Selection of Streets from a Network Using Self-Organizing Maps

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1 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 1 Selecton of Streets from a Network Usng Self-Organzng Maps Bn Jang 1 and Lars Harre 2 1 Dvson of Geomatcs, Dept. of Technology and Bult Envronment Unversty of Gävle, SE Gävle, Sweden e-mal: bn.jang@hg.se 2 GIS centre, Lund Unversty Sölvegatan 13, SE Lund, Sweden e-mal: lars.harre@lantm.lth.se Abstract We propose a novel approach to selecton of mportant streets from a network, based on the technque of a self-organzng map (SOM), an artfcal neural network algorthm for data clusterng and vsualzaton. Usng the SOM tranng process, the approach derves a set of neurons by consderng multple attrbutes ncludng topologcal, geometrc and semantc propertes of streets. The set of neurons consttutes a SOM, wth whch each neuron corresponds to a set of streets wth smlar propertes. Our approach creates an exploratory lnkage between the SOM and a street network, thus provdng a vsual tool to cluster streets nteractvely. The approach s valdated wth a case study appled to the street network n Munch, Germany. Keywords: cartographc generalzaton, model generalzaton, street networks, self-organzng map 1. Introducton Selecton of streets from a street network s an mportant generalzaton operaton, and may be a prerequste to other generalzaton operatons such as lne smplfcaton. A common technque n map producton s to select the streets based on semantc attrbutes (manly street types or functon classes). Several researchers have ponted out that ths approach s nsuffcent and have clamed that topologcal and geometrcal propertes of the streets cannot be neglected. Of note s the work of Mackaness and hs colleague (Mackaness and Beard 1993, Mackaness 1995) who recognzed the potental of graph theory n the applcaton of street network generalzaton. In ther work the streets were selected by ther connectvty propertes. Thomson and Rchardson (1995) used a graph-theoretc approach based on the concept of mnmum spannng trees to select mportant street segments wthn a street network. From a functonal pont of vew, Morsset and Ruas (1997) model the mportance of streets by the amount of street use. Thus they proposed an approach of selectng characterstc streets based on hgh frequency of street usage through an agent-based smulaton. Thomson and Rchardson (1999) used a good contnuaton prncple of perceptual organzaton to the generalzaton of networks, and of street networks n partcular. The prncple serves as the bass for parttonng a street network nto a set of lnear elements (or strokes), whch are chans of network arcs. In terms of structural measures such as length, class and connectvty, relatve mportant strokes can be derved for generalzaton purpose.

2 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 2 All the above nvestgatons are actually orented towards the selecton of mportant street segments rather than a whole named street, because street networks are modelled at a geometrc level. Recently, Jang and Claramunt (2002) proposed a set of algorthms based on a structural analyss. The structural approach s performed at a topologcal level wth a representaton, whch takes named streets as nodes and street ntersectons as lnks of a connectvty graph. Based on the graph-theoretc representaton, each street s assgned by two structural measures namely connectvty and average path length on whch the selecton of mportant streets s based. Eventually the selecton of streets s appled to an entre named street rather than a street segment usng these two structural measures. In ths paper we propose an approach that consders street attrbutes nvolvng topologcal, geometrc and semantc propertes as nput to a self-organzng map (SOM) (Kohonen, 2001). SOM s an artfcal neural network algorthm that, n our study, s used to categorse the streets n a network. Our approach adopts SOM tranng algorthm to group all streets nto dfferent categores accordng to varous attrbutes, and then selects streets at reduced map scales based on these categores. As the process s based on multple attrbutes from topologcal, geometrc and semantc perspectves, ths approach can be consdered to be comprehensve n terms of the process. Through the traned SOM a two dmensonal grd of neurons, the smlarty of streets can be nteractvely explored and vsualzed. It should be noted that the approach we propose here s a general one for categorzng objects based on multple attrbutes. Therefore t could be used for other types of spatal object selecton where multple attrbutes should be consdered. SOM has been used n many felds such as data classfcaton, pattern recognton, mage analyss, and exploratory data analyss (for an overvew, see Oja and Kask 1999). In the doman of GIS and cartography, relatvely few applcatons have been made. However, Openshaw and hs colleagues have used the SOM approach n spatal data analyss to classfy census data (Openshaw 1994, Openshaw et al. 1995). Recently some new proposals have been made n usng SOM for explorng spatal data (L 1998) and n mage classfcaton (Luo and Tseng 2000). SOM has been used for buldng typfcaton n cartographc generalzaton (Højholt 1995, Sester 2001). In the typfcaton process, a number of buldng objects were set to represent a larger set of objects. A major ssue here s that the new objects should reflect the orgnal pattern of objects. In the approach ntroduced by Højholt and Sester, new buldng objects are placed randomly on the map. Then the locatons of the new buldng objects are changed usng SOM. In ths tranng process the orgnal buldng objects are used for attractng the new buldng objects. In ths way the locaton of the new buldng objects wll gve a smlar pattern as the locaton of the orgnal buldng objects (but propertes such as parallelsm are not mantaned). The use of SOM n ths paper s rather dfferent. Here t s used for attrbute clusterng as a pre-process for selecton of streets; the locatons of the streets are not altered. The remander of ths paper s structured as follows. Secton 2 presents the basc prncple and algorthm of SOM. Secton 3 ntroduces multple attrbutes respectvely from topologcal, geometrc and semantc perspectves for ndvdual streets wthn a network. Based on these multple attrbutes, secton 4 ntroduces a SOM-based approach for the selecton of streets. Secton 5 llustrates an applcaton of our approach usng Munch street network as an example. Fnally secton 6 concludes the paper and dentfes future work.

