September 5-7 , Trento

1. International Conference on Cooperative Information Systems (CoopIS 2001) Deriving “sub-source” similarities from heterogeneous, semi-stuctured information sources D. Rosaci, G. Terracina,D. Ursino Dipartimento di Informatica, Matematica, Elettronica e Trasporti Università “Mediterranea” di Reggio Calabria September 5-7, Trento

2. Motivations Scheme Match:Finding a mapping between those elements of two schemes that semantically correspond to each other Applications:information source integration, e-commerce, scheme evaluation and migration, data and web warehousing, information source design and so on They aimed at deriving terminological and structural relationships between single concepts The need of semi-automatic techniques for carrying out this task is nowadays recognized Most of the techniques for Scheme Match proposed in the literature have been designed only for databases

3. Motivations New approaches to Scheme Match,handling semi-structured information sources,appear to be compulsory Such approaches must besomehow differentfrom the traditional ones since: • in semi-structured information sourcessignificant pieces of information are expressed in the form of groups of concepts rather than single ones • different instancesof the same concept could havedifferent structures The emphasis shifts away from the extraction of semantic correspondencies between concepts to thederivation of semantic correspondencies between groups of concepts

4. General characteristics of the approach We propose a semi-automatic technique for extracting similarities between sub-sources belonging to different, heterogeneous and semi-structured information sources The adoption of a conceptual model, capable to uniformly handle information sources of different formats, appears to be extremely useful Translation rules should be defined from classical information source formats to the adopted conceptual model Our approach exploits the SDR-Network conceptual model which meets the requirements described above

5. General characteristics of the approach Given an information source IS, the number of possible sub-sources that can be derived from it is extremely high In order to avoid handling huge numbers of sub-source pairs, we propose an heuristic technique for singling out only the most promising ones The similarity degree associated to each pair of sub-sources is determined by computing the objective function associated to a maximum weight matching After that the most promising pairs of sub-sources have been selected, their similarity degree must be computed SSi can be detected to be similar to SSj only if it possible to single out concepts of SSi and SSj that are pairwise similar in their turn

6. General characteristics of the approach The SDR-Network and its metrics have been already exploited for defining a technique for deriving synonymies and homonymies In the whole, we propose a unified, semi-automatic approach for deriving concept synonymies and homonymies, as well as sub-source similarities • We are proposing the derivation of a property which, generally, is not handled by most of the approaches for Scheme Match proposed in the literature • The technique proposed here is part of a more general framework for deriving various kinds of terminological and structural properties This is particularly interesting since:

7. The SDR-Network conceptual model • Given an information source IS, the associated SDR-Network Net(IS) is Net(IS) = < NS(IS), AS(IS) > • NS(IS) represents the set of nodes; each node is characterized by a name • AS(D) denotes a set of arcs; each arc can be represented by a triplet < S, T, LST > • S is thesource node • T is thetarget node • LST = [dST, rST] is alabelassociated with the arc

8. The SDR-Network conceptual model • dST is thesemantic distance coefficient: • it indicates how much the concept expressed by T is semantically close to the concept expressed by S • this depends from the capability of the concept associated with T to characterize the concept associated with S • rST is thesemantic relevance coefficient:it indicates the fraction of instances of the concept denoted by S whose complete definition requires at least one instance of the concept represented by T

9. The SDR-Network conceptual model • The Path Semantic Distance PSDP of a path P in Net(IS) is the sum of the semantic distance coefficients associated with the arcs included in the path • The Path Semantic Relevance PSRP of a path P in Net(IS) is the product of the semantic relevance coefficients associated with the arcs included in the path • The CD-Shortest-Path (Conditional D-Shortest-Path) between two nodes N and N’ in Net(IS) and including an arc A (denoted by  N, N’ A) is the path having the minimum Path Semantic Distance among those connecting N and N’ and including A • A D-Pathn is a path P in Net(IS) such that n  PSDP < n+1 • The i-th neighborhood of an SDR-Network node x is: • nbh(x,i) = {A|AAS(IS), A=<z,y,lzy>, x,yA is a D_Pathi, xy} i0

