AUTOMATICALLY AND ACCURATELY MATCHING OBJECTS IN GEOSPATIAL DATASETS

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1 AUTOMATICALLY AND ACCURATELY MATCHING OBJECTS IN GEOSPATIAL DATASETS L. Li a, *, M. F. Goodchild a a Dept. of Geography, Uiversity of Califoria, Sata Barbara, CA, US - (lia, good)@geog.ucsb.edu KEY WORDS: Object Matchig, Liear Programmig, Assigmet Problem, Optimizatio, Greedy ABSTRACT: Idetificatio of the same object represeted i diverse geospatial datasets is a fudametal problem i spatial data hadlig ad a variety of its applicatios. This eed is becomig icreasigly importat as extraordiary amouts of geospatial data are collected ad shared every day. Numerous difficulties exist i gatherig iformatio about objects of iterest from diverse datasets, icludig differet referece systems, distict geeralizatios, ad differet levels of detail. May research efforts have bee made to select proper measures for matchig objects accordig to the characteristics of ivolved datasets, though there appear to have bee few if ay previous attempts to improve the matchig strategy give a certai criterio. This paper presets a ew strategy to automatically ad simultaeously match geographical objects i diverse datasets usig liear programmig, rather tha idetifyig correspodig objects oe after aother. Based o a modified assigmet problem model, we formulate a objective fuctio that ca be solved by a optimizatio model that takes ito accout all potetially matched pairs simultaeously by miimizig the total distace of all pairs i a similarity space. This strategy ad widely used sequetial approaches usig the same matchig criteria are applied to a series of hypothetical poit datasets ad real street etwork datasets. As a result, our strategy cosistetly improves global matchig accuracy i all experimets. 1.1 Motivatio 1. INTRODUCTION High-quality data are always the prerequisite for meaigful aalyses. Sice o sigle geographical dataset is a complete ad accurate represetatio of the real world, we usually require data from diverse sources i scietific research ad problem solvig. I a particular geographical applicatio, we eed to obtai data from multiple sources that represet differet properties of objects of iterest. Ulike old days whe research was impeded due to lack of data, rapid developmet of techologies for data collectio ad dissemiatio creates abudat opportuities for maipulatig ad aalyzig geographical iformatio. However, it is ot always straightforward to take advatage of large volumes of geospatial data because data created by differet agecies are usually based o differet geeralizatio schemes, usig differet scales, ad for differet purposes. As it is impossible to directly collect all data by ourselves, we ofte eed to utilize secodary data sources. Thus it is usually ievitable to combie multi-source data i sciece, decisiomakig, ad everyday life. For example, i a emergecy such as Jesusita Fire i Sata Barbara, effective evacuatio requires itegrative geospatial iformatio about the affected area, probably icludig DEM, lad use, residece ad facility locatios. Aother typical applicatio is the creatio of a itegrated database from two iput datasets. It is possible that oe dataset has all ecessary features ad attributes, but the other oe bears a higher accuracy of positios. For istace, we have a old street etwork stored as vector data, ad a recet remote sesig image that covers the same area. After extractig streets i the image, we wat to idetify the same streets i the outdated vector database i order to improve its positioal accuracy. I all these cases, accurate idetificatio of objects that represet the same etity i reality is a essetial prerequisite to further aalyses. 1.2 Objective Object matchig ca be divided ito two steps: the first step is to defie a proper similarity measuremet betwee objects, ad the secod step is to search for matched pairs based o this measuremet. This paper focuses o the secod step of this procedure by providig a ew strategy for matchig objects i multiple sources give a certai criterio. Rather tha adoptig a sequetial matchig procedure that is widely used i existig literature, we propose a matchig algorithm accordig to a optimizatio model by regardig object matchig as a assigmet problem. I the remaider of this paper, Sectio 2 discusses two types of methods for object matchig: widely used greedy method ad proposed optimizatio method. I sectio 3, we describe two sets of data used i our experimets for a compariso betwee two methods. I sectio 4, we preset the percetage of correctly matched pairs usig differet methods, followed by some coclusios i sectio Related Work Object matchig i geospatial datasets has bee a fudametal research problem for decades. Most efforts have focused o the defiitio of similarity betwee objects. If two objects i differet datasets are similar i terms of positios, shapes, structures, ad topologies ad so o, it is probable that they represet the same etity i the real world. The similarity metric varies from oe applicatio to aother due to the iheret characteristics of iput data ad the availability of data properties. The most popular similarity measuremet is the proximity betwee objects. Oe typical criterio is the absolute proximity * Correspodig author. 98

