A Novel Method for Transforming XML Documents to Time Series and Clustering Them Based on Delaunay Triangulation

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1 Appled Mathematcs, 2015, 6, Publshed Onlne June 2015 n ScRes. A Novel Method for Transformng XML Documents to Tme Seres and Clusterng Them Based on Delaunay Trangulaton Narges Shafean Department of Computer Engneerng, Zanjan Branch, Islamc Azad Unversty, Zanjan, Iran Emal: nshafean@gmal.com Receved 23 Aprl 2015; accepted 7 June 2015; publshed 10 June 2015 Copyrght 2015 by author and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY). Abstract Nowadays exchangng data n XML format become more popular and have wdespread applcaton because of smple mantenance and transferrng nature of XML documents. So, acceleratng search wthn such a document ensures search engne s effcency. In ths paper, we propose a technque for detectng the smlarty n the structure of XML documents; n the followng, we would cluster ths document wth Delaunay Trangulaton method. The technque s based on the dea of representng the structure of an XML document as a tme seres n whch each occurrence of a tag corresponds to a gven mpulse. So we could use Dscrete Fourer Transform as a smple method to analyze these sgnals n frequency doman and make smlarty matrces through a knd of dstance measurement, n order to group them nto clusters. We exploted Delaunay Trangulaton as a clusterng method to cluster the d-dmenson ponts of XML documents. The results show a sgnfcant effcency and accuracy n front of common methods. Keywords XML Mnng, Document Clusterng, XML Clusterng, Schema Matchng, Smlarty Measures, Delaunay Trangulaton, Cluster 1. Introducton The man dea of ths method s based on structure of XML documents; t means that, tags and poston of elements n XML tree s herarchy are consderable. So content of documents s not mportant, n other words, t may exst two documents wth completely smlar structure, based on our method but, completely dfferent content. Input of our method mplementaton s a set of documents and output s clusterng these documents nto varous How to cte ths paper: Shafean, N. (2015) A Novel Method for Transformng XML Documents to Tme Seres and Clusterng Them Based on Delaunay Trangulaton. Appled Mathematcs, 6,

2 clusters, and f clusterng s done correctly, documents wthn a cluster have the same structure and documents belongng to dfferent clusters have fewer structural smlarty. The man contrbuton of our approach s these steps: 1) Mappng each documents to a tme seres; 2) Gettng DFTs and transformng each tme seres from tme doman to frequency doman; 3) Mappng the sgnals related to each documents to a pont n d-dmensonal space; 4) Trangulaton of ponts related to documents; 5) Clusterng documents based on ther trangulaton. For analyzng accuracy of clusterng, we use external metrc. In analyzng based on external metrcs, we would evaluate other clusterng strateges n front of our proposed clusterng method. Havng more matches between clusterng metrc and other clusterng, clusterng may have more precson too. We use two external metrcs named F-Measure and Purty as evaluator of our method. More nformaton about ths method s mentoned n [1]. The corpus of documents for evaluatng ths method s a standard corpus, whch a part of that s appled. Ths corpus has clusterng metrc tself whch we use t as a comparson versus our external metrcs. Ths corpus could download from references mentoned n [2] and s defned n [1]. The rest of the paper s organzed as follows: In Secton 2, we present some nformaton about common methods for detectng smlartes and clusterng documents. Secton 3 expresses mplementaton requrements and developng envronment. Secton 4 llustrates how the structure of an XML document can be encoded nto a tme seres, mapped to d-dmenson space, trangulated and fnally clustered; then t presents some methods for accomplshng such tasks. Secton 5 descrbes several experments we perform, on encyclopaeda data set, to valdate our approach. We sketch some ssues whch could be faced n future work on ths topc, and conclude the paper n Secton Related Work Summary Several methods for detectng the smlarty of XML documents have been recently proposed, that s based on the concept of edt dstance