An Approximation Approach to Rank Closeness Centrality Measures in a Large-Scale Workflow Affiliation Network

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1 KSII The 10 th Asia Pacific ternational Conference on formation Science and Technology(APIC-IST) Copyright c 2015 KSII 75 An Approximation Approach to Rank Closeness Centrality Measures in a Large-Scale Workflow Affiliation Network 1 Dokyoung Lee, 2 Hyun Ahn, 3 Ilkyeun Ra, 2 Kwanghoon Pio Kim 1 Collaboration Technology Research Lab Department of Management formation System KYONGGI UNIVERSITY, South Korea 2 Collaboration Technology Research Lab Department of Computer Science KYONGGI UNIVERSITY, South Korea 3 Department of Computer Science & Engineering UNIVERSITY OF COLORADO DENVER, USA [ {gaiety93, hahn, kwang}@kgu.ac.kr, ilkyen.ra@ucdenver.edu] *Corresponding author: Kwanghoon Pio Kim Abstract this paper, we propose an approximation approach to make a ranking list of workflow performers based on estimated closeness centralities measured on a large-scale workflow network. order to verify proposed approximation approach, we compare estimated to original in terms of size of a workflow network as well as sampling rate of a workflow network. As results of comparisons, average accuracies of estimated have improved 46.9% and 71.4% in cases of sizes from 120 performers to 2400 performers, and cases of sampling rates from 10% samples to 100% samples, respectively. Conclusively, we strongly believe that proposed approximation approach be reasonably acceptable as a closeness centrality ranking algorithm to be applied to large-scale workflow networks. Keywords: network, estimated closeness centrality, ranking algorithm 1. troduction competition industry, between organization to organization, and enterprise to enterprise collaborative activities are increasing to gain strategic position. The workflow-based social network's size is also increasing. For this issue, we use workflow management system to manage human resources based workflow network activity effectively. The workflow management System manages business processes, human resources, relevant data set, and application programs automatically. Through workflow-based social network which produced workflow management system we can get performer-oriented human resources and ir relevant information. Workflow-based network is one of specialized social networks, we comprehend information about activity patterns of human resource and cooperation relationships. The network is consist of performer group and activity group, so it can call two-mode network. The network can express bipartite graph and bipartite matrix, and analyze cooperation performer information of certain activity and cooperation activity information of certain performer. Along with increasing workflow-based organization scale, computational time of closeness centrality and ranking increases dramatically. This research was supported by a research grant from GRRC(Geyonggi Regional Research Center) at Kyonggi University

2 76 Dokyoung Lee e at al.: An Approximation Approach to Rank Closeness Centrality Measures According for collaborative business activities to be increased, workflow-based networks' sizess and ir human resources are increasing. To manage human resources of network more effectively and solve time complexity problem, I propose an approximation approach to measure closeness centrality ranking. this approximation approch[5], estimated closeness centrality of ranking algorithm[14] is a main point. Through this ranking algorithm, I can solve problem which occurs evaluating large-scale workflow -based network's ranking s r limitation. Also, I applied an example model to estimated closeness centrality-based ranking algorithm, and n analyze this algorithm's accuracy. 2. Relation Works information-oriented age of e 21 st century, information-overflow is a big issue. The whole world tries an effort to manage diverse information effectively and to gain accurate information which has reliability. The proposed ways for alternative, are Page Rank and search engine like Google provides optimized information and tries an effort to manage information effectively. The Page Rank computes ranking of web page through web graph based backlink. Backlink means a certain node received links, se links are lots of web nodes such as web page, directory, web site, domain. Through se links,, web graph iss made and n comprehends whichh web node is prefer and important, finally, we can measure importance between web pages[26]. The organizations and enterprises collaborative activities are increased and globlaized, se have made infinite resources. To managee se resources efficiently, some studys s on workflow mining[22]which found information from workflow model and log information, and business process intelligence like workflow discovery and rediscovery[23][24][25] have preceded. After, workflow-based social network framework[21] was proposed. The workflow collaborate network redefined an activity-performer network, and proposed activity-performerr bipartite matrix production algorithm[11] for analyzing activity-performer network. There are analyzing methods of network such as degree centrality, closeness centrality, betweenness centrality, eigenvector centrality [13]. this paper, produce a bipartite matrix from workflow network model using activity-performer bipartite matrix production algorithm[11]. For this bipartite matrix, we can calculate closeness centrality in a workflow network model and analyze a relationships between b activity or performer groups. Furrmore, I applied RAND algorithm which is a estimated methodd in workflow-based network to improve time complexity problem, and I will propose an estimated closeness centrality based on ranking algorithm. 3. Propose Estimated Algorithm this chapter, I explain a design and execution procedure of estimated closeness centrality ranking algorithm for analyzing enterprise workflow basedd network Design and implementation Before implementation estimated closeness centrality basedd ranking algorithm[15], I applies a workflow-based d network to t estimated closeness centrality based ranking algorithm, andd expresses a form of bipartite matrix which get values 1 or 0. If a certain c performer node or a certain activity node is affiliated, n it gets value 1, orwise, it gets value 0. (1) large scale s workflow-based network, I use a Floyd algorithm[17] to compute shortest path between nodes, this Floyd algorithm findss shortest pathh at a time between all nodes. Floydd algorithm has a weighted matrix as an initial value, v this weighted matrix's all diagonal matrixx values get 0, and except diagonal matrix, or values v get infinite. Result of Floyd algorithm, shortest-path matrix is made. Through this shortest-path s matrix, calculating estimated closeness centrality and original closeness centrality finds out rank by ranking algorithm, and n analyzes results. r The n network has two attribute,