2 measured as a distace, such as the Euclidea distace betwee poits or Hausdorff distace betwee polylies (Yua ad Tao, 1999), ad some other distaces i particular applicatios, like the discrete Frechet distace (Devogele, 2002) ad radial distace (Bel Hadj Ali, 1997). The Hausdorff distace has bee proved proper i calculatig the proximity betwee liear features (Abbas, 1994). It is defied as the maximum distace of the shortest distaces betwee each poit o oe liear object ad a set of poits costitutig aother polylie. Whe the distace betwee two objects is smaller tha a threshold, they may be regarded as a correspodig pair. I additio to a distace threshold, aother measuremet based o a relative proximity is usually called the earest eighbour pairig. This criterio iteds to fid the earest eighbour of a particular object i the other dataset regardless of its absolute distace. If a object A i the first dataset is the closest object for object A i the secod dataset, ad meawhile object A is the closest oe for object A i the secod dataset, objects A ad A are defied as a matched pair (Saalfeld, 1988; Beeri et al., 2004). Besides proximity, other geometric iformatio is also used i object matchig. For example, matchig betwee street segmets may be reduced to ode matchig sice odes, especially itersectios, are usually take as cotrol poits (e.g. Cobb et al., 1998; Fili ad Doytsher, 2000). The umber ad directios of coectig segmets for a ode are usually used to refie the matched cadidates as a result of proximity criterio (Saalfeld, 1988). The agles betwee two street cetrelies or betwee GPS tracks ad street etworks are also widely used i polylie ad map matchig (Walter ad Fritsch, 1999; Quddus et al., 2003). Aother category of iformatio for object matchig is sematic similarity, icludig two importat cosideratios: similarity betwee geographic types ad similarity betwee idividual geographic objects. I ay dataset that ivolves geographical classes, it is critical to establish a mappig betwee differet classificatio systems because ay classificatio etails loss of iformatio ad usually subjective judgmet. O the other had, similarity betwee geographic objects may be defied accordig to attribute values, either umeric or strig-similarity (Cohe et al., 2003). Hastigs (2008) used both types of sematic similarity - geotaxoomic ad geoomial metrics - i coflatio of digital gazetteers. Furthermore, cotextual iformatio is also helpful for refiig matchig results based o the relatioship betwee ivestigated objects ad its surroudig eviromet. For istace, Fili ad Doytsher (2000) developed a approach called roud-trip walk to take ito accout cotextual iformatio. The couterpart odes at two eds of the arc are called coected odes. Two odes are idetified as matched oly uder the coditio that they are similar eough ad at the same time their coected odes are also similar eough. Whe o explicit cotextual iformatio is available, Samal et al. (2004) proposed proximity graphs as a aid to icorporate cotext whe ladmarks are ot coected with other features by costructig topology amog them. While these differet methods all focus o the defiitio of similarity measuremet i various datasets, few efforts, if there s ay, have bee made to improve the search process ad cosequet matchig results give a selected similarity criterio. Rather tha comparig differet similarity metrics, we propose a ew search strategy that miimizes the global mismatch errors after a certai similarity measure is selected. 2. METHODS Automatic object matchig requires a objective fuctio or a series of fuctios, the solutios to which lead to matched pairs. This fuctio provides a rule to determie whether two objects should be matched ad a search path to fid all matched pairs. The variables i this fuctio could be ay similarity metrics, such as Euclidea distace or Hausdorff distace, or a combiatio of a set of measuremets. I this sectio, we will discuss two search strategies i object matchig after a similarity metric is selected: the first oe is the popular greedy method that aims to always fid the possible miimum dissimilarity betwee paired objects i each step, ad the secod oe is our proposed optimizatio strategy that iteds to miimize the total dissimilarity betwee all matched objects. 