and use graph-matchng algorthms to calculate a (mnmum cost) edt scrpt capable of transformng a document nto another. Most of these technques are computatonally expensve,.e. at least O (N3), where N s the number of element of the two documents. However, all of them are concerned wth the detecton of changes occurrng n XML documents rather than comparng them on the bass of ther structural smlarty. Some approaches have a technque for measurng the smlarty of a document versus a DTD s ntroduced. Ths technque explots a graph-matchng algorthm, whch assocates elements n the document wth element n the DTD. Ths approach does not seem to be drectly applcable to cluster documents wthout any knowledge about ther DTDs, and s not able to pont out dssmlartes among documents referrng to the same DTD [3]. Indeed, we propose to represent the structure of an XML document as a tme seres, where each tag occurrence corresponds to an mpulse. By analysng the frequences of the Fourer Transform of such seres, we can state the degree of (structural) smlarty between documents. As a matter of fact, the explotaton of the Fourer transform to check smlartes among tme seres s not completely new [3] and has been proven successful. The man contrbuton of our approach s the systematc development of an encodng scheme for XML documents, n a way that makes the use of the Fourer Transform extremely proftable. Hence, after detecton of documents smlarty we could group documents nto dfferent clusters, whch ntensvely accelerate search engne motors. Partcularly, XML document clusterng Algorthms dvded nto two groups: Par wse methods. Incremental methods. Par wse based algorthms are more common whch frst create a smlarty matrx for each par of documents. Ths matrx s ntalzed by a crteron for measurng smlarty between two documents. Fnally, after completng the matrx we can use a general clusterng algorthm such as K-means to locate a document n ts proper cluster. In ths paper we appled a new clusterng method named Delaunay trangulaton, whch s used for clusterng vdeo frames. In contrast to many of the other clusterng technques, the Delaunay clusterng algorthm s fully automatc wth no user specfed parameters [4]. 1077

3 3. Implements Requrements and Performng Our proposed method developed by java and n order to run, need JRE or JDK (6 versons). Development envronment s Eclpse (and usng SAX, Flanagan lbrary to mplement some part of the program). In one phase of project we need to trangulate some ponts n d-dmensonal space, wth Delaunay method. In consderaton of large sze of d (more than 3), ths functon extremely reduce effcency. In order to ncrease effcency, we use C++ language and CGAL lbrary [5] for mplementng ths phase. Ths program s wrtten and comple ndependently and t just trangulate ponts. 4. Clusterng Phases 4.1. Mappng Each Documents to a Tme Seres In ths phase XML documents parsed one by one and a tme seres produced, t means that a set of numbers whch are n tme ordered, produced. For producng tme seres a specal codng functon appled whch s effectvely reflect documents structure, means tags and herarchal structure of XML tree. The codng functon has two parts. One of them s local and gves a unque dentty to each tag. In order to make ths dentty for each tag we use a random order. Wth every vst of a new tag, the tag was added to a data base and an unused dentty assgned to t. From now to, wth vst of that tag, ths local code was looked up n data base and beng used. In addton, local codng based on tags, we use a general codng functon whch, take attenton to poston of tags n herarchy structure. Ths general codng, assgn a specal weght to each tags based on ts depth and herarchy structure. Detaled nformaton about labellng documents s fndng n [3]. Mappng documents to tme seres are done as below defnton. Defnton 1. Let D be a set of XML documents, d a document n D wth sk ( d ) = [ t,, 0 tn ] and γ a tag encodng functon for D. Moreover, let maxdepth (D) represent the maxmum depth of any document n D, B a fxed value and nestd ( t n) the set of tag nstances assocated wth the ancestors of the element wth tag nstance t. A multlevel encodng of d (mlemc (d)) s a sequence [ S0, S1,, Sn ], where: S t B maxdepth( D) l maxdepth t ( D) l t B t j = γ + γ (1) ( ) ( ) t