3 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 3 2. Self-organzng map SOM s a well-developed neural network technque for data clusterng and vsualzaton. It can be used for projectng a large data set of a hgh dmenson nto a low dmenson (usually one or two dmensons) whle retanng the ntal pattern of data samples. That s, data samples that are close to each other n the nput space are also close to each other n the low dmensonal space. In ths sense, SOM resembles a geographc map showng the dstrbuton of phenomena, n partcular referrng to the frst law of geography: everythng s related to everythng else, but near thngs are more related to each other (Tobler 1970). Herewth we provde a bref ntroducton to the SOM; readers are encouraged to refer to a more complete descrpton (e.g. Kohonen 2001). 2.1 Basc prncple Let s represent a d-dmensonal dataset as a set of nput vectors of d dmensons,.e. X = { x1, x2,... xn}, where n s the sze of the dataset or equally the number of nput vectors. The SOM tranng algorthm nvolves essentally two processes, namely vector quantzaton and vector projecton (Vesanto 1999). Vector quantzaton creates a representatve set of vectors, so called output vectors from the nput vectors. Let s denote the output vectors as M = { m1, m2,... mk} wth the same dmenson as nput vectors. In general, vector quantzaton reduces the number of vectors, and ths can be consdered as a clusterng process. The other process, vector projecton, ams at projectng the k output vectors (n d-dmensonal space) onto a regular tessellaton (.e., a SOM) of a lower dmenson, where the regular tessellaton conssts of k neurons. The projecton s performed as such: close output vectors n d- dmensonal space wll be projected onto neghbourng neurons n the SOM. Ths wll ensure that the ntal pattern of the nput data s kept. The two tasks are llustrated n Fgure 1, where both nput and output vectors are represented as a table format wth columns as dmenson and rows as ID of vectors. Usually the number of nput vectors s greater than that of the output vectors,.e. n f k, and the sze of SOM s the same as that of the output vectors wthout excepton. In the fgure, the SOM s represented by a transtonal color scale, whch mples that smlar neurons are beng together. It should be emphaszed that for the purpose of explanaton, we separate t nto two tasks, whch are actually combned together n SOM wthout beng sequental. ID DIM Input vectors d vector quantzaton ID DIM 1 2. c. Output vectors d vector projecton SOM n K (d-dmenson) (d-dmenson) (2-dmenson) Fgure 1: Illustraton of SOM prncple 2.2 The algorthm The above two steps, vector quantzaton and vector projecton, consttute the bass of the SOM algorthm. Vector quantzaton s performed as follows. Frst the output vectors are ntalzed randomly or lnearly by some values for ther varables. Then n the followng