2.1 Matchig Objects Usig Greedy Greedy is a simple way to achieve local optimum at each stage. Its essece is to make the optimal choice at each step eve i a problem that requires multiple steps to solve. It has bee studied i may fields such as operatios research ad computer sciece (Wu et al., 1990) ad widely implemeted i may applicatios. Oe obvious problem with the greedy algorithm is that a additio of a ew item to the solutio set may reder the solutio ot optimal ad it does ot provide a mechaism to remove items already i the solutio. For example, if we match two objects icorrectly i a previous step, there is o way to correct that mistake i later stages. Therefore, i a greedy-based algorithm, a mismatch error i ay step will result i at least two mistakes because it will make it impossible for the omitted object to be matched to the correct oe i a later stage. Two greedy methods were implemeted i MATLAB i our study. Greedy1 adopts a sequetial idetificatio ad removal procedure: it idetifies the closest pair of objects as correspodig couterparts ad removes both from the cadidate set; the it idetifies the closest pair i the remaiig objects ad removes them, util all objects are matched. Greedy2 is a modified versio of greedy1 by addig a radom compoet to the procedure i order to jump out of local optima. It starts with a radom object i oe dataset ad idetifies the closest object i the other, followed by the elimiatio of matched pairs; the it selects aother radom object ad idetifies its matched correspodece util the process is fiished. This procedure could be repeated as may times as ecessary (e.g., 100) ad the best result would be the fial result. 2.2 Matchig Objects Usig Optimizatio I order to rectify mistakes itroduced i previous stages i a greedy algorithm, we propose aother strategy to rely o a global measuremet of similarity by regardig object matchig as a assigmet problem that takes ito accout all correspodig pairs of objects simultaeously. The search for correspodig objects is based o miimizatio of dissimilarity betwee matched objects ad ca be formulated as the followig objective fuctio: Miimize c ij x (1) ij i=1 j=1 99

3 3. DATA where i = idex for the objects i the first dataset j = idex for the objects i the secod dataset = the umber of objects i each dataset c ij = the dissimilarity betwee object i i oe dataset ad object j i the other. c ij could be ay form of similarity measures or ay combiatio of multiple metrics that joitly decide the similarity betwee two objects x ij = a Boolea idicator: whe object i i the first dataset ad object j i the secod dataset are matched, it is assiged to 1, ad assiged to 0 otherwise The costraits for this objective fuctio are as follows: j=1 x ij =1, i (2) x ij =1, j (3) i=1 Two sets of data were used to test the differeces betwee greedy ad optimizatio methods i object matchig: hypothetical poit datasets ad real street etwork datasets. 3.1 Hypothetical Data Hypothetical data were geerated by a radom process. The first set of poit data were created by a bivariate poit process ad the secod set of poit data were created by the followig formula: x 2 = 0.1+x 1, y 2 = 1.1*y 1, where x 1, y 1 are the coordiates of poits i the first set of datasets, ad x 2, y 2 are the coordiates of poits i the secod set of datasets. Withi a square area, the umber of poits varies from 10 to 100 with a iterval of 5. Some examples of these datasets are demostrated i Figure 1. These two costraits esure that every object i each dataset is matched to exactly oe object i the other dataset. This form of objective fuctio is well kow as the assigmet problem i the operatios research. It is geeralized from the problem of assigig a set of tasks to a group of agets with the objective to miimize the total cost of performig all tasks, uder the costraits that each task ca oly be assiged to oe aget, ad each aget ca oly accept oe task (Hillier ad Lieberma, 2001). Our task i object matchig is to assig each object i oe dataset to its correspodig couterpart i the other oe, satisfyig the objective fuctio that miimizes the total dissimilarity betwee matched pairs. I real applicatios, two datasets that represet the same area rarely have the same umber of objects, so we relaxed the costraits: m xi, j <= 1, j i xi, j = 1, i j (4) (5) where m = the umber of objects i dataset 1 = the umber of objects i dataset 2 m<= Therefore, each object i the smaller dataset is matched to oe object i the other, ad some objects i the larger dataset will be idetified as havig o correspodig pair. This assigmet problem was implemeted usig the GNU MathProg modelig laguage i the GLPK (GNU Liear Programmig Kit) package that provides a platform for solvig liear programmig problems. The similarity criterio is Euclidea distace i the poit datasets, ad Hausdorff distace i the polylie datasets. Figure 1. Hypothetical datasets with differet umbers of poit objects 3.2 Real street data Real street data are more complex tha the hypothetical poit data, sice they are composed of multiple poits ad the offsets 100

