BRDPHHC: A Balance RDF Data Partitioning Algorithm based on Hybrid Hierarchical Clustering

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1 015 IEEE 17th Internatonal Conference on Hgh Performance Computng and Communcatons (HPCC), 015 IEEE 7th Internatonal Symposum on Cyberspace Safety and Securty (CSS), and 015 IEEE 1th Internatonal Conf on Embedded Software and Systems (ICESS) : A Balance RDF Data Parttonng Algorthm based on Hybrd Herarchcal Clusterng Yongln Leng, Zhu Chen, Fangmng Zhong, Hua Zhong School of Software Technology, Dalan Unversty of Technology, 11660, Dalan, Chna Abstract - Data parttonng s a fundamental step to acheve effectve storage and query of RDF bg data. Ths paper presents a balance RDF data parttonng algorthm based on hybrd herarchcal clusterng (), whch combnes AP and K- means clusterng. s functonalty ncludes three aspects: () a pre-processng step combnng nodes compresson and nodes remove to reduce the scale of raw data ponts, () AP clusterng algorthm s used to coarsen the RDF graph step by step and produce data blocs, and () K-means algorthm s used for data parttonng fnally. Experments on benchmar datasets demonstrate the effectveness of the proposed scheme. Index Terms - RDF; data parttonng; hybrd herarchcal clusterng I. INTRODUCTION The Resource Descrpton Framewor (RDF) s the W3C s recommendaton as the basement of the semantc web [1], whch can represent all the dentfed nformaton n the web and provde the nteroperablty between applcatons []. RDF data can be descrbed as a collecton of trples denoted as SPO (subect, predcate, obect), n whch the subect ndcates an entty, and the obect s the name of the entty or lteral n predcate. It can also be represented by a drected graph, wth the enttes (.e. subects and obects) as nodes and the predcate as drected edges from subect to obect [3]. Fg.1 (a) shows an example RDF trples, and Fg. (b) s the drected graph of RDF. (a) Example of RDF trple (b) Example of RDF drected graph Fg. 1 RDF examples Wth the wde applcaton of RDF data, RDF data sze ncreases sharply. The RDF data storage n sngle server Ths wor s supported by Proect U of NSFC and Proect of Laonng Provncal Natural Scence Foundaton of Chna. cannot meet the requrement of massve data storage and query. To tacle ths problem, the dstrbuted storage was proposed to store the massve RDF data [3, 4]. The data parttonng s a ey concern n RDF data dstrbuted storage. In other words, a bad parttonng scheme wll result n low effcency of storage and query. Typcal data parttonng algorthms adopt horzontal or vertcal parttonng based on trples [5]. Ths nd of algorthms gnores the correlatons between trples, leadng to a large number of on operatons among the compute nodes durng the RDF query. To address ths problem, graph-based approach has been proposed to partton the RDF data, whch stores the closely related nodes n the same compute node [6]. In ths scheme, most of data queres can be performed n parallel to mprove the query effcency. Moreover, ths scheme can reduce the on operaton among the compute nodes. The representatve parttonng algorthm based on graph ncludng geometrc parttonng [7], spectral parttonng [8] and multlevel parttonng algorthm [9, 10, 11]. Compared wth other graph parttonng methods, the multlevel parttonng algorthm s superor to others n tme complexty and the scale of data. However, ths nd of algorthms manly focuses on the parttonng effcency, gnorng the balance of data parttonng, resultng n the dffculty n parallel to perform. In ths paper, we present a balance RDF data parttonng algorthm based on hybrd herarchcal clusterng (), whch wors n three steps. Frstly, a pre-processng step s executed to reduce the number of raw data ponts by combnng the specal attrbutes and removng the hgh degree nodes. Secondly, the affnty propagaton clusterng algorthm (AP) s