Colloque avec actes et comité de lecture. internationale.International audienceThis paper is concerned with the modelling of maps with conceptual graphs for the design of a knowledge-based system. We first describe the maps, which are synthetic descriptions of farm territories. We then explain the modelling principles we have used: the spatial objects of the map and the relations are represented into concepts linked with arcs. The reasoning principle of the system are briefly described. We finally focus on an example of graph comparison

Le Ber, Florence

Metzger, Jean-Luc

Napoli, Amedeo

INRIA a CCSD electronic archive server

HAL Id: inria-00107555https://hal.inria.fr/inria-00107555Submitted on 19 Oct 2006HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Modelling and comparing maps with graphsFlorence Le Ber, Jean-Luc Metzger, Amedeo NapoliTo cite this version:Florence Le Ber, Jean-Luc Metzger, Amedeo Napoli. Modelling and comparing maps with graphs.ECAI Workshop on Spatial and Temporal Reasoning, Jul 2002, Lyon, France, 4 p. ￿inria-00107555￿Modelling and comparing maps with graphsFlorence Le Ber, Jean-Luc Metzger, and Amedeo NapoliLORIA UMR 7503, BP 239, 54506 Vandœuvre-l̀es-Nancy, FrancePhone: 33 3 83 59 20 00, Fax: 33 3 83 41 30 79E-mail: {leber,metzger,napoli}@loria.frAbstract: This paper is concerned with the modelling ofmaps with conceptual graphs for the design of a knowledge-based system. We first describe the maps, which are syn-thetic descriptions of farm territories. We then explain themodelling principles we have used: the spatial objects of themap and the relations are represented into concepts linkedwith arcs. The reasoning principle of the system are brieflydescribed. We finally focus on an example of graph com-parison.Keywords: graphs, similarity measure, hierarchies ofspatial relations, spatial structures, agronomy.IntroductionIn a previous work, we have used topological relations torecognize landscape patterns on satellite images [8, 7]. Weare now interested in the qualitative description of farm spa-tial organizations. We presently work with agronomists todevelop a knowledge-based system that could help them an-alyze the relationship between farm spatial organization andfunctioning. Understanding this relationship is importantfor the good management of several environmental prob-lems like water pollution, soil erosion or landscape changes.Thus, the agronomists use special maps of farm territories,calledchoremes1, that express both the spatial organizationand the functioning of the farms considered [6]. We havedecided to use graphs for modelling and comparing thesemaps. Our aim is to build a case-based explanation systemto help analyze a farm spatial organization and functioningfrom previously analyzed cases.This paper is organized as follows. The first part de-scribes the maps and the way they are modelled with graphs.The second part gives the reasoning principles used in oursystem. The third part focuses on the computation of simi-larity between graphs.1 Modelling maps with graphsAn example of a choreme which represents the spatial or-ganization and functioning of a farm in Lorraine is shownin Figure 1. Several objects are represented: a town, a vil-lage, a river, a wood, two roads, pastures and crop fields.Icons are used to point out particular situations or roles ofthe objects. Agronomists interpret the spatial organizationof these objects with respect to the farm functioning. Forexample, they say that the town is an obstacle for the farmer(since it separates the farm territory in two parts) whereasthe village is not, or that the farmer uses meadow to isolate1 Actually choremes are basic graphical units used to symbolizegeographical patterns. The maps are based on choremes, but theagronomists call themchoremes.crop fields from river and wood for protecting crops fromdampness and shade.We have chosen graphs for modelling the spatial orga-nization of a farm. Graphs are well-suited for representingcomplex real-world objects and for communicating with do-main experts. The graphs we use are inspired from concep-tual graphs [3].In our system, graphs are built with arcs and two kindsof nodes, named s-entities and s-links. A s-entity mod-els a spatial object of the choremes while a s-link mod-els a spatial relation. The s-entities and the s-links canbe qualified by different attributes. The arcs connect s-entities to s-links. They are labelled with the descriptionof the roles of the spatial objects in the relations. For ex-ample, Figure 2 shows a part of the graph associated tothe choreme of Figure 1:wood1, meadow1, cereal1 ares-entities,isolate&border1 is a s-link,isolating andisolated denote the roles of the s-entities into the s-linkisolate&border1. The s-linkisolate&border1 meansthatmeadow1 is between but borderswood1 andcereal1,and thatmeadow1 has a ‘buffer’ function: the cereal field isisolated from the wood thanks to the meadow.isolatingisolatedisolated                border1wood1          