4 betwee objects are ot uiform. I our experimet, street etwork data i Goleta CA were created uder differet stadards by two agecies. These data represet approximately the same streets i a eighbourhood of Goleta (Figure 2). These two datasets have 236 ad 223 objects, respectively. As show i the figure, there are some discrepacies betwee these two datasets, ad some streets are missig i oe versio of the data. These data were prepared i a way that they are uder the same coordiate system ad iterally cosistet. Pre-processig was performed i the datasets to maximize 1:1 correspodeces, sice our optimized object matchig strategy is desiged for 1:1 matchig. Due to the differece i geeralizatio of real streets, the same street may be represeted as differet umbers of segmets. For example, the street Hollister could be described as 5 segmets (objects) i oe dataset, ad as 7 segmets (objects) i the other. Therefore, it is helpful to make as may pairs of 1:1 correspodeces as possible. I our experimet, we merged street segmets based o the ame attribute ad the topology of polylies. I each dataset, if multiple street segmets have the same ame ad they are coected, they are merged to form oe object after pre-processig. Figure 3. Total distace of matched pairs. Figure 2. Street etworks i a eighborhood of Goleta, CA. 4. RESULTS AND DISCUSSION Both greedy ad optimizatio methods were tested i these datasets. The sum of distaces betwee matched objects usig each of the three methods is displayed i Figure 3. Whe the umber of poits is small, the total distaces calculated from differet methods are similar. As the desity of poits becomes larger, the differece of total distace becomes more obvious betwee greedy ad optimizatio methods, but the results are relatively close betwee the two greedy methods. I ay dataset, the total distace of matched pairs is cosistetly smaller usig the optimizatio method. I Figure 4, the relatioship betwee the percetage of correctly matched pairs ad the umber of poits is displayed. The tred shows that there is a drastic drop i the percetage of correct matches usig the two greedy methods as the umber of poits becomes larger. However, the percetage of correct matches usig the optimizatio method is stable ad robust i all tested datasets. While the percetage of correct matches decreases from 100% or 80% to less tha 20% usig the greedy methods, the percetage of the optimizatio method maitais at a level close to 100% eve i dese datasets. Therefore, whe the desity of poits gets larger, the probability of mismatch becomes larger, ad cosequetly the superiority of the optimizatio method becomes more obvious. Figure 4. Percetage of correct matches. The results of object matchig i real street data usig the three methods are demostrated i Table 1. The total distace betwee matched pairs is smaller usig the optimizatio method tha usig greedy methods. As a result, the percetage of correct matches usig the optimizatio method is about 10% higher tha that usig the optimizatio method. Table 1. Results of object matchig for street datasets Percetage of Total distace correct match Greedy1 Greedy % 88.56% Optimizatio % I all experimets, either with hypothetical poit data or real polylie data, object matchig usig the optimizatio method cosistetly achieves better results. Whe the desity of a dataset icreases, the probability of mismatch becomes larger, ad cosequetly, the advatage of the optimizatio method becomes more obvious. While a deser dataset makes object matchig more susceptible to mismatches, the spatial arragemet of objects withi the study area is also aother importat factor that affects the matchig result. These experimets idicate that the optimizatio method for object matchig is more robust tha greedy methods. I some datasets, object matchig usig a greedy method may also result i a good percetage of correct matches, but i other cases, the 101