used to pre-cluster the RDF graph for producng data blocs. In each AP clusterng, we merge or splt the data blocs to balance the scale of the data blocs through nteractve edge. Fnally, an nteractve edge weghted K-means clusterng method s presented to partton data blocs and to realze the partton. The rest of the paper s organzed as follows. In Secton, we present the pre-processng method for RDF graph by two steps. Secton 3 depcts the smlarty measurement based on adacency and nteractve edges. In Secton 4, we descrbe the algorthm for RDF data parttonng. Performance evaluaton s llustrated n Secton 5. Secton 6 concludes the paper. II. PRE-PROCESSING FOR RDF GRAPH In ths secton, we present the proposed pre-processng steps for RDF graph. Combnaton of the nodes wth unque /15 $ IEEE DOI /HPCC-CSS-ICESS

2 attrbute value s frst descrbed, followed by the removng of the nodes wth hgh degree. A. Combnaton of the Nodes wth Unque Attrbute Values Gven an RDF graph G ( V, E), V Ve Vl represents the node set n whch denotes the entty node set and Vl denotes the attrbute node set, whle E {( e v, v) v, v V} Er Ea denotes the drected edge set n whch Er denotes the relatonshp edge set and Ea denotes the attrbute edge set. If the value of v s only belongng to the entty node v under the condton ( v, v) Ea,then v and v must be assgned to the same storage node n the process of parttonng. For example, the node whch s the value of the attrbute edge telephone s only belongng to the entty student50. To mprove the effcency of parttonng, the paper combnes such nodes and ther correspondng entty to one node. B. Remove of Hgh Degree Nodes In the real applcatons, some nodes have hgh degrees whle others have low degrees. For example, over 90% nodes have only less than 5 neghbors whle some nodes wth more than 100, 000 neghbors n DBpeda [1]. Generally speang, when one node has more neghbors, t s quered more frequently, leadng to hgher communcaton cost [3]. To reduce the on operatons n the process of query, the paper removes the nodes wth hgh degrees before parttonng. After parttonng, the removed nodes wll be stored nto such the storage nodes wth the correspondng nodes. Ve III. SIMILARITY MEASURE Smlarty measurement s the ey to the graph clusterng technque. Ths secton descrbes two metrcs to calculate the smlarty between node pars. A. Adacency Measure In ths paper, we propose a metrc based on adacency. The smlarty measurement based on adacency s wdely used n many graph parttonng algorthms to group nodes, whch are hghly connected [13]. The dea of adacency measure can be expressed as f the neghbors of one node u are connected wth another node v, then the nodes u and v have tghter connecton. In contrast, the nodes u and v wll become looser. Furthermore, the shortest dstance between two nodes also affect the smlarty. We use l to denote the shortest dstance between two nodes. The weght between two nodes s defned as follows: wuv 1/ l (1) The smlarty between two nodes s defned as follows: smlarty(u,v) nt err(u,v) Nr(u) w w,where s the neghbor set wthn the radus r of the node and nt err ( u, v) N r ( u) N r ( v) s the ntersecton of the neghbor sets of the node u and v. For nstance, the smlarty between u and v s as shown n Fg., s(u, v) =0.667 and s(u, m) =0.5. Whereas, s(a, b) = and s(a, d)=0.5714, whch have the same number of neghbors, but they have dfferent weghts, resultng n the dfferent smlartes. Here, the computaton of smlarty neglects the drecton of edges. u Fg. An example of adacency measure B. Interactve Edge Measure Interactve edge s the edge generated by the nodes n two dfferent partton. One prncple of RDF graph parttonng s to mnmze the nteractve edge. In hybrd herarchcal clusterng, from the second layer, the data blocs n each layer are clusterng collectons of the prevous layer. In order to mnmze the nteractve edges