4 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 4 tranng step, one sample vector x from the nput vectors s randomly chosen and the dstance between t and all the output vectors s calculated. The output vector that s closest to the nput vector x s called the Best-Matchng Unt (BMU), denoted by m c : c mn x m = { x m }, [1] where. s the dstance measure. Second the BMU or wnnng neuron and other output vectors n ts neghbourhood are updated to be closer to x n the nput vector space. The update rule for the output vector s: m( t + 1) = m( t) + α( t) hc (t)[ x( t) - m ( t)] m ( t + 1) = m ( t) for N for N c c (t) (t) [2] where x(t) s a sample vector randomly taken from nput vectors, m (t) s the output vector for any neuron wthn the neghbourhood Nc(t), and α (t) and h c (t) are the learnng rate functon and neghbourhood kernel functon respectvely. The algorthm can be descrbed n a step-by-step fashon as follows. Step 1: Defne the nput vectors that defne an attrbute space. The nput vectors are lkely to be n a table format as shown n Fgure 1, where d varables determne a d-dmensonal attrbute space. Based on the nput vector space, an ntalzed SOM wll be mposed for the tranng process (c.f. step 3). Step 2: Defne the sze, dmensonalty, and shape of a SOM. The sze s actually the number of neurons for a SOM. It can be determned arbtrarly, but one prncple s that the sze should be suffcent to detect the pattern or structure of SOM (Wlppu 1997). The number of neurons can be arranged n a 1- or 2-dmensonal space (dmensonalty). Usually three knds of shape are allowed,.e. sheet, cylnder or torod, but sheet s the default shape. Step 3: Intalze output vectors m randomly or lnearly. At the ntalsaton step, each neuron s assgned randomly or lnearly by some values for the d varables. Thus an ntal SOM s mposed n the nput vector space for the followng tranng process. Step 4: Defne the parameters that control the tranng process nvolvng map lattce, neghbourhood, and tranng rate functons. The number of neurons defned can be arranged n two dfferent map lattces, namely hexagonal and rectangular lattces. However, hexagonal lattce s usually preferred because of ts better vsual effect (Kohonen 2001). The Gaussan neghbourhood functon s often adopted and s defned by: h c 2 2 d / 2 t ( t) e c σ = [3]

5 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 5 whereσ t s the neghbourhood radus at tme t, d c s the dstance between neurons c and on the SOM grd. Note that the sze of the neghbourhood N c (t) reduces slowly as a functon of tme,.e. t starts wth farly large neghbourhoods and ends wth small ones (see fgure 2). The tranng rate functon can be lnear, exponental or nversely proportonal to tme t (see Vesanto et al. 2000, pp. 10). For nstance, α( t ) = α0 /( t / T) s the functon we adopted n the followng case study, where T s the tranng length and α 0 s the ntal learnng rate. Usually the tranng length s dvded nto two perods: t 1 for the ntal coarse structurng perod and t 2 for the fne structurng perod. Step 5: Select one nput vector x, and determne ts Best-Matchng Unt (BMU) or wnnng neuron usng equaton [1]. Although Eucldan dstance s usually used n equaton [1], t could be varous other measures defnng nearness and smlarty. Dependng on the form of data measurement, other measures are allowed as long as they represent the dstance between nput and output vectors. Step 6: Update the attrbutes of the wnnng neuron and all those neurons wthn the neghbourhood of the wnnng neuron, otherwse leave alone (c.f. equaton [2]). Step 7: Repeat steps 5 to 6 a very large number of tmes (tranng length) tll a convergence s reached. The convergence s set lke ths, m ( t + 1) = m ( t), for t. In practce, the tranng length n epochs s determned by the sze of SOM (k) and the sze of the tranng data (n), for k nstance for the coarse perod t = 4 1. n Followng the above steps, all output vectors are projected on to a 1- or 2-dmensonal space, where each neuron corresponds to an output vector that s the representatve of some nput vectors. A 2-dmensonal hexagonal map lattce grd s shown n Fgure 2 where each hexagonal cell has a unform neghbourhood. a ten-by-ten (one hundred neurons) lattce space neghbourng neurons at t1 neghbourng neurons at t2 neghbourng neurons at t3 wnner neuron or BMU