5 percetage could be ot acceptable. Sice it requires a lot of time ad labour to idetify ad correct eve a small umber of mismatches, it is importat to maximize the percetage of correct matches i the automatic stage of object matchig. I terms of the choice of similarity measuremet i our experimets, whe the total distace of matched pairs is small, the percetage of correctly matched objects is high. Therefore, Euclidea distace ad Hausdorff distace are proper idicators of poit ad liear object similarity i these datasets, respectively. However, whe more attributes are available, ot oly relyig o the geometric distace i a geographical space, we ca also costruct a similarity space accordig to a weighted combiatio of these properties, ad use that metric as a similarity measuremet i our objective fuctios. Furthermore, additioal attributes may also be used to reduce search space i particular applicatios. Although the emphasis of this paper is ot the selectio of similarity measuremet, a proper similarity metric is a ecessity for effective ad efficiet object matchig. A measuremet that is a adequate idicator of the likeess betwee two objects should be icluded i the objective fuctio. 5. CONCLUSIONS Object matchig is a fudametal problem i spatial data hadlig ad may related applicatios. How to idetify objects i differet data sources that represet the same etity i reality is a prerequisite for data maipulatio ad aalyses i later stages, such as accuracy improvemet, chage detectio, ad geospatial aalysis usig multi-source data. There are two major compoets i the object matchig process: selectio of a appropriate similarity measuremet ad idetificatio of matched objects accordig to this measuremet. Most existig literature has focused o the defiitio of a proper similarity metric i particular applicatios. They usually adopt a sequetial procedure to fid object pairs oe after aother based o the chose metric. I our paper, we focus o the other aspect of the problem: how to effectively search for correspodig objects oce a similarity measuremet is chose. Rather tha usig a greedy strategy that cosecutively adds more matched pairs ito the solutio set, ad ever removes ay mismatched pairs from the solutio, our optimized object matchig takes ito accout all possible matched objects simultaeously with the aim to miimize the total dissimilarity betwee all correspodig objects. Therefore, object matchig is formulated as a assigmet problem that iteds to assig each object i oe dataset to a object i the other dataset, with the objective to miimize the sum of dissimilarity betwee object pairs. Ulike the widely used greedy procedure for fidig matched pairs, this strategy makes it possible to rectify mismatch errors made i early steps. Although oly poit ad polylie data were tested i this paper, this method ca also be applied to other types of data as log as the selected metric is adequately represetative of the resemblace betwee objects. Our experimets demostrate that optimized object matchig method is robust ad always achieves a higher percetage of correctly matched pairs i both hypothetical ad real datasets. Although our research poits out a ew research directio i object matchig, there are some limitatios. First, formulatio of object matchig as a assigmet problem etails the costraits that oe object ca oly be assiged to oe or oe object i the other dataset. Therefore, this strategy is appropriate for 1:1 correspodece. I real applicatios, there are cases whe a object i oe dataset is represeted as several parts i the other dataset (1: correspodece), or several objects are correspodig to a differet umber of objects (m: correspodece). Therefore, oe of our future research questios is to fid a way to maximize the 1:1 correspodece i differet datasets before the executio of the optimized object matchig strategy. Aother problem we are goig to ivestigate is to directly tackle the 1: ad m: relatioships by examiig partial similarity betwee objects. Fially, as the iput datasets become larger, the matchig procedure may degrade rapidly, ad makes it difficult to fiish matchig withi a reasoable time frame. Therefore, we will study the improvemet of the algorithm usig heuristics to reduce the search space, such as divide-ad-coquer techique (Preparata ad Shamos, 1985). Refereces Abbas, I., Base de doées vectorielles et erreur cartographique: problèmes posés par le cotrôle poctuel; ue méthode alterative fodée sur la distace de Hausdorf. Computer Sciece. Paris, Uiversité de Paris VII. Bel Hadj Ali, A., Appariemet geometrique des objets géographiques et étude des idicateurs de qualité. Sait-Madé (Paris), Laboratoire COGIT. Cobb, M. 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