10. Selection of promising pairs of sub-sources The number of possible sub-sources that can be identified in IS is exponential in the number of nodes of Net(IS) We have defined a technique for singling out the most promising pairs of sub-sources The proposed technique receives two information sources IS1 and IS2 and a Dictionary SD of Synonymies between nodes of Net(IS1) and Net(IS2) Synonymies are represented in SD by tuples of the form <Ni, Nj, fij>, where Ni and Nj are the synonym nodes and fij is a coefficient in the real interval [0,1], indicating the similarity degree of Ni and Nj

11. Selection of promising pairs of sub-sources • The technique works according to the following rules: • It considers those pairs of sub-sources [SSi, SSj] such that SSiNet(IS1) is a rooted sub-net having a node Ni as root, SSj  Net(IS2) is a rooted sub-net having a node Nj as root, Ni and Nj are interesting synonyms i.e., the synonym coefficient associated with them is greater than a certain threshold • It computes the maximum weight matching on some suitable bipartite graphs obtained from the target nodes of the arcs included in the neighborhoods of Ni and Nj • Given a pair of synonym nodes Ni and Nj, it derives a promising pair of sub-sources [SSik,SSjk], for each k such that both nbh(Ni,k) and nbh(Nj,k) are not empty • SSik and SSjk are constructed by determining the promising pairs of arcs [Aik,Ajk] such that Aik nbh(Ni,l), Ajk nbh(Nj,l), for each l belonging to the integer interval [0,k]

12. Selection of promising pairs of sub-sources • A pair of arcs [Aik,Ajk] is considered promising if • An edge between the target nodes Tik of Aik and Tjk of Ajk is present in the maximum weight matching computed on a suitable bipartite graph constructed from the target nodes of the arcs of nbh(Ni,l) and nbh(Nj,l) for some l belonging to the integer interval [0,k] • The similarity degree of Tik and Tjk is greater than a certain given threshold • The rationale underlying this approach is that of constructing promising pairs of sub-sources such that each pair consists in the maximum possible number of pairs of concepts whose synonymy has been already stated

13. Selection of promising pairs of sub-sources • Theorem • Let IS1 and IS2 be two information sources and let Net(IS1) and Net(IS2) be the corresponding SDR-Networks. Let nc1 (resp., nc2) be the number of complex nodes of Net(IS1) (resp., Net(IS2)). Let l be the maximum neighborhood index associated with a node of Net(IS1) or Net(IS2). Then the number of possible pairs of sub-sources is min(nc1,nc2)x(l+1) • Actually, in real applications, the number of promising pairs of sub-sources relative to IS1 and IS2 is, generally, far lesser than min(nc1,nc2)x(l+1)

14. Example The SDR-Network of the European Social Funds (ESF) information source

15. Example The SDR-Network of European Community Projects (ECP) information source

16. Example The Synonymy Dictionary associated with ESF and ECP

17. Example • The interesting pairs of synonym nodes are {<Judicial Person[ESF], Partner[ECP], 0.59>, <Payment[ESF], Payment[ECP], 0.65>, <Project[ESF], Project[ECP], 0.63>} • As an example, consider the pair of synonym nodes Project[ESF] and Project[ECP] • Since the neighborhoods of Project[ESF] and Project[ECP] are both not empty only for k=0, k=1 and k=2, our technique obtains three promising pairs of sub-sources relative to Project[ESF] and Project[ECP] • In order to provide an example of the behaviour of our technique, we show the derivation of the promising pairs of sub-sources associated with Project[ESF] and Project[ECP] for k=0

18. Example • The bipartite graph and the associated maximum weight matching are

19. Example • The technique selects only those arcs of nbh(Project[ESF],0) and nbh(Project[ECP],0) which participate to the matching and have a similarity coefficient greater than a certain given threshold • The promising pair of sub-sources associated with nbh(Project[ESF],0) and nbh(Project[ECP],0) is [SS1, SS2]: • SS1 = { < Project[ESF], Country[ESF], [0,1]>, Project[ESF], Type[ESF], [0, 0.9]>, <Project[ESF], ESF_Contribution[ESF], [0, 0.75]>, <Project[ESF], Country_Share[ESF], [0,0.9]>} • SS2 = { < Project[ECP], Country[ECP], [0,1]>, Project[ECP], Type[ECP], [0, 0.6]>, <Project[ECP], ESF_Contribution[ECP], [0, 0.8]>, <Project[ECP], Country_Share[ECP], [0,1]>} • The technique works analogously for k=1 and k=2 as well as for the other interesting synonym pairs

