=Paper=
{{Paper
|id=Vol-344/paper-7
|storemode=property
|title=Probabilistic Metamodel Merging
|pdfUrl=https://ceur-ws.org/Vol-344/paper7.pdf
|volume=Vol-344
|authors=Robert Lagerstrom,Moustafa Chenine,Pontus Johnson,Ulrik Franke
|dblpUrl=https://dblp.org/rec/conf/caise/LagerstromCJF08
}}
==Probabilistic Metamodel Merging==
https://ceur-ws.org/Vol-344/paper7.pdf
Probabilistic Metamodel Merging
Robert Lagerström1, Moustafa Chenine1, Pontus Johnson1, and Ulrik Franke1
1
The Royal Institute of Technology, Industrial information and control systems, Osquldas
v.12, 10044 Stockholm, Sweden
{robertl, moustafac, pj101, ulrikf}@ics.kth.se
Abstract. This paper proposes the use Bayesian networks for the automatic
merging of metamodels. The proposed Bayesian networks calculate the
probability that a merge of two metamodel elements is suitable, thus suggesting
what to merge.
Keywords: Metamodel merging, Bayesian networks.
1 Introduction
In recent years, both researchers and practitioners have discovered the emerging
possibilities of using metamodels and ontologies. As a consequence, a large quantity
of metamodels and ontologies now exists within all sorts of different applications.
The distributed environment of metamodel and ontology development has led to large
overlaps within and between metamodels. Since these diverse metamodels often
describe similar aspects of systems, developers and users would gain large benefits if
metamodels could easily be merged and aligned with each other. Therefore,
integration and merging of metamodels and ontologies has received an increasing
interest lately [1][2].
This paper proposes an approach to metamodel merging where a probabilistic
inference engine is employed to evaluate candidate metamodel concepts suitable for
merging. The proposed approach uses Bayesian networks to assess the probability
that a merge of two elements is suitable. The Bayesian network evaluates a merge
based on various syntactic and semantic characteristics of the candidate concepts,
such as the similarity of names and associations to other concepts.
The concepts described in this paper all pertain to a certain type of metamodels
called abstract models. Abstract models have previously been proposed as a notation
for describing and analyzing enterprise systems [3]. The models represent the
architectures of these systems as well as other expert knowledge and empirical
observations that can be instantiated and used for analysis. An abstract model contains
classes and class associations, augmented with attributes and attribute associations. A
UML description of abstract models can be seen in Fig. 1.
26 Proceedings of CAiSE’08 Forum
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Fig. 1. UML description of abstract models.
2 Merging Metamodels using Bayesian Networks
A Bayesian network, B=(G, P), is a representation of a joint probability
distribution, where G=(V, E) is a directed acyclic graph consisting of vertices, V, and
edges, E. The vertices denote a domain of random variables X1,…, Xn, also called
chance nodes. Each chance node, Xi, may take on a value xi from the finite domain
Val(Xi). The edges denote causal dependencies between the nodes, i.e. how the nodes
relate to each other. The second component, P, of the network B, describes a
conditional probability distribution for each chance node, P(Xi), given its parents
Pa(Xi) in G. More comprehensive treatment on Bayesian networks can be found in
e.g. Jensen [4].
When merging abstract models, there are two concerns. Firstly, do any of the
classes in the source models represent the same concepts? Secondly, when two classes
have been merged, do any of the attributes in the merged class represent the same
concepts? If these two concerns are correctly handled, then all associations separately
holding in the source models will also be correctly transferred into the target model.
Therefore, two Bayesian networks were developed; one describing class merges and
one describing attribute merges, c.f. Fig. 2.
The nodes in the class merge network have the following scales: Class Merge =
{Yes, No}, Class Similarity Association = {Yes, No}, Class Names = {Identical,
Similar, Dissimilar}, Class References = {SamePublication, SameAuthor,
DifferentAuthors}, Class Attributes = {All, Some, None}, and Class Associations =
{All, Some, None}.
The nodes in the attribute merge network have the following scales: Attribute
Merge = {Yes, No}, Attribute Similarity Association = {Yes, No}, Attribute Names =
{Identical, Similar, Dissimilar}, Attribute References = {SamePublication,
SameAuthor, DifferentAuthors}, and Attribute Associations = {All, Some, None}.
Proceedings of CAiSE’08 Forum 27
Fig. 2. Bayesian networks representing class and attribute merge.
To illustrate the application of the Class Merge network c.f. the Bayesian network
screenshot from GeNIe [5] in Fig. 3.
Fig. 3. The Bayesian network for class merges with example values.
Assume that a package, i.e. a set of abstract models, contains the abstract models
presented in Fig. 4.
Fig. 4. Abstract models to be tested for possible merges.
The method starts by comparing the pairs of classes from the models presented in
Fig. 4. Then, the classes with the highest probability are merged. In this example, the
class pair Documentation and Document received the probability P = 100 %, and are
therefore merged.
28 Proceedings of CAiSE’08 Forum
The next step is to compare all pairs of attributes in the merged class
Documentation. Then, the attributes with the highest probability are merged. In this
example, the pair Readability and Readability received the probability P = 100 %, and
are therefore merged.
It all starts over from the beginning by comparing all pairs of classes and iterates
until no classes receive probabilities over a predefined merging threshold. The
resulting model in this example is presented in Fig. 5.
[1]s
Affect
Influences [1][2]
[2]
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Influe
Affects [1][2]
Fig. 5. The resulting abstract model after employing the proposed Bayesian networks.
4 Conclusions
This paper addresses the issue of metamodel merging, using the probabilistic
framework of Bayesian networks. It was shown that Bayesian networks can be used
to guide the merging of metamodels, by considering some key features of the classes
and attributes at hand: basically their names, references, and associations. With this
information it is possible to discern the probability that the concepts are sufficiently
similar to be merged.
References
1. Noy, N., Musen, M.A.: The PROMPT suite: interactive tools for ontology merging and
mapping. Internationl Journal of Human-Computer Studies, Vol. 59, No 6, p. 983-1024
(2003)
2. Doan, A., Madhaven, J., Domingos, P., Halevy, A.: Learning to map between ontologies on
the semantic web. In the proceedings of the 11th International Conference on World Wide
Web (2002)
3. Johnson, P., Johansson, E., Sommestad, T., Ullberg, J.: A Tool for Enterprise Architecture
Analysis, In Proceedings of the 11th IEEE International Enterprise Distributed Object
Computing Conference (EDOC), Vol. 11, Annapolis USA (2007)
4. Jensen, F.: Bayesian Networks and Decision Graphs. Springer-Verlag (2001)
5. GeNIe: Decision System Laboratories, About GeNIe and SMILE, University of Pittsburgh,
http://genie.sis.pitt.edu/about.html (2007)