isolate&         cereal1meadow1Figure 2. Part of the graph associated to the choreme of figure 1(graph A).2 Reasoning principlesThe purpose of our system is to compare the spatial organi-zation and functioning of farms. The farms previously stud-ied are stored in a case base. The analysis of a new farmis based on the case-based reasoning (CBR) paradigm, thatis, it uses past experiences (called cases) to solve new prob-lems [9]. CBR is based on three main operations: retrieval,adaptation and storage. The goal of retrieval is to find a casesrce in the case base similar to the target problemtgt.Adaptation uses the retrieved casesrce in order to build asolutionSol(tgt) totgt. If the new case (tgt, Sol(tgt))is of interest, it is stored in the case base. Similarity be-tween cases is defined according to domain knowledge andaccording to the characteristics of the current problem.At the moment, we have worked on the retrieval opera-tion and on case representation. In our system, a case is agraph representing a spatial organization associated with afunctional explanation. For instance the graph A of Figure 2and the following explanation“the meadow isolates cropfields from the wood and thus protects crops from dampnessand shade due to the wood”constitute a case.We propose to define the similarity between two casesusing graph properties and a hierarchical representation ofdomain knowledge. In our system, domain knowledge in-cludes agronomic concepts and qualitative spatial relationsand their inter-relations. A part of the hierarchy used is de-scribed in Figure 3. The spatial relations are those used bythe agronomists to describe spatial organization (e.g. sep-arate, isolate, near, far, cross over, etc.), i.e. they includespatial and functional aspects. They are organized accord-ing to the usual spatial relations proposed in the QSR do-main [11, 5, 12]. For instance,Separate andIsolate areconsidered to be sort ofIs-Between relation with differ-ent functional meanings. The relationIsolate&Border, assaid before, is a combination of the relationsBorder andIsolate. The relationBorder is itself a kind of the topo-logical relationEC, where the regions share a line rather thana single point.The cases and the concept hierarchy are implementedwith the description logic system RACER [4] which is veryexpressive and capable of dealing with concepts as well aswith individuals. In particular, the classification mechanismof RACER is used for graph comparison as shown below.3 Similarity between graphsThe similarity between two graphs is computed with thehelp of anedition distancethat relies on three operations,deletion, addition or substitution of nodes, as proposedin [1]. The substitution of nodes relies on a classificationmechanism acting upon the concept hierarchies. The dele-tion or addition of nodes rely on specific rules. The distancebetween two graphs is evaluated on the basis of the typeand number of operations needed to transform a graph intoanother.Let us take an example. Suppose we want to compare thegraph A of Figure 2 with the graph B described in Figure 4,that represents a field of cereal bordered by a wood.borderingborderingwood2          border2          cereal2Figure 4. Another graph (B).First the nodes of the two graphs are classified accordingto the hierarchy of Figure 3. The nodem adow1 of graphA is classified into the conceptMeadow, while the nodescereal1 and cereal2 of graph B are classified into theconceptCereal. The nodeswood1 andwood2 are classi-fied into the conceptWood. The nodeborder2 is classifiedinto the conceptBorder and the nodeisolate&border1 isclassified into the conceptIsolate&Border that is a sub-concept ofIs-Between.The next step is to match the nodes of the twographs:cereal1 and cereal2 can be matched as theybelong to the same concept;wood1 and wood2 can bematched for the same reason;meadow1 could be matchedwith cereal2 as they belong to the same super-conceptAgricultural-Land, but the matching ofcereal1 andcereal2 is better; on the contrary,wood1 andcereal2 can-not be matched as woods and cereals have completely dif-ferent function in the farms considered. The matchings areevaluated according to the distance between concepts w.r.tthe hierarchy.Finally, the problem is to match the s-linkborder2that represents a binay relation with the s-linkisolate&border1 that represents a ternary relation.This is done as follows. First the nodesmeadow1 andcereal1 can be classified into the same super-conceptAgricultural-Land. Furthermore, as the relationIsolate&Border is a kind of Is-Between relation, thefollowing rule can be applied:if a regionb is between andborders two regionsa andc, andb can be assimilated toaor c, then the two regionsa andc border each other. Thus,the two nodesmeadow1 and cereal1 are substituted byonly one nodeagri-land1, the nodeisolate&border1is deleted and a new nodeborder1 is created that connectsagri-land1 andwood1. Finally the graph A is transformedinto the new graph A’ (Figure 5).bordering borderingwood1           