among the compute nodes, we assume that the more the number of nteractve edges between two data blocs, the larger the smlarty s, and the data blocs are easly clustered nto a collecton. Gven two data blocs C and C, cut( C, C ) represents the number of nteractve edges. As shown n Fg.3, n the frst layer, the nodes {a, b, c, d, e, f} are clustered nto a data bloc C1 and the nodes {g, h,, } are clustered nto another data blocc,socut( C1, C) 5. Fg. 3 Example of nteractve edge We use a lnear functon converson to normalze the smlarty between data blocs, where cut ( ) mn C and cut ( ) max C denote the mnmum and maxmum number of nteractve edges n data blocs. v () 1756

3 cut( C, C )! cutmn ( C) smlarty( C, C ) (3) cut ( C )! cut ( C ) max IV. ALGORITHM In ths secton, we frst present the framewor of algorthm, whch smultaneously consders both nteractve edge and balance. Then, the detaled steps are descrbed. The framewor of algorthm s shown n Fg.4. mn Fg. 4 Framewor of algorthm A. Herarchcal AP Clusterng AP clusterng algorthm was proposed by Brendan J. Frey and Delbert Duec, whch s a new clusterng algorthm. Compared wth the tradtonal clusterng algorthms, AP clusterng does not requre a pre-specfed number of clusters, and t teratvely transmts real-valued messages among the data ponts to gradually fnd the potental exemplars for formng a collecton of hgh qualty exemplars. AP clusterng algorthm taes a smlarty matrx between data ponts as an nput, where the smlarty s (, ) ndcates how well the data pont wth ndex s suted to be the exemplar for data pont [13]. AP teratvely updatng a responsblty matrx R, sent from data pont to canddate exemplar pont, whch reflects the accumulated evdence for how well-suted pont s to serve as the exemplar for pont, consderng other potental exemplars for pont, and an avalablty matrx A, sent from canddate exemplar pont to pont, whch reflects the accumulated evdence for how approprate t would be for pont to choose pont as ts exemplar, tang nto account the support from other ponts that pont should be an exemplar. To begn wth, the avalabltes matrx A are ntalzed to zero. Then, the responsbltes are computed usng the rule. r (, ) s (, )! max{ a (, )( s (, )} (4) The followng avalablty update gathers evdence from data ponts as to whether each canddate exemplar would mae a good exemplar: a r r (, ) mn{0, (, ) ( max{0, (, )}} # {, } a (, ) max{0, r (, )} (5) In each teraton, there are generally n data pars whose responsblty and avalablty values need to be calculated, thus the computaton complexty s On ( ). When the number of teratons s T, the computaton complexty s OTn ( ). Ths greatly affects the performance especally when the data are large. It has been ponted out n [14] that the sparsty of the constructed graph wll lead to faster calculaton snce the nformaton propagaton only needs to be performed on the exstng edges. So for a sparse smlarty matrx, the complexty wll up to OTn ( )[15]. The goal of RDF graph parttonng s to cluster the closely connected nodes n a compute node. So the smaller smlarty between two nodes, the less possblty two nodes cluster together. In order to mprove the effcency of clusterng, we set the smlarty equal to!) f the smlarty values less than. As a result, the sparsty of the matrx mproved and tme complexty n AP clusterng s reduced. Algorthm 1: Herarchcal AP Clusterng Algorthm(HC) Input: RDF graph G ( V, E) cluster threshold T Output: Cluster set C C1, C,, Cm%,where m& T Method: 1. Construct a sparse smlarty S based on (). Execute AP clusterng on matrx S and generate m clusters 3. If m T, compute the smlarty among the m clusters usng (3) to produce a new smlarty matrx S 4. Tae S as a new nput contnue to run, untl m& T B. Parttonng-balance Adustment The balance of the subgraph scales plays an mportant role n dstrbuted storage and query when a huge