j nest j dt ( ) We usually set B as the number of dstnct symbols encoded by (e.g., B = tnames ( D) + 1 n the case of nvarant γ d ). In ths way, we avod mxng the contrbutons of dfferent nestng levels and can reconstruct the path from the root to any tag by only consderng the correspondng value n the encoded sequence. In fact, the summaton on the rght-hand sde of the above formula can be nterpreted as the nteger whose B-base represenγ t t nest t, ordered by ncreasng nestng levels of the cor- { j j d } taton s the sequence of the tag codes n ( ) ( ) respondng tags. Notce that such a property s stronger than WSL, and s not mandatory for guaranteeng njectvty n the encodng functon. For example n the documents below, we could realze that (a) and (b) documents are more smlar to document (c). In order to approve t va ther transferred format, we should notce the next phase Gettng Dscrete Fourer Transform (DFT) and Transferrng Each Tme Seres from Tme Doman to Frequency Doman Tme seres produced n prevous phase are n tme doman means that these seres reveal tags wth ts specal structure, durng tme doman. The Length of these sgnals s dfferent and comparson of them s dffcult. In order to capture smlartes and structural dfferences, sgnals transfer from tme doman to frequency doman. So we could compare two sgnals magntudes n specfc frequency. Ths comparson reflected n structural dfferences between documents. Consder Fgure 1, representng the documents of Fgure 2. Observe that all the sgnals have dfferent shapes. Notwthstandng, the dfference among the sgnals can be summarzed as follows: Each book element s assocated wth a unque subsequence wthn the sgnals assocated wth book 1 and book 2. Nevertheless, the sub sequences number s occurrences are dfferent. 3 has two dfferent sub sequences assocated wth the book elements. Moreover, the frst subsequence s dfferent from the ones n book 1 and book 2. A comparson n the tme doman (accomplshed usng the tme-warpng dstance) wll result n a hgher 1078

4 Fgure 1. Nonzero frequency components of the book 1, book 2, and book 3 documents n Fgure 2, Dscrete fourer transform. XML XML Ttle Author Ttle Author (a) Ttle Author Ttle Author Ttle Author (b) XML Ttle Author Ttle Author Name Emal (c) Fgure 2. (a) 1 and (b) book 2 have the same elements, but wth dfferent cardnalty. By contrast, (c) book 3 nduces a dfferent structure for the author element. 1079

5 smlarty between book 1 and book 3 than between book 1 and book 2. Nevertheless, each dfferent subsequence trggers a dfferent contrbuton n the frequency doman, thus allowng for detectng the above descrbed dssmlartes. To better understand how the dfferences between two documents reflect on the frequency spectra of ther assocated encodngs, we can always consder these dfferences separately and explot the lnearty property of the Fourer transform. Defnton 2. Let d 1, d 2 be two XML documents, and enc a document encodng functon, such that = enc ( d ) and h enc ( d ) h1 1 2 = 2. Let DFT be the Dscrete Fourer Transform of the (normalzed) sgnals. The explotaton of the Fourer transform to check smlartes among tme seres s not new, for more nformaton see, [3]. The man contrbuton of our approach s the systematc development of effectve encodng schemes for XML documents, n a way that makes the use of the Fourer Transform extremely proftable. The choce of comparng the frequency spectra follows both effectveness and effcency ssues. Indeed, the explotaton of DFT leads to abstract from structural detals whch, n most applcaton contexts, should not affect the smlarty estmaton (such as, e.g., dfferent numbers of occurrences of a shared element or small shfts n the actual postons where t appears). Ths eventually makes the comparson less senstve to mnor msmatches. Moreover, a frequency-based approach allows us to estmate the smlarty through smple measures (e.g., vector dstances) whch are computatonally less expensve than technques based on the drect comparson of the orgnal document structures. We defne the Dscrete Fourer Transform dstance of the documents as the approxmaton of the dfference of the magntudes of the DFT of the two encoded documents: ( ) M 2 dst ( d1, d2) = DFT ( h1) ( k ) DFT ( h2) ( k ) k = 1 (2) where DFT s an nterpolaton of DFT to the