearly 1M books were annotated, including
307K books with GTT concepts only; 490K with Brinkman
concepts only; 222K with both.
A. Feature selection for similarity calculation
On top of the similarity calculated using book metadata,
as introduced in Section II, we also measured the relative
edit distance as the lexical distance between two concepts.
The Jaccard similarity measure used in [3] is also included.
Note that the Jaccard measure is calculated from dually
annotated books only. If two concepts are never used to
annotate dually indexed books, we set the Jaccard measure
to be the average of all calculated Jaccard measures. The
features used are listed in Table I and all similarity values
are normalised to have zero mean and unit variance in order
to make comparison of i meaningful.
The lexical and Jaccard similarity are of course strong
indicators of concept mappings, and may seem to give arti-
ficially high results for our instance-based method. However,
it is a great advantage that we can include any information
in the features, and let the machine decide on their relative
importance. For reference, Figure 1 includes how the MRF
performs when these two features are removed (“MRF 3-
30”). It shows that we still obtain quite good results from
the instances only, although the best results are obtained with
the combination (“MRF 1-30”).
B. Control-Experiment: Quality of Learning
First, we used human labelled pairs to carry on 10-fold
cross validation in order to check validity of our learned
mappings. These pairs of concepts were judged by a human
evaluator who assigned a “mapping” or “non-mapping” label
to each pair of concepts. The similarity between these pairs
of concepts were calculated as introduced above. The whole
data set was divided into 10 folds, each time using 9 folds
to train the probabilistic model and the remaining fold to
test the model.

0
0.2
0.4
0.6
0.8
1
Precision Recall F-measure
MRF 1-30
MRF 3-30
ES
SVM
0
0.2
0.4
0.6
0.8
1
Precision Recall F-measure
Figure 1. Precision, recall and F-Measure for mappings with a positive
label (top) and a negative label (bottom). Error bars indicate one standard
deviation over the 10 folds of cross-validation.
In the testing step, the predicted mappings were compared
with the real mappings. The positive precision is the propor-
tion of real mappings among all predicted positive mappings,
and the positive recall is the proportion of true predicted
mappings among all real mappings. The negative precision
is the proportion of the non-mappings among all predicted
negative mappings and the recall is the proportion of the
predicted non-mappings among all non-mappings. Figure 1
shows the performance of the three classifiers. These show to
be generally quite good for the MRF and ES methods, with
performances comparable to the results of state-of-the-art
mappers [12]. Our deployment of SVM generally performs
worse than MRF and ES. One possible reason for this may
be the tuning of the parameters
and C. Another reason
may be our choice of the RBF kernel which is perhaps
not optimal for this problem. However, those results clearly
show that our chosen classifier are highly competitive and
perform favorably wrt. state of the art matching tools.
C. Relative importance of features
An important benefit of our first two methods is that
the solutions are interpretable by humans. In an attempt
to work out which features of our instances are important
for mapping, we explored whether the value of i reflects
the intuitive importance of feature i. Figure 2 depicts how
the weights (the values of ) varied over the 10 folds of
cross-validation for the MRF and ES classifiers, as well as
the mutual information between the mapping label and each
similarity feature.
A first observation is that ES lambdas are not really
conclusive: the 10 solutions are much less consistent than
MRF ones. Reassuringly, however, ES lambdas that are most
inconclusive correspond to the least informative features (as
shown by the mutual information). Focusing on the MRF,
then, we can observe that apart from a few exceptions,
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Av
er
ag
e
va
lue
(+
-st
d d
ev
iat
ion
)
Index of lambda, MRF
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Index of lambda, ES
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Av
er
ag
e
va
lue
Index of feature, Mutual Information
Figure 2. Values of  and mutual information between features and labels
important features in terms of mutual information are as-
sociated to large weights, while unimportant features are
normally associated to small weights. Notice in that respect
that feature 1 is a distance measure, while all other features
are similarity measures. Some less informative features still
have large weights (e.g., feature 25), however. This may
be explained by the fact that the mutual information was
computed independently for all features. A feature may be
completely random overall, yet be informative conditionally
on some other feature. The combination of such features will
still be informative and result in larger weights. Similarly,
a feature may be very informative by itself, yet not provide
any supplementary value (and may even be detrimental) if
another feature already provides the same information, thus
explaining some features with high mutual information have
low weights.
A more detailed examination of the weights allows us to
compare the learnt importance of features with the intuitions
provided by the application context. A first set of features
has large weights as expected, such as the similarity between
the concept labels (feature 1), their co-occurrence in the set
of dually-annotated books (feature 2) and the subject (feature
28). A few features are expected not to play a significant role
and have indeed low importance: size of the book (16), (rare)
format description (17) and language (22), for instance.
Some features, more surprisingly, were given an impor-
tance level that conflicts with what one could have antici-

pated: description (15) and abstract (8), which give readable
descriptions of book content, happen to be only marginally
important, less than for example the date of copyright (14).
The latter, for instance, may mirror phenomena like the
publication of a number of books on the same subject in
short periods of time or, perhaps, that some concepts are
used a lot for a short period, and much less before and after
that period.
This last category illustrates how learning can help mak-
ing decisions in dubious cases. For instance, it is well known
that book titles (30) do not always cover their subject en-
tirely. Our experiments demonstrate that similarity between
these rather hints at conceptual dissimilarity — even though
this is less clear for the alternative titles (9). Similarly, two
books may refer to different subjects while being written by
the same author(s). This is especially true when homonymy
is not dealt with. — creator, author, contributors, respectively
11, 12, 13 — or published by the same publisher (24).
This observation tends to show that when many different
description features interact, there is no systematic correla-
tion between what a learning method could find and what
an application expert may anticipate. And in such cases it
is highly valuable, for tuning mappers exploiting instance
similarities, to apply learning techniques instead of relying
solely on human judgement.
V. CONCLUSION
In this paper, we take the instance-based mapping tech-
nique one step further and investigate what instance features
are important in this context. Our analysis has shown that
the overall similarity of instances is too coarse a measure:
the similarity of some features is very indicative of a valid
mapping while some are not and, even worse, the similarity
of some instance features actually indicates concept dissim-
ilarity.
Two different machine learning techniques are used to
automatically identify meaningful features. Both methods
assign mostly consistent importance to the features, which
agrees with the domain characteristics of the data.
The two classifiers we propose, the MRF and the ES,
result in a performance in the neighbourhood of 90%,
showing the validity of the approach. Their performance is
not significantly different, but both significantly outperform
the SVM, an off-the-shelf classifier.
In the future, we would like to investigate how instance
similarity can be used to infer multi-concept mappings (n
to m mappings). We would also like to learn the type of
mapping (for example “broader than,” “narrower than,” as
defined in the SKOS standard [13]), using multiple labels in
the classification process.
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