Presently, the notion of multigranulation has been brought to our attention. In this paper, the multigranulation technique is introduced into incomplete information systems. Both tolerance relations and maximal consis...Presently, the notion of multigranulation has been brought to our attention. In this paper, the multigranulation technique is introduced into incomplete information systems. Both tolerance relations and maximal consistent blocks are used to construct multigranulation rough sets. Not only are the basic properties about these models studied, but also the relationships between different multigranulation rough sets are explored. It is shown that by using maximal consistent blocks, the greater lower approximation and the same upper approximation as from tolerance relations can be obtained. Such a result is consistent with that of a single-granulation framework.展开更多
Community structure is one of the most important features in real networks and reveals the internal organization of the vertices. Uncovering accurate community structure is effective for understanding and exploiting n...Community structure is one of the most important features in real networks and reveals the internal organization of the vertices. Uncovering accurate community structure is effective for understanding and exploiting networks. Tolerance Granulation based Community Detection Algorithm(TGCDA) is proposed in this paper, which uses tolerance relation(namely tolerance granulation) to granulate a network hierarchically. Firstly, TGCDA relies on the tolerance relation among vertices to form an initial granule set. Then granules in this set which satisfied granulation coefficient are hierarchically merged by tolerance granulation operation. The process is finished till the granule set includes one granule. Finally, select a granule set with maximum granulation criterion to handle overlapping vertices among some granules. The overlapping vertices are merged into corresponding granules based on their degrees of affiliation to realize the community partition of complex networks. The final granules are regarded as communities so that the granulation for a network is actually the community partition of the network.Experiments on several datasets show our algorithm is effective and it can identify the community structure more accurately. On real world networks, TGCDA achieves Normalized Mutual Information(NMI) accuracy 17.55% higher than NFA averagely and on synthetic random networks, the NMI accuracy is also improved. For some networks which have a clear community structure, TGCDA is more effective and can detect more accurate community structure than other algorithms.展开更多
基金This paperis partiallysupported by Programfor NewCentury Excellent Talentsin University, National Natural Science Foundation of China under Grant(60373111) , Natural Science Foundation of Chongqing,and Science & Technology Research Programof the Municipal Education Commitlee of Chongqing under Grant(040505) .
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 61170165, 61100116, 61272419, 61373062）, Natural Science Foundation of Jiangsu Province of China （BK2011492, BK2012700, BK20130471）, Qing Lan Project of JiangsuProvince of China, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information （Nanjing University of Science and Tech- nology）, Ministry of Education （30920130122005）, Key Laboratory of Arti- ficial Intelligence of Sichuan Province （2013RYJ03）, Natural Science Foun- dation of Jiangsu Higher Education Institutions of China （13KJB520003, 13KJD520008）.
文摘Presently, the notion of multigranulation has been brought to our attention. In this paper, the multigranulation technique is introduced into incomplete information systems. Both tolerance relations and maximal consistent blocks are used to construct multigranulation rough sets. Not only are the basic properties about these models studied, but also the relationships between different multigranulation rough sets are explored. It is shown that by using maximal consistent blocks, the greater lower approximation and the same upper approximation as from tolerance relations can be obtained. Such a result is consistent with that of a single-granulation framework.
基金partially supported by the National HighTech Research and Development (863) Program of China (No. 2015AA124102)the National Natural Science Foundation of China (Nos. 61402006 and 61175046)+3 种基金the Provincial Natural Science Research Program of Higher Education Institutions of Anhui Province (No. KJ2013A016)the Provincial Natural Science Foundation of Anhui Province (No. 1508085MF113)the College Students National Innovation & Entrepreneurship Training program of Anhui University (No. 201410357041)the Recruitment Project of Anhui University for Academic and Technology Leader
文摘Community structure is one of the most important features in real networks and reveals the internal organization of the vertices. Uncovering accurate community structure is effective for understanding and exploiting networks. Tolerance Granulation based Community Detection Algorithm(TGCDA) is proposed in this paper, which uses tolerance relation(namely tolerance granulation) to granulate a network hierarchically. Firstly, TGCDA relies on the tolerance relation among vertices to form an initial granule set. Then granules in this set which satisfied granulation coefficient are hierarchically merged by tolerance granulation operation. The process is finished till the granule set includes one granule. Finally, select a granule set with maximum granulation criterion to handle overlapping vertices among some granules. The overlapping vertices are merged into corresponding granules based on their degrees of affiliation to realize the community partition of complex networks. The final granules are regarded as communities so that the granulation for a network is actually the community partition of the network.Experiments on several datasets show our algorithm is effective and it can identify the community structure more accurately. On real world networks, TGCDA achieves Normalized Mutual Information(NMI) accuracy 17.55% higher than NFA averagely and on synthetic random networks, the NMI accuracy is also improved. For some networks which have a clear community structure, TGCDA is more effective and can detect more accurate community structure than other algorithms.