3 The 10 th Asia Pacificc ternational Conference on formation Science and Technology(APIC-IST) 2015, July performer and activity, so when I apply estimated closeness centrality based ranking algorithm, I can gain two type of information. Fig. 1 is an estimated closeness c centrality ranking algorithm which combines c estimated closeness centrality algorithm and original closeness algorithm[2]. The estimated closeness centrality ranking algorithm startss when I decide type of ranking nodes and number off sampling nodes for RAND algorithm. When type of ranking nodes are performers, each node calculates estimated closeness centrality and original closeness centrality through ranking algorithm, and finds out rank of value by descending order. Finally, returned value of closeness centrality and estimated closeness c centrality. At last compare closenesss centrality rank and n estimated closeness centrality rank and n, algorithm is completed. Table 1 is ranking results of workflow performers based on estimated closeness centrality ranking algorithm. I evaluated algorithm in same envrionment, number of performer model nodes is 2400, number of ranking nodes is i 20 and sampling rate is 20%. I set number of o rank nodess to 20, so we can c see ranking just top 20. All of envrionemnt factors are changeable. A node 1821 get firstt grade and its estimated closeness centrality is Some nodes have same estimated closenss centrality, beacause of input workflow model. When I made an exam model, I extended model m like multiplication. So, y have same closenesss centrality value, inevitably. But,, this limit of algorithm is caused c by workflow model which inputs algorithm. If you use this algorithm, using real workflow model, n its results were diffierent. Table 1. Estimated Closeness Centrality Rankings Result of Estimated Closeness Centrality Ranking Performerr Size=2400, Rank Size=20 Closenesss node id rank Centralityy Measurements node 1821 node 2037 node 453, node 681 node 549 node 1065 node 657, node 140 1, node 1881, node , node 2133 node 501, node , node 2121, node node 729 node 2001, node 224 1, node 2265 no 1 2 3~ ~11 12~ ~ ode 153 Fig. 1. Estimated Closeness Centrality Ranking Algorithm 3..2 The Approximation Approach The computing closeness centrality of network means finding out single source shortest path[3] between certain node and or nodes in t network. There is a limitation when I compute shortest path between all nodes to all nodes because of f workfloww based network size becomes bigger and bigger. The (2)( is an estimated closeness centrality mamatical formula.

4 KSII The 10 th Asia Pacific ternational Conference onn formation Science and Technology(APIC-IST) Copyright c 2015 KSII 78 sample matrix s_avg. Table 2. Accuracy analysis of estimated closeness centrality ranking algorithm 10% 20% % 40% % 50% 60% 70% % 90% % 100% m_avg (2) The part of d, means average of shortest path between one node and all nodes in network. Draw estimated closeness centrality throughh RAND algorithm can save more time than original closeness centrality calculating time,, this approach solvess problem in accordance with network's scale. 4. Accuracy Analysis of Estimated Algorithm this paper, I verified reliabilityy of a proposed estimated closeness centrality based ranking algorithm and applied example model to algorithm and n, implemented. The estimated closeness centrality based ranking algorithm can analyze as two perspectives. One is an accuracy analysis of t matrix size, or is an accuracy analaysis of sampling rate. The evaluating accuracy environment conditions are all equal, type of example node is performer, number of ranking node is 20. To evaulate reliablity of accuracy, compare result of estimated closeness centrality ranking withh result of original closeness centrality ranking. And n, evaluating how much se results are equivalent, degree of t equivalent can interprete its degree of reliability. Table 2 is result of accuracy analysis of estimated closeness centrality ranking algorithm. Fig. 2 is analyzing result of accuracy of matrixx size. As a result, in case of sample rate=40% %, if matrix size=120 n, its accuracy is 56%, since Fig. 2. Accuracy analysis in matrix sizes matrix size=1200, its accuracies are 100%. As you can see in Table 2, case of matrix size=120, accuracy average of matrix size is 52.7% and case of matrix size=2400, accuracy average of matrix size is 99.6%. e or words, accruacy average of matrix size raise 46.9%. conclusion, as matrix size became bigger, estimated closeness centrality based ranking algorithm saw accuracy more higher, regardless of sampling rate. Fig. 3. Average accuracy analysis in samplingg rates

5 The 10 th Asia Pacific ternational Conference on formation Science and Technology(APIC-IST) 2015, July Fig. 3 is a graph of accuracy average of sampling rate. case of sampling rate=10%, its average accuracy is 27.8%, whereas sampling rate=100%, its accuracy average is 99.2%. It improved average accuracy about 71.4%. or words, sampling rate become larger, n average of accuracy become higher. conclusion, as workflow- supported network scale became enlarge and randomly selected sampling rate became higher, it saw higher accuracy. 5. Conclusions As workflow-supported networks enlarge, human resources such as a large amount of activity patterns and information of task and performer are overflowed. To solve this problem, I have proposed approximation approach[5] to evaluate ranking of workflow performers based on estimated closeness centrality algorithm[14]. Also, I have analyzed accuracy of estimated closeness centrality based ranking algorithm to verify its reliability. conclusion, as size of workflow supported network and sampling rate are increased, I have attained high degree of accuracy. or words, we strongly believe that proposed approximation approach be reasonably acceptable as closeness centrality ranking algorithm to be applied to large-scale workflow networks. Acknowledgement This research was supported by contents convergence software research center at Kyonggi University funded by GRRC program of Gyeonggi Province, Sourth Korea. References [1] K. Okamoto, W. Chen and X.Y. Li, Ranking of Closeness Centrality for Large-Scale Social Networks, Lecture Notes in Computer Science of Frontiers in Algorithmics, Vol 50, No. 59, pp , [2] A. Battestseg, H. Ahn, Y. Lee, M. Park, H. Kim, W. Yoon, K. Kim, Organizational Closeness Centrality Analysis on Workflow-supported Activity-Performer Affiliation Networks, Proceedings of 15th ternational Conference on Advanced Communication Technology, pp , [3] E. W. Dijkstra, A Note on Two Problems in connextion with Graphs, Numerische Mamatik, Vol. 1, ino. 1, pp , [4] Phillip Bonacich, Power and Centrality: A Family of Measures, American Journal of Sociology, Vol. 92, No. 5, pp , [5] D. Eppsten, J. Wang, Fast Approximation of Centrality, Journal of Graph Algorithms and Applications, Vol. 8, No. 1, pp , [6] K. Faust, Centrality in netwokrs, Social Networks, Vol. 19, No. 2, pp , [7] Borgatti, Stephen P., and Daniel S. Halgin, "Analyzing networks." The Sage handbook of social network analysis, pp , [8] H. Ahn, C. Park, K. Kim, "A correspondence analysis framework for workflow-supported performer-activity networks", Advanced Communication Technology (ICACT), th ternational Conference on. IEEE, [9] E. Yan, D. Ying, "Applying centrality measures to impact analysis: A coauthorship network analysis." Journal of American Society for formation Science and Technology, Vol. 60, No. 10, pp , [10] T. Frank, "A Family of Affiliation dices for Two-Mode Networks." Journal of Social Structure Vol. 14, [11] H. Ahn, K. Kim, An Activity-Performer Bipartite Matrix Generation Algorithm for Analyzing Workflow-supported Human-Resource Affiliations, Journal of Korean Society for ternet formation, Vol. 14, No. 2, pp , [12]K. Kim, Discovering Activity-Performer Affiliation Knowledge on ICN-based Workflow Models, Journal of formation Science and Engineering, Vol. 29, No. 1, pp , [13] D. Knoke, S. Yang, SOCIAL NETWORK ANALYSIS - Edition, Series : Quantitative

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