frequences appearng n both d 1 and d 2, and M s the total number of ponts appearng n the nterpolaton,.e., M = Nd + N 1 d. Fgure 3 dsplay the DFT value of each j par of a, b and c document, showng sequentally 1.xml, 2.xml and 3.xml, whch calculated value obvously show smlarty between documents, lower value means more smlarty. Hence, produced frequency sgnals, completely present documents structural dfferences, whch s turned out n smlarty matrx, too. Means that bgger value of the cell, related to documents, reveal more dstance and also lower smlarty. In order to transferrng tme seres from tme doman to frequency doman, Dscrete Fourer Transform (DFT) has exploted. We use JAVA lbrary to perform ths transferrng. Ths lbrary usng FFT algorthm whch have sutable tme cost too. For more nformaton refer to [3] Mappng Sgnal Correspondng to Each Document to a Pont n d-dmensonal Space Fnally we could samplng the sgnal consequence from prevous phase and make a dscrete sgnal. If samplng was done for the same frequency and sgnals magntude compared n these postons, documents smlarty can estmated. More samplng conclude to more accurate comparson and, n other hand, tme cost of other reman calculaton was ncreased. Thus, choosng a degree for samplng, have ntensve nfluence to clusterng effcency and accuracy, so s a trade-off. After ths phase, each document mapped to sgnal pont n d-dmenson space, whch d s the sze of appled samplng. Now there are some ponts n d-dmenson, whch should be clustered. In other applcatons, we could Fgure 3. Smlarty matrx corresponds to (a), (b), (c) documents. 1080

6 map component of vdeos, mages, sounds and etc. to ponts and use a clusterng method for them too. Afterwards, we could compare ths clusterng method wth others. In other word, we could gve these ponts to them and compare the results. Each pont can be as a feature vector Trangulate Ponts Correspondng Documents From ths phase, ponts correspond to documents s n d-dmenson, trangulaton was exploted because of followng reasons: nsde of produced trangles was no pont or ponts. It means that each pont s at the corner of one or more trangles but not n the any trangle. Ths good feature s desrable for hgh effcency clusterng whch, s defned n the followng part. Notce that trangle are not only n only two-dmenson and be any shape lke pyramd and etc. n hgher dmensons. In d-dmenson space each trangle made up d + 1 corner. Consequence of ths phase s a graph whch vertex are ponts and ts edges are sdes of trangles produced from ths trangulaton method. The graph s saved as a fle tll, clusterng algorthm used t. Trangulaton n ncremental way was mplemented by CGAL lbrary, whch s complcated and when the dmenson be hgher, t s done very slowly. Other trangulaton methods exst for Delaunay but ther problem was dmensons, too. Trangulaton was done as below defntons. The formal defntons for the mean edge length and local standard devaton for each data pont follows from Defntons 3 and 4. Defnton 3. The mean length of edges ncdent to each pont p s denoted by Local_Mean_Length (p ) and s defned as 1 d( p ) Local_Mean_Length ( p ) = e j= 1 j (3) p p where d(p ) denotes to the number of Delaunay edges ncdent to p and e j denotes to the length of Delaunay edges ncdent to p. Defnton 4. The local standard devaton of the length of the edges ncdent to p s denoted by Local_Dev(p ) and s defned as ( ) ( ) ( Local_Mean_Length ( ) ) 1 Local_Dev p p e d ( p ) 2 = 1 j j (4) = d( p ) To ncorporate both global and local effects, we take the average of local standard devaton of the edges at all ponts n the Delaunay dagram as a global length standard devaton as defned n Defnton 5. Defnton 5 the mean of the local standard devaton of all edges s denoted by Global_Dev(P) and s defned as 1 N Global_Dev ( P) = Local_Dev ( p ) = 1 (5) N where N s the number of total ponts and P s the set of the ponts. All edges that are longer than the local mean length plus global standard devaton are classfed as nter-edges (Defnton 7) and form the separatng edge between clusters. The formal defnton for short and separatng edges n terms of mean edge length of a pont and mean standard devaton are captured n Defntons 4 and 5 below. Defnton 6. A short edge (ntra-cluster edge) s denoted by Short_Edge(p ) and s defned as { } ( p ) e e ( p ) ( P) Short_Edge = < Local_Mean_Length Global_Dev (6) j j Defnton 7. A Separatng edge (nter-cluster edge) s denoted by Separatng_Edge (p ) and s defned as { } ( p ) e e ( p ) ( P) Sepratng_Edge = > Local_Mean_Length Global_Dev (7) j j Delaunay Trangulaton can be done effectvely n O(nlogn) tme and the dentfcaton of nter and ntra edges can be done n O(n) tme where n s the number of documents processed. For detaled nformaton refer to [4] Clusterng Documents Based on Ther Trangulaton The trangles obtaned from prevous phase are appled for clusterng. The trangulaton method has a feature that, havng no pont nsde of any trangles, was guaranteed. Wth ths key feature, analysng every sdes of any tr- 1081

7 angles to recognzng nearest and farthest ponts, could be possble. Hence, we could dsconnect lnks between ponts of graph by deletng farly bg edges. Fnally, Graph was dvded nto some ndvdual sectons. Each of them made a new cluster. Recognzng farly bg edges, was done n the way was llustrated n [4]. We use a parameter for control deletng bgger edges. Ths parameter that named clusterng factor, demonstratng what rate of edges devatons expressed the edges should be deletng. Ths way s farly complcated for, length mean of every edges end up to each vertex, ther standards devatons and average of all standard devaton, should be computed. Fnally some fle produced whch, each of them contan some documents, were nsde of a cluster. Wth hgher value of clusterng parameter, number of produced cluster became bgger. Ths parameter should choose n the way that sutable number of clusters been produced. We could do clusterng more tmes for each set of XML documents to fnd ts sutable clusterng factor value. 5. Clusterng Evaluaton s Parameters and Notfcatons As mentoned before, for evaluatng accuracy of proposed method, we use two parameters named Purty and F-Measure. These two parameters computaton method was llustrated n [1]. For computng the parameter whch was n external type, a clusterng metrc was needed. Corpus of the used data set has ths metrc, ths corpus explaned n [6] as ths: Closer value of these parameters to 100 percent means clusterng accuracy rate was hgher, and n verse. Clusterng a set of documents wth proposed method expressed that, these parameter sn t hgh enough. Mean that, ths knd of clusterng method sutable for clusterng the data set. Three parameters have nfluenced to clusterng effcency and accuracy, nvolved: Number of sampled ponts from documents frequency: more number of ponts s samplng from documents frequences (produced dagram of transferrng tme seres from tme doman to frequency doman), made documents comparsons better. Ths parameter expressed the ponts space dmensons. For ntensve neffcency trangulaton n hgher dmensons, ncreasng number of samplng made clusterng run slowly; whch also, exclude to lower performance n trangulaton and clusterng. Clusterng parameter: hgher value of ths parameter, made number of produced clusters hgher. Ths parameter defned expressed whch edges are farly bg. We could fnd out the sutable value of ths parameter by dong some tral and error. However, the value of ths parameter s not nfluenced to the method effcency but s nfluenced to consequence s accuracy. The parameter should respectvely that, number of produced clusters be about the number of clusters n clusterng metrc. β parameter: Ths parameter s appled n clusterng evaluaton, (for F-Measure calculaton). Settng ths parameter wth 5 s a good choce, n realty, we could assgn other values to t, whch s fnally ddn t mpact on clusterng effcency. Notce that, n evaluatng other methods based on ths F-Measure, the parameter must be fxed. Number and length of documents, tag s length and knds: these parameters nfluenced to clusterng effcency, especally, n parsng documents level means n tree structural presentaton, so t expressed overall effcency. User couldn t choose them but, could choose the set of documents. 