6 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 6 Fgure 2: The characterstcs of a 10x10 SOM (t1<t2<t3 wth h c (t) n equaton 3) 3 Topologcal, geometrc and semantc propertes of streets wthn a network It s mportant to note a dstncton between a named street and a street segment. A named street refers to an entre street apparently dentfed by a unque name or ID, and usually conssts of multple street segments, whle a street segment s just part of a named street (streets and named streets wll be used nterchangeably hereafter n the paper). In earler studes such as Thomson and Rchardon (1995), Morsset Ruas (1997), and Thomson and Rchardson (1999) the generalsaton of street network s based on street segments (n our termnology), but the study presented here s based on the entre named street. For a street network, each street has dfferent roles and there are numerous attrbutes that govern the roles of ndvdual streets from topologcal, geometrc and semantc perspectves. Before present these attrbutes, we shall ntroduce some bascs on graph theory and a graphtheoretc representaton of street networks. 3.1 Graph and a graph-theoretc representaton of street networks A graph G conssts of a fnte set of nodes (or vertces) V and a fnte set of lnks (or edges) E. A graph s often denoted as G(V,E) where V s the set of nodes, V = v, v,..., v }, and E s { 1 2 n the set of lnks, E = { v v j}. For computatonal purposes we represent a connected, undrected and unweghted (.e. all lnks wth a unt dstance) graph by an adjacency matrx R(G): [ r j ] n n R( G) = where r j 1 = 0 f v v E otherwse j [4] It should be noted that for an undrected graph G, ths adjacency matrx R(G) s symmetrc,.e. r j rj = rj. Also all dagonal elements of R(G) are equal to zero so are not needed. Thus the lower or upper trangular matrx of R(G) s suffcent for a complete descrpton of the graph G. For a more complete ntroducton to graph theory, readers can refer for example to (Gross and Yellen 1999). A graph-theoretc representaton of street works, whch take named streets as nodes and street ntersectons as lnks of a connectvty graph, llustrates many nce propertes for the understandng of the topology of street networks (Jang and Claramunt 2002). For nstance, fgure 3 shows a street network of a small urban area, and ts correspondng connectvty graph. In ths connectvty graph the streets are modelled as nodes and the junctons as lnks. From ths representaton, we observe that ths network s relatvely closed: a bell-shaped street (Sätrahöjden) consttutes a form of boundary, and t s nternally connected by two streets (Norrbågen, and Nyöstervägen) that form an nternal communcaton lnk. These three man streets form the man structure of ths network to whch other short streets are connected.

7 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 7 (a) (b) Fgure 3: A small street network (a) and ts connectvty graph (b) (Note: every node n (b) s labeled by the correspondng street name, and the sze of nodes shows the degree of connectvty of ndvdual streets) 3.2 Topologcal propertes Topologcal propertes of a street network are the propertes that are nvarant n a homeomorphc (rubbersheet) transformaton. Examples of such propertes are ntersecton, and connectedness. We assume that there are no prohbted turns or drvng drectons nvolved n the street networks, so the connectvty graph ntroduced above s an undrected graph, and the correspondng adjacency matrx s symmetrcal. Dstnct from conventonal geometrc vews of street networks, the connectvty graph takes a topologcal vew of the network. It should be noted that geometrc propertes, e.g. Eucldean dstances, are not stored n a connectvty graph. Concepts such as shortest path and shortest dstance are here purely graph-based and should not be confused wth ther counterparts n a geometrc network. In a connectvty graph, the shortest dstance s defned as the mnmum number of lnks between two nodes. By usng the connectvty graph representaton, many topologcal propertes regardng the status of ndvdual streets can be measured. Among many other measures ntally developed from Socal Network Analyss (SNA) (Scott 2000), centralty s one of mportant structural propertes and t nvolves three mportant measures: degree, closeness and betweenness (Freeman 1979). Degree centralty, also called connectvty, measures the number of streets that nterconnect a gven street. In a correspondng connectvty graph, degree s the number of nodes that lnk a gven node. Formally the degree centralty for a gven node v s defned by: C D n ( v ) = r( v, v ). [5] k= 1 k Closeness centralty measures the smallest number of lnks from a street to all other streets. In a correspondng connectvty graph, t s the shortest dstance from a gven node to all other nodes wthn a network. It s defned by:

8 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 8 C C n 1 ( v ) = n, [6] d ( v, v ) k= 1 ( k k where d v, v ) s the shortest dstance between nodes v and v k. Betweenness centralty measures to what extent a street s between streets. In a correspondng connectvty graph, t reflects the ntermedary locaton of a node along ndrect relatonshps lnkng other nodes. Formally t s defned by: n j 1 pkj CB( v ) = [7] p j= 1 k= 1 j where pj s he number of shortest paths from to j, and pkj from to j that pass through k, so pj through k. p kj s the number of shortest paths s the proporton of shortest paths from to j that pass These three centralty measures descrbe a street status from a topologcal perspectve. We can remark that degree shows topologcal relatonshp between a street and ts mmedate neghbourng street(s), whle closeness shows structural relatonshp between a street and all other streets. Both can be characterzed as a local measure and a global measure respectvely. A street wth hgh connectvty does not guarantee that t wll be well connected to all other streets. Also a street wth few drect connectons does not mean that t s less mportant, snce t can play a brdge role, whch means that wthout t a network may be broken nto two peces. Ths property s controlled by betweenness. 3.3 Geometrc and semantc propertes Common sense tells us that long and wde streets tend to be more mportant. Thus length and wdth are two most mportant geometrcal propertes. In practce length s often used for selecton of street n a network. For example, n the database specfcatons from Lantmäteret (the Swedsh natonal mappng agency) t s stated that drt roads should be represented n the target data set f they: lead to settlements (drt roads between m are represented as ramps) or other cartographc objects (mnmum length 250 m), connect roads, are along shores or have a length of more than 500 m (Lantmäteret 1997, p. 142; authors translaton). It s apparent that ths rule s, apart from the length of the road, also based on connectvty propertes. Semantc attrbutes such as functon classes (hghway, motorway, and normal street) speed lmt (90km, 70km and 50km) are mportant attrbutes to consder n the course of selecton. Examples of other nterestng propertes are semantc propertes that can be derved from lngustcs and ontology. There are dfferent names n Englsh for a street such as road, path, avenue, boulevard, and square. These names usually mply dfferent levels n terms of mportance and functon class, e.g. a boulevard s more mportant than a path. Based on such

9 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 9 a semantc analyss, each street can be quantzed wth a number to show dfferent levels, and t can then be consdered together wth topologcal and geometrc propertes as well. However snce such a semantc property s language dependent, we leave t out of our current study. 4 A SOM-based selecton approach consderng multple propertes Cartographc generalzaton nvolves two types of processes: model-based (the ntal choces of the relevant nformaton to be presented on the map) and geometrc-based (the smplfcaton of graphc characterstcs of objects) (Webel 1995). Model generalzaton takes place pror to geometrc generalzaton. For example, generalsng a street network can be dvded nto the followng processes. Select the street objects to be presented on the map (model-based generalsaton); Smplfy, smooth and dsplace the streets to make the map readable (geometrc-based generalsaton). In ths study we just consder model-based generalsaton of a street network. The process of our selecton approach s as follows: 1) Each named street consttutes a vector n attrbute space. Ths space s spanned by attrbutes of the types that were descrbed n secton 3. 2) These vectors then are used to tran a SOM as descrbed n secton 2. In ths SOM, neurons correspond to smlar streets n terms of attrbutes ntroduced. 3) Selecton s based on the two basc categores dentfed by the SOM. From a more practcal perspectve, the streets and ther correspondng attrbutes are used to create nput vectors. Tranng process s performed usng SOM Toolbox assocated wth Matlab (Vesanto et al. 2000). Although the number of output vectors (or neurons) of a SOM can be arbtrarly determned, we usually choose a number that s smaller than the number of nput vectors. Through the tranng process, each street acqures a best matchng unt from the set of neurons wthn the SOM. It helps to set up a lnkage between a SOM and correspondng street network. The specfc procedure for settng up such a lnkage n ArcVew GIS platform s as follows: 1. Create a polygon theme n whch each polygon has a hexagonal shape, representng a neuron wth output vectors as attrbutes n a table (SOM table) 2. Create a lnk table (LINK table) wth two felds, namely BMU and street ID 3. Lnk the SOM table and LINK table (note felds SOM-ID and BMU are equvalent) 4. Lnk the LINK table and NETWORK table through common feld street-id Through the above procedure, a lnkage s set up between a SOM and a correspondng street network (Fgure 4). SOM table LINK table NETWORK table SOM-ID d BMU street-id street-id d c c. c. m n n Fgure 4: Lnkage between SOM and a street network

