摘要
聚类分析是模式识别与人工智能中发现知识的重要途径之一，传统的聚类分析是一种硬划分。大数据时代出现了高维海量数据，它们往往具有不完备性、不精确性、不一致性等特征，传统聚类算法很难满足这些数据的聚类需求。粒度计算是不确定信息处理的重要工具，是当前计算智能领域中模拟人类思维和解决复杂问题的新方法。粒度计算的兴起将聚类分析拓展到了软计算领域，实用价值进一步提高，理论意义更加贴近现实。通过粒度的变换，聚类可以在不同层次、不同角度进行，使得“亦此亦彼”的聚类有了研究的理论基础和实践方法，弥补了传统聚类的不足，有利于问题的解决。
本文将粒度计算与聚类分析融合在一起，对粒度聚类方法做了深入研究。将粒度的思想贯穿到聚类的数据预处理与聚类分析的整个过程，同时将聚类作为属性粒化与样本粒化的手段，用聚类的目标函数、参数的值来描述粒化的角度和层次。本文主要工作有以下几个方面：
1.针对聚类分析预处理中属性约简时间、空间复杂度高的问题，采用聚类的方法对属性并行粒化。基于属性区分能力和AP聚类的属性粒化方法利用AP聚类算法将属性分为若干簇类后在每个簇类中依据信息熵、属性重要度等指标选取代表属性构成最后的属性集合，从而完成属性粗粒化的要求。对大数据集的特征降维，这种算法比传统的属性约简算法大大提高了运算效率，在属性粒化精度要求不是很严格的情况下，算法优势明显。基于AP聚类的并行属性约简算法可以在保持分类能力不变的情况下提高传统属性约简算法的效率，但是由于并行约简中仍然采用的是传统的算法，所以对规模特别大的数据集，算法的时效性有一定的局限性。
2.将粒度计算与聚类算法相结合，一般只是将粒度计算的模型应用到聚类算法中去。聚类结果之间仍然无法自由转换。由于所有聚类算法统一在粒度的思想下，提出基于聚合网络的变粒度二次聚类方法，通过粒度计算将两种聚类算法融合在一起，首次聚类的目的并不是完成对整个数据集的聚类操作，而是找到合适的聚合粒层，是在较细的粒度上进行，用以寻找数据局部结构，并依据粒度的粗细形成聚合网络中的某一聚合粒层，二次聚类在此基础之上完成对论域的聚类操作。提出基于K均值与层次聚类的变粒度自适应二次聚类方法，可以同时解决K均值算法易受初始聚类中心的影响而聚类错误、不能识别任意形状数据集和层次聚类速度较慢的问题。提出的基于AP聚类的变粒度二次聚类方法首次聚类采用AP聚类，效果稳定，一次聚类粒度较细，正确率高，寻找合适粒度时间少。
3.为了解决AP聚类不能适用于子空间聚类的问题，提出了两种改进算法。一种是属性样本同步粒化的AP熵加权软子空间聚类算法去除冗余属性后，在每次聚类算法的迭代过程中增加一步修改属性权重。迭代终止时，就得到了兴趣度子空间的准确的属性集的粒化结果。另一种属性样本异步粒化的AP子空间聚类方法是一种异步软子空间聚类算法，首先通过计算属性的基尼值与联合基尼值得到属性的关系矩阵，然后将子空间的查找转换成查找矩阵的极大全1子矩阵，降低了时间复杂度，最后在各兴趣度子空间使用AP算法聚类，完成子空间聚类的任务。算法既保留了AP聚类算法的优点，又克服了AP算法不能进行子空间聚类的不足。
4.对并行程序的粒化方法做了研究，在细粒度并行思想的指导下，提出基于改进属性约简的细粒度并行AP聚类算法。算法将粒度思想引入到并行计算中，首先分析了程序并行计算中的粒度原理，对传统的基于差别矩阵的属性约简算法做了改进与并行化处理，降低了它的时间空间复杂度，然后对AP算法做了细粒度并行化处理，提高了算法的效率。整个算法将任务划分到多个线程同时处理。
Clustering analysis is one of the important ways of knowledge discovering inpattern recognition and artificial intelligence. Traditional clustering is a kind of harddivision. As the time for big data is coming, high-dimensional, incomplete, complex,vague, massive data are produced. These plentiful data and their high dimensionalcharacter make the traditional data analysis method be outshone. Granular computingis an important tool of uncertain information processing, and it is also new method tosimulate human thinking and solve complex problems in the field of computationalintelligence. The rise of granular computing develops the field of clustering into softcomputing which further promotes its value for practical uses and makes thetheoretical significance of clustering more close to reality. Clustering analysis can beperformed from different levels and different angles through the change of granularity,thus "either the one or the other" clustering has its research foundation and practicemethod. This might make up for the shortage of the traditional clustering and ishelpful for the solution of the problem.