6. Expermental Results We have two knds of data sets n evaluaton, one used n [2], s Englsh Sngle Label Categorzaton Collecton- XML Document, whch have 10 categores of documents, each category nclude 10 documents. And synthesze data set whch s produce by pecng the set of tags wth dfferent depth and length but sngle subject together n a sngle category; we need to use of 5 categores nclude 10 documents n each category. The below fgures presents the results of runnng the system, on both real n Fgure 4 and syntheszes data sets n Fgure 5 for dfferent value of clusterng factor and also sngle dmenson. (x-axs reveals dfferent clusterng factor and y-axs reveals calculated value of number of clusters, Purty and F-Measure by precent.) In Fgure 6, we compare common methods of clusterng XML documents wth proposed system on executon tme (x-axs reveals number of xml documents and y-axs reveals calculated executon tme by msec), and we fnd out, our method due to usng transferrng to tme seres approach, gettng the best nformaton about the 1082

8 Fgure 4. Dagram of runnng the system on real dataset n dfferent value for clusterng factor. Fgure 5. Dagram of runnng the system on synthesze dataset n dfferent value for clusterng factor. Fgure 6. Executon tme comparson on varyng number of XML documents n msec. documents very quckly, so t can have less tme to clusterng documents too. In verse of other clusterng methods, lkes catchng common structure n document s tree, whch needed to search the entre document. Below fgures, present result of runnng common and proposed system on dfferent number of documents. (x-axs reveals number of XML documents and y-axs reveals calculated Purty by percent n Fgure 7 and also 1083

9 x-axs reveals number of XML documents and y-axs reveals calculated F-Measure by percent n Fgure 8), Dagrams reveal proposed method do the best n a constant value of dmenson and clusterng factor parameter, as we expected. 7. Conclusons and Future Works Evaluaton results are desrable enough. Clusterng metrcs are based on subject and content of documents. But our proposed method clusters them based on structure of documents. So comparng ths clusterng method wth clusterng metrc s sutable enough but not completely admrable. In fact, t should be a clusterng metrc based on documents structure to explot n evaluatng, or nstead of usng external metrc, nternal metrc used. In order to evaluate clusterng, we could analyse the dstance of the cluster s ntra ponts wth each other and wth others n other clusters. Ths crteron named nternal metrcs. Effcency of the proposed method depended on trangulaton s effcency whch, n hgh dmenson had lower performance or even mpossble. On the other hand, space dmensons greatly affect the comparson accuracy. As a result, we recommend a smpler method, but for a smaller number of ponts used n hgh dmensons that can be used as a sutable alternatve. Ths means that the use of methods other than Delaunay, samplng parameter not only wll enhance, but also wll gan good results. Acknowledgements Ths work s a revsed, extended verson of the paper that appeared n [7] [8]. The authors are very grateful to Fgure 7. Purty of varyng methods on dfferent number of XML documents. Fgure 8. F-Measure of varyng methods on dfferent number of XML documents. 1084

10 Mchael Thomas Flanagan for provdng Java Scentfc Lbrary. Ths work was exploted other standard java lbrary lke SAX, moreover, appled CGAL and also boost lbrary for codng C++ part of the program. References [1] Hwang, J. and Ryu, K. (2010) A Weghted Common Structure Based Clusterng Technque for XML. [2] Algergawy, A., Nayak, R. and Saake, G. (2010) Element Smlarty Measures n XML Schema Matchng. [3] Flesca, S., Manco, G., Mascar, E., Ponter, L. and Puglese, A. (2005) Fast Detecton of XML Structural Smlartes. IEEE Transactons on Knowledge and Data Engneerng, 7, [4] Mundur, P., Rao, Y. and Yesha, Y. (2006) Key Frame Based Vdeo Summarzaton Usng Delaunay Clusterng. Internatonal Journal on Dgtal Lbrares, 6, [5] Fabr1, A., Gezeman, G., Kettner, L., Schrra, S. and Schonherr, S. (1999) On the Desgn of CGAL a Computatonal Geometry Algorthms Lbrary. [6] Denoyer, L. and Gallnar, P. (2006) The Wkpeda XML Corpus. [7] Yuan, J.-S., L, X.-Y. and Ma, L.-N. (2008) An Improved XML Document Clusterng Usng Path Feature. 5th Internatonal Conference on Fuzzy Systems and Knowledge Dscovery. [8] Naresh, N. and Ashok, B. (2010) Clusterng Homogeneous XML Documents Usng Weghted Smlartes on XML Attrbutes. IEEE 2nd Internatonal Advance Computng Conference, Patala, February 2010,