10 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 10 One prncple of our approach s that all streets should be nterconnected, whch s partally controlled by the betweenness measure. If the orgnal network s an ntegrated one, t should be kept as one n the reduced map scale and never broken nto peces. To meet ths requrement, we must select some less mportant streets to jon separated street clusters. Ths was acheved nteractvely. 5 A Case study To llustrate the selecton approach, a case study was carred out usng the street network of Munch, whch nvolves a total of 785 streets. We used seven attrbutes namely degree, closeness, betweenness, length, lanes (a modfed verson of wdth), speed lmt and functon class as descrbed n secton 3. These attrbutes ncely descrbe topologcal, geometrc and semantc propertes of ndvdual streets wthn the network. They were used to defne nput vectors for the followng tranng process. 5.1 Input vectors Our frst step was to derve a connectvty graph based on the network. The structural representaton provdes a sense as to how each street nterconnects to others. The process, wth reference to equaton [4], was performed wth an Avenue scrpt wth ArcVew GIS,.e. for each street (), check f t ntersects every other street (j), f yes, r j = 1, otherwse r j = 0. Thus a connectvty graph can be derved to represent such nterconnectons. Fgure 5 llustrates the street network and ts connectvty graph. Based on the connectvty graph, the topologcal propertes can be calculated; t s performed usng a network analyss software package called Pajek (Batagelj and Mrvar 1997). The remanng propertes are drectly derved from a GIS database wth the network. Both length and lanes were transformed from street segments to ndvdual streets by takng an average value of each attrbute assgned to the street segments. It s mportant to note that the attrbutes class and speed are n an ordnal scale, e.g. 1 for the street wth the hghest speed lmt and 8 for the lowest. Furthermore, functon class and speed lmt are nversely proportonal to the mportance of a street,.e. the hgher the value, the less mportant the street. In ths case, we take a recprocal value of these attrbute values for the tranng process. Thus all seven attrbutes have the same order n terms of the mportance of the streets. The seven attrbutes consttute an attrbute space n whch each nput vector has a unque locaton. Table 1 shows part of the nput vectors of the multdmensonal dataset contanng 785 records. (a) (b)

11 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 11 Fgure 5: The Munch street network (a) and ts connectvty graph (b) Table 1: The frst 10 nput streets of the Munch network Street-name Degree Closeness Betweenness Length Lanes Speed Class ACKER ADALBERT ADAM-ERMINGER ADELGUNDEN ADELHEID ADLZREITER ADOLF-KOLPING AGILOLFINGER AGNES AIGNER Intalzaton and SOM tranng process Wth the nput vectors we are ready to do the second step namely ntalsaton and tranng. To ths end, we frst defne a map sze of 100,.e. a SOM n a two-dmensonal grd. Then usng lnear ntalzaton we create output vectors, each of whch has 7 attrbutes. The ntalsed output vectors were traned based on the nput vectors. The varaton of ndvdual attrbutes noted from Table 1 s very large, so we determned to transform the dataset nto a unt nterval [0, 1] to guarantee that all varables have the same varaton. From cartographc generalzaton practse, we determned that functon class has the hghest prorty n street selecton, and ths s followed by geometrcal and topologcal propertes. Therefore we adopt the weght vector [1, 1, 1, 2, 2, 2, 3] for the seven attrbutes n the order: [degree, closeness, betweenness, length, lanes, speed, class]. Users can adopt a dfferent weght vector accordng to ther dfferent generalzaton purposes. Durng the tranng process, a Gaussan neghbourhood functon was chosen. Other detaled parameter settngs are lsted n table 2. Table 2: Parameter settngs for the SOM tranng Parameter Value Sze (m) 100 Dmensonalty 2 Shape Sheet Map lattce Hexagonal Neghbourhood Gaussan Learnng rate (α ) α ( t ) = α0 /( t / T) Intal learnng rate ( α 0) 0.5 for the coarse perod 0.05 for the fne perod Tranng length n epochs (T) 0.51 epochs for the coarse perod 2.04 epochs for the fne perod Intal neghbourhood radus ( σ 0 ) 5 Fnal neghbourhood radus 1.25 for the coarse perod