graph s parttoned nto several subgraphs. Specally, a bad balance wll lead to a low effcency of query. Therefore, to preserve the balance, the parttonng-balance wll be adusted n each clusterng. Gven a graph G ( V, E), we dvde the graph nto parttons P { P1, P,, P }. The parttonng-balance of a -way parttons should satsfy 1! e1 & PB & 1( e,where PB V / m and m V /. The parttonng-balance adustment approach s outlned n Algorthm. Algorthm : Parttonng-balance Adustment Input: Partton P { P1, P,, P } Output: New parttonng-balance P { P1, P,, P t } Method: 1. Compute parttonngbalance PB { PB1, PB,, PB }.. For p =1 to 1757

4 f PB 1! e1 merge( P, P ),where Cut( P, P ) s max and PB 1( e. else f PB 1( e Partton P use KL algorthm untl1! e & P & 1( e. 1 C. Fnal Parttonng Durng the Herarchcal AP clusterng, we use the AP clusterng to gradually reduce the scale of the RDF graph. But the number of clusters n AP clusterng s uncertan because of the nfluence of preferences. When the compute node s specfed, AP clusterng cannot acheve the fnal partton. In ths phase, we use K-means clusterng method to perform the fnal clusterng. Algorthm 3: K-means Clusterng Input: nteractve edge matrx S, the number of clusters Output: cluster set C C1, C,, C% Method: 1. Select ntal cluster centers C c, c,, c %. 1. Assgn each data obect to ts closest center accordng to smlarty between data obects and cluster centers. 3. Update the cluster centers. 1) Compute the average vector Sv ( ) of clusterc. 1 Sv ( ) Sv (, v), + v V C v C ) Fnd the new cluster center c. c arg mn S( v )! S( v ) v C 4. Repeat step and 3, untl the clusterng obectve E functon converges. 1 v C E S( v )! S( v ) D. Complexty Analyss There are three man operatons n the desgned algorthm. The frst one s the smlarty calculaton wth the tme complexty of On ( ). The second one s the Herarchcal AP clusterng wth the tme complexty of OTn ( ),wheretsthe number of teratons. The last one s the -means clusterng wth the tme complexty of OKTm ( ), where K s the number of clusters and m s the number of clusterng collectons. Therefore, the total tme complexty of s approxmatelyon ( ). A. Datasets and Envronment In ths secton, we present a set of experments on the Lehgh Unversty Benchmar (LUBM) [16] and the DBLP Bblography datasets [17]. The number of edges and nodes are shown n Table I. All experments were performed on an GHz PC runnng Wndows XP wth 4GB man memory. TABLE ISTATISTICS OF DATASETS USED IN EXPERIMENTS Degree V E Frst merge mn max LUBM DBLP B. Interactve Edge Rato and the Tme Performance Gven a graph G ( V, E), we dvde the graph nto clusters P 1 ( V 1, E 1 ), P ( V, E ),..., P ( V, E), then the nteractve edge rato can be descrbed as follows: cut( P, G \ P) 1 IER (6) E,where cut( P, G \ P) s the number of edges between P and the rest of the graph. The adacency measurement radus r s set to n the experment. Table II shows the number of removed nodes and edges under r= of dfferent datasets. Fg. 5 shows the nteractve edge rato on dfferent dataset and Fg. 6 presents runtme of the partton. TABLE II STATISTICS OF REMOVE NODES AND EDGES LUBM DBLP Remove condton Remove nodes Remove edges > > > > > > > > Interactve edge rato LUBM DBLP Fg. 5 Interactve edge rato on dfferent remove condton V. EXPERIMENTS 1758

5 Runtme(sec) LUBM DBLP Runtme(sec) 15 x Fg. 6 Partton effcency on dfferent remove condton From the result, we can see that the nteractve edge rato decreases and the tme performance mproves wth the remove of hgh degree nodes. s a multlevel graph parttonng method, whch uses a Fast Samplng algorthm to coarsen the nput sparse graph and chooses a small number of fnal representatve exemplars. For these exemplars, uses a densty-weghted spectral clusterng to partton the exemplars. Fnally, all data ponts can be assgned through the correspondng representatve exemplars [10]. In ths paper we compared algorthm and algorthm n nteractve edge rato and runtme. The results are shown n Fg.7 and Fg.8. Fg.7 (a) and (b) present the nteractve edge rato n LUBM and DBLP dataset respectvely. It can be seen that the nteractve edge rato of algorthm s hgher than. Interactve edge rato Interactve edge rato (a) LUBM (b) DBLP Fg. 7 Edge-cut on dfferent datasets Runtme(sec) (a) LUBM 10 x (b) DBLP Fg. 8 Partton effcency on dfferent datasets C. Parttonng-Balance Table III and Table IV shown the comparson of parttonng-balance between and n LUBM and DBLP datasets. We calculate PBmax and PBmn usng (10) and (11). PBmax max( V ) / m (10) PBmn mn( V ) / m (11) From Table III and Table IV, the balance obtaned by the proposed algorthm s better than that obtaned by. Furthermore, the removng of the nodes wth hgh degree results n a good balance, whch demonstrates the effectveness of the proposed algorthm. TABLE III PARTITIONING- BALANCE OF LUBM Remove condton PB max PB mn PB max PB mn > > > > TABLE IV PARTITIONING-BALANCE OF DBLP Remove condton PBmax PBmn PBmax PBmn > > > > VI. CONCLUSION In ths paper, we proposed a balance RDF data parttonng algorthm based on hybrd herarchcal clusterng, ncludng AP clusterng and K-means algorthm. Frstly, for 1759

6 the sae of parallelzaton, balance adustment algorthm s used to ensure the balance n each level AP clusterng. Further, to mprove the effcency of RDF graph parttonng, hgh degree nodes are removed before clusterng. Fnally, the expermental results demonstrate that our proposed algorthm outperforms by a better balance. REFERENCES [1] RDF model and syntax specfcaton / [] F. Du, Y. Chen, X. Du, et al, Survey of RDF query processng technques, Journal of Software, vol. 4, no. 6, pp: 1-141, 013. [3] K. Zeng, J. Yang, H. Wang, et al, A dstrbuted graph engne for web scale RDF data, Proceedngs of the VLDB Endowment, vol. 6, no. 4, pp: 65-76, 013. [4] Q. Zhang, Z. Chen, A weghted ernel possblstc c-means algorthm based on cloud computng for clusterng bg data, Internatonal Journal of Communcaton Systems, vol. 7, no. 9, pp: , 014. [5] K. Lee, L. Lu, Y. Tang, et al, Effcent and customzable data parttonng framewor for dstrbuted bg RDF data processng n the cloud, 013 IEEE Sxth Internatonal Conference on Cloud Computng (CLOUD), pp: , 013. [6] J.Huang,D.Abad,K.Ren, ScalableSPARQLqueryngoflargeRDF graph, Proc. of the VLDB endowment, vol. 4, no. 11, pp: , 011. [7] M. Heath, P. Raghavan, A Cartesan parallel nested dssecton algorthm, SIAM Journal on Matrx Analyss and Applcatons, vol. 16, no. 1, pp: 35-53, [8] A. Pothen, H. Smon, K. Lou, Parttonng sparse matrces wth egenvectors of graphs, SIAM Journal on Matrx Analyss and Applcatons, vol. 11, no. 3, pp: , [9] METIS, [10] F. Shang, L. Jao, J. Sh, et al, Fast affnty propagaton clusterng: A multlevel approach, Pattern recognton, vol. 45, no. 1, pp: , 01. [11] R. Ma, X. Wang, J. Dng, Multlevel core-sets based aggregaton clusterng algorthm, Journal of Software, vol. 4, no. 3, pp: , 013. [1] S. Auer, C. Bzer, G. Koblarov, et al, DBpeda: A nucleus for a web of open data, Sprnger Berln Hedelberg, 007. [13] S. Schaeffer, Graph clusterng, Computer Scence Revew, vol. 1, no. 1, pp: 7-64, 007. [14] B. Frey, D. Duec. Clusterng by passng messages between data ponts, Scence, vol. 315, no. 5814, pp: , 007. [15] Y. Ja, J. Wang, C. Zhang, et al, Fndng mage exemplars usng fast sparse affnty propagaton, Proceedngs of the 16th ACM nternatonal conference on Multmeda, ACM, pp: , 008. [16] Y. Guo, Z. Pan, J. Hefln, LUBM: A benchmar for OWL nowledge base systems, Web Semantcs: Scence, Servces and Agents on the World Wde Web, vol. 3, no., pp: , 005. [17] J. Tang, J.Sun,C.Wang, et al, Socal nfluence analyss n large-scale networs, Proceedngs of the 15th ACM SIGKDD nternatonal conference on Knowledge dscovery and data mnng ACM, pp: ,