border1         agri-land1Figure 5. The new graph A’ transformed from A.In graph B, the nodecereal2 can be classified into thesuper-conceptAgricultural-Land and thus can be sub-stituted with a nodeagri-land2. The resulting graph B’ isidentical to graph A’. The distance between A and B can beevaluated according to the operations used to transform Ainto A’ and B into B’, that is a substitution (of two nodes byone node), a deletion and a creation on the one hand, and asubstitution on the other hand. The sequence of the opera-tions used to transform a graph into another graph defines asimilarity path, that can be used in CBR for the adaptationoperation [10]. In our example, the explanation associatedto graph A should be adapted into a new explanation asso-ciated to graph B, e.g.,“crop fields are not isolated from thewood and thus crops are not protected from dampness andshade due to the wood”.It should be noticed that a graph C representing a woodbordering a meadow can be compared with B with fewertransformations and can lead to another explanation. A ma-jor problem is thus to choose the good matching betweengraphs or to combine the results of several matchings.SummaryThis paper presents a preliminary work done on the designof a case-base explanation system for helping agronomistsanalyze the relationship between farm spatial organizationand functioning. In our system, a case is a graph represent-ing (part of) a farm spatial organization associated with afunctional explanation. The reasoning principle is to use thepast cases to help the analysis of a new case. The retrievaloperation is based on graph similarity that is computed withthe help of an edition distance.Graphs are described with agronomic spatial objects andspatial and functional relations. The matching between twographs relies on domain knowledge and on spatial infer-ences. This paper gives an example of the knowledge andinferences used, but there is still a lot of work to be done,especially to define general rules for matching spatial struc-tures and then for adapting functional explanations.REFERENCES[1] H. Bunke and B.T. Messmer, ‘Similarity Measures for Struc-tured Representations’, inProceedings of the First EuropeanWorkshop on Case-Based Reasoning (EWCBR’93), Kaiser-slautern, eds., M.M. Richter, S. Wess, K.-D. Althoff, andF. Maurer, pp. 26–31, (1993).[2] M. Capitaine, ‘Graphical representation of farm spatial or-ganisation in Lorraine’. INRA Internal Document, 2001.[3] M. Chein and M.-L. Mugnier, ‘Conceptual graphs: Funda-mental notions’,Revue d’Intelligence Artificielle, 6(4), 365–406, (1992).[4] V. Haarslev, R. M̈oller, and A.-Y. Turhan. Racer user’s guideand reference manual. Hamburg Universität, 2001.[5] D. Herńandez,Qualitative Representation of Spatial Knowl-edge, LNAI 804, Springer-Verlag, 1994.[6] S. Lardon, C. Capitaine, and M. Benoı̂t, ‘Les mod̀elesgraphiques pour représenter l’organisation spatiale des ac-tivit és agricoles.’, inRepŕesentations graphiques dans lessyst̀emes complexes naturels et artificiels. Journées deRochebrune, pp. 127–150. ENST, (2000).[7] F. Le Ber, L. Mangelinck, and A. Napoli. Design and com-parison of lattices of topological relations for spatial repre-sentation and reasoning. INRIA Research Report RR-4321,2001. 57 pages.[8] F. Le Ber and A. Napoli, ‘Representation of spatial rela-tions and structures in object-based knowledge representa-tion systems’, inECAI Workshop on Current Issues in Spatio-Temporal Reasoning, ed., R. V. Rodŕıguez, pp. 81–86, Berlin,(2000).[9] Case-Based Reasoning. Experiences, Lessons, & Future Di-rections, ed., D. B. Leake, AAAI Press / The MIT Press,1996.[10] J. Lieber and A. Napoli, ‘Correct and Complete Retrieval forCase-Based Problem-Solving’, inProceedings of the 13thEuropean Conference on Artificial Intelligence (ECAI’98),Brighton, UK, ed., H. Prade, pp. 68–72. John Wiley & SonsLtd., (1998).[11] D. A. Randell, Z. Cui, and A. G. Cohn, ‘A Spatial Logicbased on Regions and Connection’, in3rd International Con-ference on Principles of Knowledge Representation and Rea-soning, pp. 165–176. Morgan Kaufmann Publishers, (1992).[12] L. Vieu, ‘Spatial Representation and Reasoning in Artifi-cial Intelligence’, inSpatial and Temporal Reasoning, ed.,O. Stock, 5–42, Kluwer Academic Publishers, (1997).Figure 1. A choreme representing the spatial organization and functioning of a farm in Lorraine (east of France) [2].TOPAGRONOMIC-OBJECT SPATIAL-RELATIONSURFACE LINEWOOD AGRICULTURAL-LANDGRASSLAND CROPLANDBINARY-RELATION TERNARY-RELATIONPO EC DCBORDERIS-BETWEENISOLATE SEPARATEPASTURE MEADOW CEREALRIVER ROADISOLATE&BORDERFigure 3. Part of the concept hierarchy designed for the representation of agronomic knowledge and spatial relations.

Modelling and comparing maps with graphs

Hal-Diderot

HAL Descartes

https://hal.inria.fr/inria-00107555/document

Modelling and comparing maps with graphs

Abstract

Similar works

Full text

Available Versions

INRIA a CCSD electronic archive server

Hal-Diderot

HAL Descartes