12 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 12 1 for the fne perod It s mportant to note that the sze of SOM has a sgnfcant mpact on detectng clusters (Wlppu 1997), but the sze we chose seemed suffcent to detect the pattern. Table 3 llustrates the frst 10 neurons of the traned map of the SOM; each row of the table corresponds to a neuron of the SOM. The 10 neurons correspond to the most left column of the SOM shown n fgure 6. It should be noted that followng the tranng process, the vectors have been transformed back to ntal data ranges. The rows n tables 1 and 3 correspond to nput vectors and output vectors respectvely n fgure 1. Table 3: The frst 10 neurons wth the SOM Neuron-ID Degree Closeness Betweenness Length Lanes Speed Class Vsualzaton of the SOM The traned SOM s composed of neurons n a two dmensonal space that preserve the ntal pattern n the attrbute space of the nput streets (or nput vectors n terms of SOM). In other words, the seven dmensonal dataset s now mapped nto a two dmensonal SOM, retanng the ntal pattern. Such a pattern can be seen clearly from vsualzng the SOM n terms of ndvdual attrbutes. It should be noted that each cell or neuron s not a partcular street(s), but nstead t represents a group of smlar streets n terms of the seven attrbutes. Fgure 6 llustrates component vews of SOM from the perspectve of the seven attrbutes. We can remark that the smooth colour transtons wth the vsualzatons mply smlar neurons beng together, and some of attrbutes have sgnfcant correlaton, e.g., degree and length.

13 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 13 Fgure 6: Component vsualzatons of the SOM The two dmensonal SOM arranges smlar neurons wthn a neghbourhood, but s does not convey how smlar or dssmlar adjacent neurons are. Instead, a unfed dstance matrx (Umatrx) between the output vectors of adjacent unts of a SOM llustrates the degree of smlarty by calculatng dstances among them (Ultsch and Semon 1990). Thus t helps to llustrate the cluster structure of the SOM. Fgure 7(a) s the U-matrx representaton, where sx hexagons around each neuron show the smlarty between neurons,.e. the lghter the hexagon the greater the smlarty. Fgure 7(b), (c) and (d) shows varous ways of vsualzng the U-matrx usng dfferent vsual varables such as colour ntensty, sze of cells and colour hues, notng that the D-matrx s a dstance matrx from a neuron to ts neghbourng neurons. Our am s not to make a detaled clusterng analyss, but rather to make a dstncton between those that are selected or elmnated. From the set of vsualzatons, we note that there are two clusters as ndcted by A and B, although the boundary of the two clusters s not so clear-cut, and smlarty wthn cluster B s not as homogeneous as n cluster A. However the dstncton between the two clusters mght be more clearly reflected n the correspondng network as llustrated n the followng subsecton.