This paper focuses on granularity clustering through combining granularcomputing and clustering analysis together. The thought of granularity runs throughthe procedure of data preprocessing and clustering analysis. And at the same time,clustering is a main method of attribute granulation and sample granulation. Thepaper describes different levels and different angles of granulation through objectfunction and the values of parameter of clustering. This paper mainly includes thefollowing aspects:
To reduce time and space complexities of attribute reduction in clusteringproceeding, we granulate attributes through clustering method in parallel. Attributegranulation based on attribute discernibility and AP clustering method calculates thesimilarity of attributes according attribute discernibility first, and then clustersattributes into several group through affinity propagation clustering algorithm. At last,representative attributes are produced through some algorithms to form a coarserattribute granularity. The method is a more efficient algorithm than traditionalattribute reduction algorithm for large data set. It has obvious advantages under thecondition of less strict precision of attribute granularity. A parallel attribute reductionalgorithm based on affinity propagation clustering improves the efficient of attributereduction under maintained the same classification ability. But it is limited when the data set is large scale because traditional attribute reduction algorithm is selected inparallel reduction.
We can apply granular computing model to clustering method in order tocombine them together. But the clustering results are unable to translate freely.Because all clustering algorithms are uniformed by granular thought, this paperpresents a new twice clustering method based on the variable granularity andclustering network(VGTC). VGTC combines two clustering algorithms togetherthrough granularity computing in order to have better performance than any singlemethod. The aim of the first clustering is not to complete the task of clustering forthe whole data set, but to find an appropriate clustering layer. On this basis, secondaryclustering completes clustering operation for domain. Variable granularity twiceclustering based on K-means algorithm and hierarchical clustering (an example ofVGTC) can cluster the non-spherical shape data sets correctly, and avoid someproblem of K-means(such as it is influenced by initial clustering center) andhierarchical clustering(such as the lower efficiency). Furthermore, the algorithm canimprove the accuracy and efficiency of clustering. Another twice clustering ofvariable granulation based on AP and hierarchical clustering selects AP algorithm asthe first clustering method, so the granulation of clustering is finer, the result is stableand has high accuracy. The time of searching appropriate granulation is shorter thanK-means.
AP algorithm is not appropriate for subspace clustering. In order to solve thisproblem, two improved AP algorithms are put forward. An entropy weighting APalgorithm for subspace clustering based on asynchronous granulation of Attributesand Samples removes the redundant attributes first, and then a step of modifyingattribute weight is added to the clustering procedure in order to obtain the exactweight value. At the end of clustering, an accurate result of attribute granularity willbe produced. Another method is AP subspace clustering algorithm based on attributesrelation matrix. It is asynchronous soft subspace clustering algorithm. This algorithmfilters out redundant attributes by computing the gini coefficient. To evaluate thecorrelateion of each two non-redundant attributes, the relation matrix is constructedbased on two dimensional united gini coefficients. The candidate of all interestingsubspaces is achieved by looking for the maximum sub-matrixes which contain only1.Finally, all subspace clusters can be gotten by AP clustering on interesting subspaces.The method obtains interesting subspaces correctly and reduces time and space complexity at the same time. It keeps the advantages of AP clustering and overcomethe shortage of it.
Research on granularity of parallel program is done in this paper. Under theguidance of fine-grain parallelism, an AP clustering algorithm based on improvedattribute reduction and fine-grain parallelism is proposed. Firstly, granularity thoughtis introduced into parallel computing and granularity principle is applied as well.Secondly, data set is preprocessed by the method of improved attribute reductionalgorithm through which elements in discernibility matrix will be calculated andselected in parallel, in order to reduce the complexity of time and space. Finally, dataset is clustered by the means of parallel AP algorithm. The whole task can be dividedinto multiple threads to be processed simultaneously.
引文
[1]王国胤,李德毅,姚一豫,等.云模型与粒计算[M].北京:科学出版社,2012.
[2] Leslie V. A theory of the learnable[J]. Communications of the ACM,1984,27(11):1134-1142.
[3] Judea P. Causality: Models, Reasoning, and Inference[M]. England: Cambridge UniversityPress,2000.
[4] Yao Y Y. Granular computing: basic issues and possible solutions. In: Proceedings of the5thJoint Conference on Information Sciences[C]. USA: Elsevier Publishing Company,2000:186-189.
[5] Zadeh L A. Fuzzy logic: computing with words[J]. IEEE Transactions on Fuzzy Systems,1996,1(2):103-111.
[6] Zadeh L A. Towards a theory of fuzzy information granulation and its centrality in humanreasoning and fuzzy logic[J]. Fuzzy Sets and Systems,1997,19:111-127.
[7] Zhang B, Zhang L. Theory and Applications of Problem Solving[M]. North-Holland: ElsevierScience Publishers B.V.,1992.
[8]苗夺谦.不确定性与粒计算[M].北京:科学出版社,2011.
[9]王国胤,张清华,马希骜,等.知识不确定性问题的粒计算模型[J].软件学报,2011,22(4):679-694.
[10]苗夺谦,王国胤,刘清,等.粒计算:过去、现在与展望[M].北京:科学出版社,2007.
[11] Chen Y H, Yao Y Y. Multiview intelligent data analysis based on granular computing[C].Proceedings of2006IEEE International Conference on Granular Computing. Shanghai,2006
[12] Yao Y Y. Three perspectives of granular computing[J]. Journal of Nanchang Institute ofTechnology,2006,25(2):16-21.
[13] Yao Y Y. Granular computing: past, present and future[C].2008IEEE InternationalConference on Granular Compting. Beijing:2008.
[14] Zhu H, Ding S F, Xu L, Zhang L W. Research and Development of Granularity Clustering[J].Communications in Computer and Information Science:2011,159(5):253-258
[15] Ding S F, Xu L, Zhu H, Zhang L W. Research and Progress of Cluster Algorithms based onGranular Computing[J]. International Journal of Digital Content Technology and itsApplications,2010,4(5):96-104.
[16]张铃,张钹.模糊商空间理论（模糊粒度计算方法）[J].软件学报,2003,14(4):770-776.
[17]刘玉超,李德毅.基于云模型的粒计算[G].//苗夺谦.不确定性与粒计算.北京：科学出版社,2011.
[18]李德毅,孟海军,史雪梅.隶属云和隶属云发生器[J].计算机研究与发展,1995,32(6):16-21.
[19]王国胤,姚一豫,于洪.粗糙集理论与应用研究综述[J].计算机学报,2009,32(7):1229-1246.
[20]刘清,孙辉,王洪发.粒计算研究现状及基于Rough逻辑语义的粒计算研究[J],计算机学报,2008,31(4):543-555.
[21]朱红,丁世飞,许新征.基于改进属性约简的细粒度并行AP聚类算法[J].计算机研究与发展,2012,49(12):2638-2644.
[22] Science staff. Introduction to special issue: Challenges and opportunities[J]. Science,2011,331(11):692-693
[23] Viktor Mayer Schonberger, Kenneth Cukier著,周涛译.大数据时代:生活、工作与思维的大变革[M].浙江人民出版社,2012,12.
[24] Zadeh L A. The concept of a linguistic variable and its applications in approximate reasoning(I),(II),(III)[J]. Information Science,1975.8:199–249;8:301-357;9:43-80.
[25] Demirci M. Genuine sets[J]. Fuzzy Sets and Systems,1999,105:377-384.
[26] Gau W L, Buehrer D J. Vague Sets[J]. IEEE Transactions on Systems Man on Cybernetics,1993.23(2):610-614.
[27] Bustince H, Burillo P. Vague sets are intuitionistic fuzzy sets[J]. Fuzzy Sets and Systems,1996,79:403-405.
[28] Hirota K. Concepts of probabilistic sets[C]. Proc. IEEE Conf. on Decision and Control. NewOrleans,1977:1361-1366.
[29] Hirota K. Concepts of probabilistic sets[J]. Fuzzy Sets and Systems,1981,5:31-46.
[30] Mendel J M. Advances in type-2fuzzy sets and systems[J]. Information Sciences,2007,177:84–110.
[31] Mendel J M. Type-2fuzzy sets and systems: An overview[J]. IEEE Computation IntelligenceMagazine,2007,2:20-29.
[32] Wu D, Mendel J M. A vector similarity measure for linguistic approximation: interval type-2and type-1fuzzy sets[J]. Information Sciences,2008,178:381-402.
[33] Wu H, Wu Y, and Luo J. An interval type-2fuzzy rough set model for attribute reduction[J].IEEE Transactions on Fuzzy Systems,2009,17(2):301-315.
[34] Ma Z M，Yang W, Hu B Q. Soft set theory based on its extension[J]. Fuzzy Information andEngineering,2010,4:423-432.
[35] Hu B Q, Kwong C K. On type-2fuzzy sets and their t-norm operations[J]. InformationSciences,2012,6
[36] Hu B Q, Wang C Y. On type-2fuzzy relations and interval-valued type-2fuzzy sets[J]. FuzzySets and System,2012,6.
[37] Wu D, Mendel J M. Uncertainty measures for interval type-2fuzzy sets[J]. InformationScience,2007,177:5378-5393.
[38] Ziarko W. Variable precision rough set model[J]. Journal of Computer and System Sciences,1993,46(1):39-59.
[39] Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal ofGeneral Systems,1990,17:191-209.
[40] Yao Y Y, Wong S K M. A decision-theoretic framework for approximating concepts[J].International Journal of Man-machine Studies,1992,37(6):793-809.
[41]李华雄,王国胤等.决策粗糙集理论及其研究进展[M].北京:科学出版社,2011.
[42] Slezak D. Rough sets and bayes factor[J]. Transactions on Rough SetsⅢ,Lecture N otes inComputer Science,2005:202-229.
[43]李道国,苗夺谦,张东星,张红云.粒度计算研究综述[J].计算机科学,2005,32(9):1-12.
[44] Qian Y H, Liang J Y, Yao Y Y, et al. MGRS: a multigranulation rough set[J]. InformationSciences,2010,180:949-970.
[45] Liu D, Li T R, Hu P, et al. Multiple-category classification with decision-theoretic roughsets[C]. The5thInternational Conferences on Rough Set and Knowledge Technolosy,2010.
[46] Yao Y Y. Three-way decisions with probabilistic rough sets[J]. Information Science,2010,180(3):341-353
[47]丁浩,丁世飞.基于粗糙集的属性约简研究进展[J].计算机工程与科学,2010,32(6):92-94.
[48]杨明.一种基于改进差别矩阵的属性约简增量式更新算法[J].计算机学报,2007,30(5):815-822
[49]王国胤,于洪,杨大春.基于条件信息熵的决策表约简[J].计算机学报,2002,25(7):759-766
[50]徐章艳,刘作鹏,杨炳儒,等.一个复杂度为max(O(|C||U|),O(|C|2|U/C|))的快速属性约简算法[J].计算机学报,2006,29(3):391-399
[51]刘少辉,盛秋戬,吴斌,史忠植,胡斐．Rough集高效算法的研究[J]．计算机学报,2003,26(5)：524-529
[52]叶东毅,陈昭炯.一个新的差别矩阵及其求核方法[J].电子学报,2002,30(7):1086-1088
[53]潘丹,郑启伦.属性约简自寻优算法[J].计算机研究与发展,2001,38(8):904-910
[54] Tong C, Ding S F, Zhu H, et al. A Granularity Attribute Reduction Method Based on BinaryDiscernibility Matrix[J]. IJACT: International Journal Advancements in ComputingTechnology,2012,4(12):213-221
[55] Qian Y H. Positive approximation: an accelerator for attribute reduction in rough settheory[J]. Artificial Intelligence,2010,174(9-10):597-618.
[56]钱进,苗夺谦,张泽华.云计算环境下知识约简算法[J].计算机学报,2011,34(12):2332-2343.
[57] Deng D Y, Yan D X, Wang J Y. Parallel reducts based on attribute significance[G].//Yu J.RSKT2010, LNAI6401,2010:336-343.
[58] Bargiela A, Pedrycz W. Granular Computing: An Introduce[M]. Boston, MA: KluwerAcademic Publishers,2003.
[59] Bargiela A, Pedrycz W. Recursive information granulation: aggregation and interpationissues[J]. IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics,2003,33(1):96-112.
[60] Pedrycz W, Keun K C. Boosting of granular models[J]. Fuzzy Sets and Systems,2006,157(22):2934-2953.
[61] Xie Y, Raghavan V V, Dhatric P, Zhao X.Q. A new fuzzy clustering algorithm for optimallyfinding granular prototypes[J]. International Journal of Approximate Reasoning,2005,40(1-2):109-124.
[62] Su C T, Chen L S, Yih Y. Knowledge acquisition through information granulation forimbalanced data[J]. Expert Systems with Applications,2006,31(3):531-541.
[63]卜东波,白硕,李国杰.聚类/分类中的粒度原理[J].计算机学报,2002,25(8):810-815
[64]张讲社,梁怡,徐宗本.基于视觉系统的聚类算法[J].计算机学报,2001,24(5):496-501.
[65]安秋生,沈钧毅,王国胤.基于信息粒度与Rough集的聚类方法研究[J].模式识别与人工智能,2003,16(4):412-417.
[66]朱树人,匡芳君,王艳华.基于粒度原理的蚁群聚类算法[J].计算机工程，2005,31(23):162-163
[67]刘白.基于群智能算法的聚类分析方法研究[D].南宁:广西民族大学,2006.
[68]贺玲,吴玲达,蔡益朝.数据挖掘中的聚类算法综述[J].计算机应用研究,2007,24(1):10-13.
[69]张丽娟,李舟军,陈火旺.粒度计算及其在数据挖掘中的应用[J].计算机科学,2005,32(12):178-180
[70] Zadeh L A. Fuzzy sets[J]. Information and Control,1965,8(3):338-353.
[71] Ruspini E H. A new approach to clustering[J]. Information and Control,1969,15(1):22-32.
[72] Pedrycz W, Loia V, Senatore S. Fuzzy Clustering With Viewpoints[J]. IEEE Transactions onFuzzy Systems,2010,18(2):274-284.
[73] White B S, Shalloway D. Efficient uncertainty minimization for fuzzy spectral clustering[J].Physical Review E,2009,80(5):056705.
[74] Celikyilmaz A. Soft-Link Spectral Clustering for Information Extraction[C].2009IEEEThird International Conference On Semantic Computing (ICSC2009),2009:434-441.
[75] