COVER SHEET. Copyright 2005 Association for Computing Machinery

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1 COVER SHEET Walker, Arron and Pham, Bnh and Moody, Mles (25 Spatal Bayesan learnng algorthms for geographc nformaton retreval. In Proceedngs 3th annual ACM nternatonal workshop on Geographc nformaton systems, pages pp. 5-4, Bremen, German Copyrght 25 Assocaton for Computng Machnery

2 Spatal Bayesan Learnng Algorthms for Geographc Informaton Retreval Arron R. Walker Queensland Unversty of Technology 2 George St Brsbane Q 4 Australa ar.walker@qut.edu.au Bnh Pham Queensland Unversty of Technology 2 George St Brsbane Q 4 Australa b.pham@qut.edu.au Mles Moody Queensland Unversty of Technology 2 George St Brsbane Q 4 Australa m.moody@qut.edu.au ABSTRACT An ncreasng amount of freely avalable Geographc Informaton System (GIS data on the Internet has stmulated recent research nto Geographc Informaton Retreval (GIR. Typcally, GIR looks at the problem of retrevng GIS datasets on a theme by theme bass. However n practce, themes are generally not analysed n solaton. More often than not multple themes are requred to create a map for a partcular analyss task. To do ths usng the current GIR technques, each theme s retreved one by one usng tradtonal retreval methods and manually added to the map. To automate map creaton the tradtonal GIR paradgm of matchng a query to a sngle theme type must be extended to nclude dscoverng relatonshps between dfferent theme types. Bayesan Inference networks can and have recently been adapted to provde a theme to theme relevance rankng scheme whch can be used to automate map creaton [2]. The use of Bayesan nference for GIR reles on a manually created Bayesan network. The Bayesan network contans causal probablty relatonshps between spatal themes. The next step n usng Bayesan Inference for GIR s to develop algorthms to automatcally create a Bayesan network from hstorcal data. Ths paper dscusses a process to utlze conventonal Bayesan learnng algorthms n GIR. In addton, t proposes three spatal learnng Bayesan network algorthms that ncorporate spatal relatonshps between themes nto the learnng process. The resultng Bayesan networks were loaded nto an nference engne that was used to retreve all relevant themes gven a test set of user queres. The performance of the spatal Bayesan learnng algorthms were evaluated and compared to performance of conventonal non-spatal Bayesan learnng algorthms. Ths contrbuton wll ncrease the performance and effcency of knowledge extracton from GIS by allowng users to focus on nterpretng data, nstead of focusng on fndng whch data s relevant to ther analyss. Categores and Subject Descrptors H.3.3 [Informaton Search and Retreval]: Retreval Models. General Terms Algorthms, Expermentaton. Keywords Spatal Bayesan learnng, learnng Bayesan networks, geographc nformaton system, geographc nformaton retreval, nformaton retreval.. INTRODUCTION The amount of GIS data on the nternet has been growng explosvely n recent years. Some of the reasons for ths growth are that spatal data tself s gettng cheaper, n fact some governments and organsatons gve data away free of charge [3]. For example, Geoscence Australa [4] and ESRI s Geography Network [5] provde access to some free GIS data. Another contrbutng factor was the released of GIS Web standards lke Web Map Servce (WMS by Open GIS Consortum (OGC [6]. Snce ts ntroducton, the major commercal GIS companes have supported the WMS specfcaton. Numerous free web based WMS vewers lke Intergraph s OGC WMS Vewer [7] and ESRI s ArcExplorer have been developed. ArcExplorer not only supports WMS, but also provdes the ablty to download maps of a varety of standards, thus, allowng dfferent datasets from dfferent servers as well as local data to easly be combned nto sngle map vsualsaton. GIR technques have not kept pace wth ths exploson of GIS web based data. Typcally, GIR looks at the problem of retrevng GIS datasets on a theme by theme bass. However n practce, themes are generally not analysed n solaton. More often than not multple themes are requred to create a map for a partcular analyss task. To do ths usng the current GIR technques, each theme s retreved one by one usng tradtonal retreval methods and manually added to the map. To automate map creaton the tradtonal GIR paradgm of matchng a query to a sngle theme type must be extended to nclude dscoverng relatonshps between dfferent theme types. GIR should be able to create mult theme maps from a smple user query. Bayesan Inference networks offer one such technque to retreve multple spatal themes gven a smple user query. Recently a