14 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 14 (a) (b) A B (c) (d) Fgure 7: U-matrx vsualzatons of the SOM 5.4 Selecton or elmnaton of streets at dfferent levels of detal The above SOM s mported nto ArcVew GIS as a polygon theme and each hexagon represents a neuron wth an output vector to be stored n the theme table. Usng the prncple gven n secton 4, we set up a lnkage between the SOM and the Munch network. The 785 streets have been grouped nto 100 neurons, and each of them represents a cluster. The tranng process can be consdered as a transformaton of generalzaton and clusterng. We have also seen the two clusters n terms of a dstance matrx. In the correspondng network, we can see that cluster A represents a set of unmportant streets, perhaps elmnated n the course of generalzaton. Fgure 8 llustrates two levels of detal for streets ntended for elmnaton (dark lnes n the network vew and dark cells n the SOM vew). In the smlar way, fgure 9 llustrates two levels of detals for those streets to be retaned. We note that the selected neurons n fgure 9 are those neurons wth hgher values for the varous attrbutes shown n fgure 6.

15 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 15 Fgure 8: Two levels of detal of streets to be elmnated. Fgure 9: Two levels of detal of streets to be selected.

16 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 16 These fgures llustrate how the SOM-based approach can be used to select and elmnate streets from a network. The approach s robust and flexble, as t consders multple attrbutes nvolvng topologcal, geometrc and semantc propertes. Furthermore, a dynamc lnkage has been set up between the SOM and the correspondng network for selecton or elmnaton purposes. 6. Concluson and future work From the model generalzaton perspectve, ths paper adopts a street-centred vew and consders multple attrbutes from topologcal, geometrc and semantc aspects for the selecton of streets from a network. Our approach clusters streets n dfferent categores accordng to the smlarty dstance n a hgh dmensonal attrbute space usng the SOM tranng algorthm. Through a lnkage between the SOM and the orgnal street network, end users are able to select streets for model generalzaton purposes. The case study appled to Munch network llustrates that the SOM-based approach can be used as an effectve way for the selecton of streets. It also shows that t s an effectve tool for data vsualzaton and exploraton for mult-dmensonal geospatal data. It s mportant to note that for a gven dataset and defned SOM propertes, the SOM tranng process s dependent on the parameter settngs. The settngs we adopted are default settngs (table 2) recommended by the SOM toolbox. Ths ssue deserves further research. Furthermore the seven varables are certanly not exhaustve; other combnaton and weghtngs mght be more approprate. Although SOM s appled to the selecton of streets, t could be appled to the selecton or generalzaton of other spatal objects, as long as such selecton s governed by multple attrbutes. Our future work wll seek to apply the approach to the generalzaton of other spatal objects. Acknowledgements The authors thank the referees for ther constructve comments and suggestons that sgnfcantly mproved the qualty of ths paper. The Munch dataset was provded by NavTech from the year References: Batagelj V. and Mrvar A. (1997), Networks/Pajek: Program for Large Networks Analyss, avalable at (access on ). Freeman L. C. (1979), Centralty n Socal Networks: Conceptual Clarfcaton, Socal Networks, 1, pp Gross J. and Yellwn J. (1999), Graph Theory and ts Applcaton, CRC Press: London. Højholt P. (1995). Generalzaton of buld-up areas usng Kohonen-networks, Proceedngs of Eurocarto XIII, 2-4 October, Ispra, Italy. L B. (1998), Explorng Spatal and Temporal Patterns wth Self-Organzng Maps, GIS/LIS 98, Bethesda, Maryland: Amercan Socety for Photogrammetry and Remote Sensng, pp

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18 NOT FOR CITATION, TO BE PUBLISHED IN TRANSACTIONS IN GIS 18 Vesanto J. (1999), SOM-Based Data Vsualzaton Methods, Intellgent Data Analyss, Elsever Scence, Volume 3(2), pp Vesanto J., Hmberg J., Alhonem E. and Parhankangas J. (2000), SOM Toolbox for Matlab 5, Report A57, Helsnk Unversty of Technology, Lbella Oy, Espoo. Webel R. (1995), Three Essental Buldng Blocks for Automated Generalsaton, n: Muller J. C., Lagrange J. P. and Webel R. (eds.), GIS and Generalzaton: Methodology and Practce, Taylor and Francs: London, pp Wlppu E. (1997), The Vsualzaton Capablty of Self-organzng Maps to Detect Devatons n Dstrbuton Control, TUCS Techncal Report No 153, Turku School of Economcs and Busness Admnstraton, Fnland.