20. Derivation of sub-source similarities • The technique for deriving sub-source similarities from a given pair of information sources consists of two steps • The first one computes the similarity degree relative to each promising pair of sub-sources derived previously • The second one constructs a Sub-source Similarity Dictionary SSD by selecting only those pairs of sub-sources whose similarity degree is greater than a certain, dinamically computed, threshold • More formally, the technique can be encoded as follows: SSD = ((SPS,SD)) • where: • SPS is the set of promising pairs of sub-sources • SD is the Synonymy Dictionary

21. Derivation of sub-source similarities • For each promising pair of sub-sources SSi and SSj, the function  calls a function ’ which computes the corresponding similarity degreeSSS =  (SPS, SD) = { < SSi, SSj, ’(SD, ’(SSi), ’(SSj))> | [SSi, SSj] SPS} • The function ’ receives a rooted sub-net SS and returns the nodes of SS • The function ’ derives the similarity degree associated with SSi and SSj by computing a suitable objective function associated with the maximum weight matching on a bipartite graph, constructed from the nodes of SSi and SSj’ (T,P,Q) = (1 – ((|P|+|Q|-2|E’|)/(|P|+|Q|)) x (’(E’)/|E’|)

22. Derivation of sub-source similarities • The function  is called for constructing the Sub-source Similarity Dictionary SSD by taking those similarities of SSS having a coefficient greater than a certain, dynamically computed, threshold SSD =  (SSS) = {<SSi, SSj, fij> | <SSi, SSj, fij>  SSS, fij>thSim} • Here thSim is the dinamically computed threshold thSim = min ((FMax+FMin)/2, thM) • where • FMaxis the maximum coefficient associated with the similarities of SSS • FMinis the minimum coefficient associated with the similarities of SSS • thMis a limit threshold value

23. Example • Consider the SDR-Networks ESF and ECP SSD = ((SPS,SD)) • As for the pair of sub-sources [SS1, SS2]  SPS derived previously,  calls ’(SD, ’(SS1), ’(SS2)) • The bipartite graph and the associated maximum weight matching relative to ’(SS1) and ’(SS2) are

24. Example • The objective function associated to the maximum weight matching is (1 – ((5+5-2*5)/10))*(0.63+1+1+1+1)/5=0.93 • In the same way the similarity degrees associated with all the other promising pairs of sub-sources are obtained • Then SSS is provided in input to the function  which constructs the Sub-source Similarity Dictionary SSD • SSD is determined by selecting those triplets of SSS whose similarity coefficient is greater than thSim • In this example all similarities of SSS are valid and SSD = SSS

25. Applications Sub-source similarities can be exploited in several contexts All applications of Scheme Match relative to synonymies between single concepts can be extended to similarities between sub-sources Information Source Integration E-commerce In particular, sub-source similarities can be exploited for: Semantic Query Processing Data and Web Warehouse Source clustering and cataloguing

26. Conclusions We have presented a semi-automatic technique for deriving similarities of sub-sources belonging to information sources having different formats The technique is based on a conceptual model, called SDR-Network, which allows to uniformly represent information sources of different formats We have pointed out that the derivation of sub-source similarities is a special case of the more general problem of Scheme Match It consists of two steps: the first one selects a set of promising pairs of sub-sources, whereas the second one computes a similarity degree to associate with each pair of the set Finally, we have illustrated a set of applications which could benefit of sub-source similarities

27. Present and Future Work • We have already designed an approach which exploits sub-source similarities for carrying out information source integration • In the future we plan to: • Develop techniques which exploit sub-source similarities in the other possible application contexts we have previously mentioned • Define techniques for deriving other terminological and structural properties in the context of semi-structured information sources

28. For more information... Domenico Ursino Dipartimento di Informatica, Matematica, Elettronica, Trasporti Università Mediterranea di Reggio Calabria E-mail: ursino@ing.unirc.it Web: http://www.ing.unirc.it/didattica/inform00/gruppo