3 GIR system was developed by Walker [2] that used a Bayesan network to assgn causal relatonshps between spatal theme. The system used Bayesan nference theory to rank all avalable themes gven that one theme has been found relevant to the query. In effect, the ntal theme s retreved va a typcal GIR method, but once selected t becomes the evdence n a Bayesan Inference network to allow the related themes to t to be ranked and subsequently retreved. Bayesan Inference wll be explaned n more detal later n ths paper. At the heart of a Bayesan Inference retreval system s the Bayesan network whch contans the ntellgence about whch themes are related to each other and how strong the relatonshps between them are. Walker s system requred an ntal Bayesan network to be calculated manually by doman experts. Ths was a slow and dffcult job. For Bayesan Inference networks to become feasble solutons for GIR, the creaton of ths Bayesan network must be performed automatcally usng readly avalable stored expert knowledge. The process of dentfyng the best Bayesan network and ts assocated condtonal probabltes s known to experts n ths area as Learnng Bayesan Networks. Ths paper descrbes three new spatal Bayesan learnng algorthms that automatcally create Bayesan networks. The Bayesan learnng approaches presented here consders spatal data aspects as part of ther learnng algorthms, therefore, addressng the defcency n the non-spatal Bayesan learnng approaches. The sgnfcance s the removal of the last manual process n Walker s Bayesan GIS retreval system. The remander of ths paper s structured as follows. Sectons 2, proves background to how GIS data are managed n spatal themes. Secton 3 revews the current use of Bayesan networks for nformaton retreval. Secton 4 nvestgates work n the area of learnng Bayesan networks. Secton 5 outlnes a process to extract spatal relatonshp between GIS datasets. Secton 6 proposes two spatal Bayesan learnng algorthms and one parameter learnng algorthm that ncorporate spatal relatonshps. Secton 7 revews the sutablty of usng current IR evaluaton measures for GIR. Secton 8 outlnes the experment conducted to evaluate the proposed algorthms. Fnally, secton 9 presents the conclusons and comments on future work. 2. GIS DATA MANAGEMENT Ths secton gves a quck overvew of how maps are created and then stored for later use n GIS. It wll be shown later n ths paper how ths nformaton can be used as to way to access exstng stored knowledge of relatonshps between themes. 2. SPATIAL THEMES The man prncple of data organsaton of a GIS s to group the spatal data nto themes or spatal data layers. Each theme has an assocated dataset and meta data. These themes are generally layered one on top of the other n the vsualsatons nterface of the GIS, as shown n fgure. Categorsng data nto themes ncreases the effcency of data queryng. It allows easy addton of new data by smply overlayng a new theme layer to create a map whch s useful for some analyss task. Fgure. Spatal Themes [] 2.2 WORKSPACES Themes n solaton don t provde the user wth a spatal context when they are analysng GIS data. Therefore, t s common practce to load multple themes nto a GIS before analyss begns. Most GIS remember ths multple theme confguraton through a manual process called workspace creaton. Here users must manually select the themes of nterest and explctly save them to a workspace. Consequently, a workspace for each user analyss task s requred. These workspaces are a statc record of the themes loaded nto the GIS, and thus do not dynamcally update themselves as new themes become avalable. Large organzatons that use GIS wll generally have experts ntally setup and mantan these workspace fles. There s an opportunty to use these hstorcal workspace fles to create a Bayesan network that assmlates the expert knowledge stored n them. Such a Bayesan network should llustrate good performance n retrevng GIS datasets. Ths paper presents such a method for learnng a Bayesan network from workspace fles. 3. BAYESIAN INFERENCE FOR IR Tradtonal nformaton retreval (IR systems were developed to retreve text documents that are relevant to a gven query. The use of Bayesan Inference for IR s wdely accepted [8-]. These systems use key terms n the query as evdence n the Bayesan network. From ths evdence, the documents are ranked, n order of relevance, to the query. Over the years, Bayesan nference has been used n other nformaton retreval areas outsde document retreval. For example, Heckerman and Horvtz [] developed a Bayesan help program, whch retreves relevant help topcs gven a user query. Ther Bayesan network establshes a casual relatonshp between help topcs and the query terms. Ther system has become the bass for the Mcrosoft Offce Help program. It demonstrates the usefulness of Bayesan nference n all areas of nformaton retreval. Some extensons to the tradtonal nference model combne Bayesan nference wth heurstcs wth the am of understandng queres [2]. These systems have shown retreval performance mprovements over the tradtonal method n certan doman areas. Bayesan nference, as mentoned n the ntroducton, has been used by Walker [2] for GIR wth good retreval performance. Hs Workspace s a MapInfo term and the same process s known as Projects n ArcGIS.

4 system, establshes a casual relatonshp between spatal themes. The next secton gves some background nto Bayesan networks. 3. Bayesan Networks Bayesan networks are graphcal models for defnng probablstc relatonshps between varables. These relatonshps can nvolve uncertanty, unpredctablty or mprecson. The relatonshps may be dscovered automatcally from data fles, or created by experts, or developed by a combnaton of the two. An advantage of Bayesan networks s that they capture knowledge n a form people can understand ntutvely, and whch allows a clear vsualsaton of the relatonshps nvolved. Bayesan probablty of an event x s a person s degree of belef n that event. Ths s somewhat dfferent from a classcal probablty of an event x whch s a physcal property of that event n the world (e.g. probablty that a con wll land heads. Bayesan networks used a drected acyclc graph (DAG to represent assertons of condtonal ndependence (See fgure 2. The nodes n the graph represent the varables and the drected arcs defne the condtonal relatonshps. The advantages of drected graphc models over undrected models are the noton of causalty. Causalty ndcates that f an arc s drected from A to B n the network, then A causes B. Bayes theorem s used to calculate causal nference about the varables. Bayes theorem states: p ( B A ( A B p ( B p ( A p = where =,..., (,2 r Bayes theorem allows the updatng of the probabltes regardng uncertan events when fresh nformaton s receved [3]. That s, once you know certan events have occurred then one can recalculate the probablty of other events occurrng. The graphcal and probablstc structure of a Bayesan network represents a sngle jont probablty dstrbuton. Ths dstrbuton s obtaned usng the Product (Chan Rule for Bayesan networks: h MAP P max h H ( D h P( h P( D Because P(D s ndependent of h, t can be dropped, resultng n h max P MAP h H ( D h P( h Ths process of rankng hypotheses gven evdence s known as Bayesan Inference. Bayesan networks have been used n many dfferent domans [2, 6-9] to provde decson support. For example, medcal dagnostc systems based on Bayesan networks compute the best dagnoses gven the exstence of certan patent symptoms (or evdence [7]. Of more nterest to ths research, s the use of Bayesan networks n IR, ths wll be dscussed n the next secton. 3.2 Bayesan Networks n GIR To rank spatal theme n order of relevance to each a Bayesan network must be constructed that represents the causal relatonshps between themes. An example of a Bayesan network for spatal themes used by the Gold Coast Cty Councl s shown n fgure 2. If we consder the query as the selecton of one theme, then ths theme can be used as the evdence for Bayesan nference. Consequently, the MAP hypothess for each theme n the network can be calculated and ranked. The resultng rankng represents the themes most related to the query theme. More detals on how Bayesan nference has been adapted to GIR can be found n [2]. p n ( X... X n = p( X pa ( X = Applyng Bayes decson rule performs classfcaton [4]. For example, assume that there are two hypotheses n the classfcaton doman, Bayes decson rule states that A should be assgned to the hypothess for whch the posteror probablty s a maxmum. That s, choose; B B : : f f P P ( B A > P ( B A ( B A > P ( B A Where P(B A and P(B A can be calculated usng Bayes rule. If the above example was extended to nclude more than just two hypotheses, then the problem can be vewed as searchng through the set of all possble hypotheses wth the goal of fndng the best hypothess. The best hypothess can be defned as the most probable hypothess gven the evdence of the data D n the hypothess space H. Such a hypothess s referred to as the maxmum a posteror (MAP hypothess [5]. From Bayes rule, ( h D h max P MAP h H Fgure 2. Bayesan Network of GIS Themes 4. LEARNING BAYESIAN NETWORKS The process of learnng a Bayesan network from data has two parts: Structure Learnng and 2 Parameter Learnng. In Bayesan networks, the DAG s known as the structure and the condtonal probablty dstrbutons are known as the parameters [2]. In the past, these propertes had to be learnt manually wth nput from doman experts. For large networks, ths task becomes mpossble; as a result, researchers have developed methods to learn both the structure and the parameters of Bayesan networks automatcally. In the followng secton, the man methods for Bayesan Learnng wll be outlned. 4. Structure Learnng Structured learnng s the process of dscoverng the DAG that best descrbes the causal relatonshps n the data. The number of possble DAGs grows exponentally wth the number of nodes. Robnson [2] equaton below gves the number of DAGs:

5 f ( n = n = ( ( + n 2 ( n f ( n n > 2 For example n=, gves approxmately 4.2x 8 and n=6 approxmately x 36, therefore, exhaustvely consderng all DAG patterns s computatonally nfeasble [2]. Consequently, approxmate algorthms that fnd the most probable structure have been developed. The two most popular methods are DAG search algorthm and K2 algorthm. Both of these algorthms approach the structure learnng problem by assgnng equal pror probabltes to all DAG patterns and thus search the for the pattern that maxmses the probablty of the data, d, gven the DAG, G, (.e. P(d G. Ths probablty s known as the Bayesan score (score B. score B ( d, G = ( G n q ( G r ( G ( G j jk jk ( G ( G ( G = j = Γ ( N j + M j k = Γ ( a jk Γ ( N Γ ( a + s The man dfference between the two algorthms s how they determne the search space of DAG patterns to score. DAG search was developed by Chckerng [22, 23] and uses a straghtforward greedy search method and a set of operatons. The operatons are Add, Delete and Reverse edges n the DAG. The algorthm proceeds as follows: The ntal DAG has no edges. At each step of the search, lnks are added, deleted and reversed and the new DAG score calculated. The algorthm stops when no operaton ncreases the score. In contrast, the K2 algorthm developed by Cooper and Herskovts [24] s a greedy search method wth a sngle operaton. Ths operaton s the addton of a parent to a node. K2 reles on the assumpton that the order of allowable parents s know. Ths pror node orderng s created manually from expert knowledge. The Bayesan score can only be calculated from data when the probabltes are relatve frequences. In the GIS doman, hstorcal records of prevous workspaces provde a measure of relatve frequency of the use of datasets. Ths paper present two new structure learnng algorthms that are based on DAG search and K2, but nclude spatal relatonshps between datasets to alter the search space set of DAG patterns. These algorthms are presented n secton Parameter Learnng Parameter values can only be learnt from data when the probabltes are relatve frequences. As mentoned above, n the GIS doman, hstorcal records of prevous workspaces provde a measure of relatve frequency of the use of datasets. In addton, t s assumed that a theme s presence n a workspace s bnomnal, that s, t has only two values (present and not present. Fnally, parameter learnng assumes that relatve frequences have a beta dstrbuton. Wth these assumptons, a standard parameter learnng equaton from [2] was used to dscover the probablty dstrbuton for the Bayesan network. To update the dstrbutons from the workspace data, the relatve frequency gven the data are calculated by usng: p ( f d = beta( f : a + s, b + t Where d s a bnomal sample wth parameter f, f s the relatve frequency of varable, a and b are the ntal beta functon parameters (set to for equally lkely s s the number of varables n d equal to (present and; t s the number of varables n d equal to 2 (not present. Because n parameter learnng the network s known, the updated dstrbutons can now be used to calculate all condtonal probabltes Maxmum Lkelhood Parameter Estmaton The parameter Learnng algorthm used n ths experment was maxmum lkelhood parameter estmaton (MLE. MLE s a well known algorthm and an mplementaton of MLE was avalable n Bayes Net [25]. Ths code was easly modfed and also provded a control for comparson wth the new spatal MLE algorthm. The dea behnd MLE s to determne the parameters that maxmse the probablty (lkelhood of the sample data. MLE algorthm wants to maxmse the lkelhood of the parameter set θ gven by dataset D and solve for θ : For bnomal data, gves θ as: L m ( θ D = p ( x j θ θ = j = N N + N Where N and N are the number of tmes x equals and respectvely. Therefore, MLE hypothess asserts that the actual proporton of a parameter s equal to the observed proporton n the tranng set. Ths paper wll utlse spatal relatonshps to ntroduce pror weghts nto MLE algorthm. Ths algorthm s presented n secton SPATIAL RELATIONSHIPS The new contrbuton of ths work s the ncluson of spatal relatonshps nto Bayesan learnng algorthms. Ths secton descrbes the method used to dscover the spatal relatonshps between the GIS themes. Tobler s frst law of Geography states: everythng s related to everythng else but nearby thngs are more related than dstant thngs [26]. In spatal data analyss ths Tobler s nter-dependence between spatal data can not be gnored [27]. One way to measure spatal relatonshps s to use the Moran s I measure[27]. Moran s I measure s dependent on the desgn of a contguty matrx W whch reflects the nfluence of neghbourhood. For example, a spatal neghbourhood contguty matrx s shown n fgure 3. Fgure 3. A spatal neghbourhood and ts contguty The matrx can have multple weghts to record dfferent degrees of relatonshp between objects. In fgure 3, the spatal

6 relatonshps of adjacent and overlaps are represented by the weghts of and 2 respectvely. 5. Spatal Relatonshps for GIR The spatal relatonshps used to construct the contguty matrx for GIS data were: same pont, contans, overlaps, adjacent, object extent overlaps, extent overlaps, separated and same object. 7: Same 3: Object Extent Overlaps 6: Contans 5: Overlaps 4: Adjacent 2: Extent Overlaps Fgure 4: Spatal Relatonshps The weghts gven to each relatonshp are lsted n table and the spatal relatonshps are llustrated n fgure 4. Table. Contguty Matrx Weghts Spatal Relatonshp Weght One element n A at Same pont as one element n B 7 At least one element n A Contans at least one element n B At least one element n A Overlaps at least one element n B At least one element n A s Adjacent to at least one element n B At least one element n A Object Extent Overlaps at least one element n B : Separated The extent of A Extent Overlaps the extent of B 2 All elements n A Separated from all elements n B (Same object 5.2 Spatal Causal Relatonshps Because the spatal relatonshps are to be used n a Bayesan learnng algorthm the relatonshps must be translated nto a language smlar to that used n Bayesan probablty theory. Thus the noton of spatal causal relatonshps s presented here. Spatal relatonshps between objects can be consdered as spatal causal relatonshps n the context of nformaton retreval. Consder three GIS datasets of Australan Ctes, Amercan Ctes and the Australan Contnent. From Tobler s frst law of Geography, we can see that Australan Contnent and Australan Ctes wll be more related than Australan Contnent and Amercan Ctes. Ths s because Australan Contnent s spatally closer to Australan Ctes than to Amercan Ctes The Bayesan nformaton retreval system used n ths paper s based on cause and effect relatonshps. Accordngly, the assumpton s made that nearby objects have causal effects on each other. That s f a person quered the GIS for Australan Contnent t s more probable that they are nterested n Australan Ctes than Amercan Ctes because of ths assumed spatal causal relatonshp. 5.3 Translaton of Spatal Relatonshps to Spatal Causal Relatonshps The spatal relatonshps dscovered n the contguty matrx were translated nto ther equvalent spatal causal relatonshp. The resultng translaton s lsted table 2: Spatal Relatonshps Table 2: Causal Spatal Relatonshps Spatal Causal Relatonshps Same object A No lnk Extent separated Extent overlaps Object extent overlaps Adjacent Overlaps Contans At same pont A B No lnk A B A B A B A B A B A B Lnk, drecton unknown Lnk, drecton unknown Lnk, drecton unknown Lnk, drecton unknown Drected lnk Lnk, drecton unknown weak average good strong strong Very strong 6. SPATIAL BAYESIAN LEARNING Three new spatal Bayesan learnng algorthms are dscussed n ths secton. The frst two are structure learnng algorthms. They are called Spatal K2 and Spatal DAG. These algorthms ncorporate spatal relatonshps nto the two popular structure learnng algorthms. Fnally n ths secton a new parameter learnng algorthm s dscussed. Ths algorthm ncorporates spatal relatonshps nto MLE whch s an exstng Bayesan parameter learnng algorthm. 6. Spatal K2 Ths algorthm automatcally calculates the node order for use n the K2 algorthm. It uses the Spatal relatonshps between datasets (from contguty matrx to calculate the spatal causal orderng. Apart from ths automated order calculaton, the orgnal K2 algorthm s unchanged

7 Spatal K2 Algorthm: Calculate contguty Matrx W; 2 Derve spatal causal order from Matrx W (See Dervng Spatal Orderng below; 3 Run K2 usng ths order. Dervng Spatal Causal Orderng: Sum the columns n W; 2 Place n descendng order; (Note value that has maxmum number has most nfluence on more neghbours 3 Loop through ths lst; Swap the order of same value nodes f node has a greater score when only consderng the current parents n lst; If score the same just keep arbtrary order; For example, consder the spatal relatonshps n fgure 3, the resultng spatal causal order would be C, B, D, E, A 6.2 Spatal DAG Spatal DAG modfes Chckerng s DAG search algorthm to nclude spatal causal relatonshps. It only allows the operatons of add, delete and reverse to be used wthn the search algorthm f they agree wth the dscovered spatal relatonshps. Ths should lmt the number of DAG patterns that needs to be searched n order to fnd a maxmum, thus t should take less tme to dscover the Bayesan network. In addton, the resultng Bayesan network should match the causal spatal relatonshps n the data. Spatal DAG Algorthm: Calculate contguty Matrx W; Do Score only DAGs that are n neghbourhood (.e. add, delete, reverse AND n contguty Matrx W; If (any ncrease the score Modfy result DAG to the one that ncreases the score the most; Whle (some operaton ncreases the score; 6.3 Spatal MLE Pror knowledge of the Bayesan relatonshps can be used to nfluence the MLE process. The method proposed here takes spatal relatonshps between data and converts them nto a pror metrc for use n an MLE algorthm. The process for ntroducng pror knowledge about data nto the MLE algorthm s detaled n Bayes Net [25]. It states; f we let N jk = the number of tmes X =k and Pa =j occurs n the tranng set, where Pa are the parents of X, then the maxmum lkelhood estmate s: T jk = N jk / N j (where N j = sum k N jk, whch wll be f N jk =. To prevent us from declarng that (X = k, Pa = j s mpossble just because ths event was not seen n the tranng set, we can pretend we saw value k of X, for each value j of Pa some number (α jk of tmes n the past. The MLE s then: θ jk = ( N jk + α jk ( N + α Ths paper proposes to modfy the above, so α jk = α j = spatal pror weght. Ths wll have the affect of basng the probablty toward the parent that has a spatal relatonshp wth the chld n the Bayesan network. j j Algorthm for calculatng α j (spatal pror weght: For each,j If j have a parent chld relatonshp If j have spatal relatonshp wth weght greater than 3 End for α j = RETRIEVAL EVALUATION Once the Bayesan networks were learnt, the respectve Bayesan networks had to be evaluated aganst each other. In order to do ths, a recall and precson measure that suted GIS dataset retreval was establshed. 7. Recall and Precson In tradtonal IR, recall and precson are generally descrbed n terms of documents retreved. The standard recall and precson measures [28] for document retreval are:. Recall s the fracton of relevant documents retreved to the total number of relevant documents. recall = R R 2. Precson s the fracton of the retreved documents, whch are relevant. precson = The same recall and precson measures were used n ths experment by smply consderng datasets retreval as equvalent to document retreval as far as performance s concerned. To evaluate the retreval performance of the Bayesan networks over all test queres, the precson fgures are averaged at each recall level and a graph of recall versus precson s construct [28]. 8. EXPERIMENT AND RESULTS Ths secton descrbes the experment conducted to evaluate the proposed spatal Bayesan learnng algorthms. 8. Gold Coast Cty Councl Database The experment used GIS datasets suppled by the Gold Coast Cty Councl (GCCC. The datasets were typcal spatal data of nterest to councl planners (.e. property boundares, water mans, etc. In addton, 2 workspace fles currently used by GCCC for GIS dataset retreval provded a measure of relatve frequency of the use of datasets. The workspace data was organsed nto a form sutable for the Bayesan learnng algorthms (.e. workspace x GIS datasets. Each dataset was a dscrete varable and was marked as present or absent from a partcular workspace. 8.2 Calculaton of Spatal Relatonshps A C# program usng MapObjects 2.2 was wrtten to calculate the contguty matrx for 7 GIS datasets. The GIS datasets were real lfe datasets suppled by Gold Coast Cty Councl n Australa. a Ra A

8 The algorthm used for calculatng contguty matrx W was a smple heurstc search algorthm: for each GIS dataset par, determne the spatal relatonshp between them and add to contguty matrx. In order to test the correctness of the calculated spatal relatonshps, eleven spatal datasets consstng smple pont, lnes and polygons were evaluated. The smple test GIS themes and the resultng contguty matrx s shown n fgure 5. The tme requred to calculate spatal relatonshps for large GIS datasets was consderable. faster than the DAG and Spatal DAG. The process tme to calculate the contguty matrx has not been ncluded n the table. Ths would ncrease the processng tme for both spatal methods equally. Once the network structure was learnt, both the standard MLE and Spatal MLE parameter learnng algorthms were used to calculate the a pror and condtonal probablty tables of the respectve Bayesan networks. The orgnal Bayes Net MLE algorthm allowed exact condtonal probabltes of. and.. Ths allowed for no uncertanty and affected the nference algorthm s ablty to rank the posteror probabltes. As a result, the algorthm was modfed to produce condtonal probabltes of.9999 for. and. for Dsplay and Inference The Bayes Net Toolbox does not have nce graphcal output for Bayes networks, therefore, a functon was wrtten the save the resultng DAG to the Mcrosoft s MSBN fle format. Ths allowed MSBN [29] to be used to dsplay the BN and run nference calculatons. The resultng Bayesan networks created by the four Bayesan learnng algorthms are shown n fgures 6 to 9. The man dfference n the structures s the maxmum number of parents. K2 and Spatal K2 was lmted to 2 parents to allow the algorthm to process fast. The DAG and Spatal DAG network, whch had no lmt, averaged 6 parents per node and therefore, are more complex networks. Fgure 5. Testng Spatal Relatonshp Calculatons 8.3 Implementng Spatal Bayesan Learnng All the Bayesan learnng algorthms were mplemented n Matlab usng Bayes Net toolbox [25]. The man advantage was that the orgnal K2, MLE and many Bayes related functons were already mplemented n the toolbox. As a result, Spatal K2, DAG, Spatal DAG, Spatal MLE and Dervng Spatal Causal Orderng functons were wrtten n Matlab. Table 3. Structure Learnng Algorthm Process Tme The process tme for each of the structure learnng algorthms s shown n table 3. As expected, Spatal K2 and K2 are consderably Fgure 6. Network constructed by K2

9 8.5 Evaluaton To obtan the recall and precson measures, a set of queres and answers was devsed. Tradtonal GIR can match queres to datasets of smlar themes. Ths evaluaton tests the respectve Bayesan Network s ablty to match a theme to related, but not necessarly smlar, themes. Therefore, to smplfy our queryng process we assume that a dataset has been matched to a general query usng tradtonal methods. Followng ths assumpton, we used a sngle dataset as query nput, and evaluated ts ablty to retreve all related datasets. The orgnal workspace data provded a means of testng ths type of retreval. Each dataset n the workspace became a query and the answer to that query was all the remanng datasets n the workspace. The four dstnct Bayesan networks were evaluated usng 7 sngle word queres. A C# functon was added to the Bayesan GIS dataset retreval system developed n [2] to automatcally query the learnt Bayesan networks. Fgure 7. Network constructed by Spatal K2 2 Interpolated Precson 8 Precson Fgure 8. Network constructed by DAG Fgure 9. Network constructed by Spatal DAG Recall K2 Spatal K2 Spatal DAG DAG Fgure : Bayesan Structure Learnng Comparson Fgure shows the recall and precson fgures for the four Bayesan structure learnng algorthms evaluated n ths experment. Each of the structure learnng algorthms shown here used the MLE parameter learnng algorthm. From fgure, t can be seen that all algorthms performed smlar between to 3% recall, however, dfferences became obvous n the 4% to 9% recall range. Spatal DAG produced the best retreval performance wth Spatal K2 the next best performer. Both spatal algorthms performed better than the non-spatal algorthms of K2 and DAG. Fnally, the MLE and the Spatal MLE parameter learnng algorthms were evaluated on the four Bayesan networks that have been constructed. From fgures and 2 we can see that ncludng spatal parameter learnng gves an advantage only when the algorthm s run on a Bayesan structure dscovered usng tradtonal non-spatal algorthms. That s, f the Bayesan structure was dscovered usng a spatal learnng algorthm and then the parameters were dscovered usng a spatal algorthm we

10 n fact get poorer retreval performance than f we had a spatal structure wth tradtonal parameters. Precson Interpolated Precson Recall K2 Spatal K2 K2 Spatal Parameters Spatal K2 Spatal Parameters Fgure : Parameter Learnng Comparson (K2 & SK2 Precson Interpolated Precson Recall Spatal DAG DAG DAG Spatal Parameters Spatal DAG Spatal Parameters Fgure 2: Parameter Learnng Comparson (DAG & SDAG 9. CONCLUSIONS AND FUTURE WORK Ths paper shows that Bayesan learnng algorthms can automatcally create Bayesan networks sutable for use n a Bayesan nference GIR system. The algorthms utlsed expert knowledge currently stored n GIS workspace data fles. Consequently, no manual expert nput would be requred to set up a Bayesan nference GIR system. The paper presented two spatal structure learnng algorthms that demonstrate the advantages of ncorporatng spatal relatonshps when compared to tradtonal structure learnng algorthms. The spatal structure learnng algorthms yelded mproved retreval performance over non-spatal algorthms. Ths mprovement was offset by the addtonal tme requred to calculate the network. The major overhead beng the tme requred calculatng the spatal relatonshps n large GIS datasets. The processng tme s of less mportance as the algorthms are only run once at the ntalsaton stage of a Bayesan GIS retreval system. The ncorporaton of spatal relatonshps nto the parameter learnng MLE algorthm dd mprove retreval performance, but not to the same degree as the spatal structured learnng algorthms. Interestngly, the retreval performance was the best for the spatal structured learnng networks when they used a nonspatal parameter learnng algorthm. If the spatal parameter learnng algorthm was used wth non-spatal structure learnng then the retreval performance was better than f just a non-spatal parameter learnng algorthm was used. Ths was an unexpected result; t was thought that the best retreval performance would have come from a combned spatal structure and spatal parameter learnng algorthm. The only explanaton for ths s that the pror bas calculaton for the spatal MLE algorthm s cancellng out the structure learnt durng the spatal structure learnng process. More nvestgaton nto ths wll be requred n the future. In future work, some addtonal parameter learnng algorthms wll be modfed to nclude spatal relatonshp. It s also planned to mprove the GIR system developed n [2]. The major beneft of ths work s ts ablty to tap nto stored expert knowledge (workspace fles to allow effcent retreval of GIS themes. Not all users possess the expert knowledge to match spatal themes to analyss task. Furthermore, users usually do not have the tme to study the meta data for all avalable datasets to make these decsons. Technology such as WMS has greatly ncreased the number of datasets avalable for analyss. Wth so many data sources avalable, the manual process of selectng datasets for partcular analyss tasks s not trval, hence the need for an automatc process. A statc workspace requres users to constantly check for new datasets, but a dynamc GIR envronment that automatcally loads new datasets would ensure that users decson makng s based on the best avalable data.. ACKNOWLEDGMENTS The Cooperatve Research Centre for Satellte Systems (CRCSS s establshed and supported under the Australan Government s Cooperatve Research Centres Program. Ths research s support by the Bult Envronment Research Unt, Dept of Publc Works of the Queensland Government. The Gold Coast Cty Councl provded the GIS datasets for use n the experment.. REFERENCES [] "ArcVew," Envronmental Systems Research Insttute, 23, accessed on: 4-Jan-23. [2] A. Walker, B. Pham, and A. Maeder, "A Bayesan framework for automated dataset retreval n Geographc Informaton Systems," presented at The th Internatonal

11 Conference on Mult-Meda Modelng, Brsbane, Australa, 24. [3] Queensland Government, "Usng spatal nformaton for a sustanable SEQ," presented at 22 SEQ Spatal Informaton Expo, Brsbane, 22. [4] "Geoscence Australa," Australan Government, 24, accessed on: 29-Nov-24. [5] "Geography Network," ESRI, 25, accessed on: 3-May- 25. [6] "Open GIS Consortum," 23, accessed on: 3-June-23. [7] "OGC WMS Vewer," 23, accessed on: 4-July-23. [8] R. Fung and B. Del Favero, "Applyng Bayesan networks to nformaton retreval," Communcatons of the ACM, ACM Press, vol. 38, pp , 995. [9] H. Turtle and W. B. Croft, "Evaluaton of an nference network-based retreval model," ACM Transactons on Informaton Systems (TOIS, vol. 9, pp , 99. [] B. A. Rbero-Neto and R. Muntz, "A belef network model for IR," n Proceedngs of the 9th annual nternatonal ACM SIGIR conference on Research and development n nformaton retreval. Zurch, Swtzerland: ACM Press, 996, pp [] D. Heckerman and E. Horvtz, "Inferrng Informatonal Goals from Free-Text Queres: A Bayesan Approach," presented at Fourteenth Conference on Uncertanty n Artfcal Intellgence, Madson, WI, 998. [2] H. M. Meng, W. Lam, and K. F. Low, "A Bayesan approach for understandng nformaton-seekng queres VO - 4," presented at IEEE Internatonal Conference on Systems, Man, and Cybernetcs, 999. IEEE SMC '99 Conference Proceedngs., 999. [3] T. Leonard and J. S. J. Hsu, Bayesan Methods - An Analyss for Statstcans and nterdscplnary Researchers. Cambrdge, Unted Kngdom: Cambrdge Unversty Press, 999. [4] A. A. Skabar, "Inductve Learnng Technques for Mneral Potental Mappng," n School of Electrcal and Electronc Systems Engneerng. Brsbane: Queensland Unversty of Technology, 2, pp [5] T. M. Mtchell, Machne Learnng. New York: McGraw- Hll, 997. [6] A. Jameson, B. Gro[ss]mann-Hutter, L. March, R. Rummer, T. Bohnenberger, and F. Wttg, "When actons have consequences: emprcally based decson makng for ntellgent user nterfaces," Knowledge-Based Systems, vol. 4, pp , 2. [7] P. Haddawy, J. Jacobson, and C. E. Kahn Jr., "BANTER: a Bayesan network tutorng shell," Artfcal Intellgence n Medcne, vol., pp. 77-2, 997. [8] N. Lem and P. Haddawy, "Answerng queres from context-senstve probablstc knowledge bases," Theoretcal Computer Scence, vol. 7, pp , 997. [9] M.-L. Shyu and S.-C. Chen, "A Bayesan network-based expert query system for a dstrbuted database system VO - 3," presented at IEEE Internatonal Conference on Systems, Man, and Cybernetcs, 2. [2] R. E. Neopoltan, Learnng Bayesan Networks. Upper Saddle Rver: Person Educaton, 24. [2] R. W. Robnson, "Countng unlabeled acyclc dgraphs," Lecture notes n mathematcs, 622: Combnatoral mathematcs V, New York: Sprnger-Verlag, 977. [22] D. M. Chckerng, "Learnng Equvalence Classes of Bayesan Network Structures," n Proceedng of Twelfth Conference Uncertanty n Artfcal Intellgence, E. Horvtz and F. Jensen, Eds., 996, pp [23] D. M. Chckerng, "Learnng Equvalence Classes of Bayesan-Network Structures," Journal of Machne Learnng Research, vol. 2, pp , 22. [24] G. F. Cooper and E. Herskovts, "A Bayesan Method for the Inducton of Probablstc Networks from Data," Machne Learnng, vol. 9, pp , 992. [25] "Bayes Net Toolbox for Matlab," MIT, 24, accessed on: May-24. [26] W. R. Tobler, Cellular Geography, Phllosophy n Geography. Dordrecht: Redel, 979. [27] S. Chawla, S. Shekhar, W. Wu, and U. Ozesm, "Modelng spatal dependences for mnng geospatal data: An ntroducton," n In Geographc data mnng and Knowledge Dscovery(GKD, H. Mller and J. Han, Eds. Taylor and Francs, 2. [28] R. Baeza-Yates and B. Rbero-Neto, Modern Informaton Retreval. New York: ACM Press, 999. [29] "MSBNx: Bayesan Network Edtor and Toolkt," Mcrosoft, 23, accessed on: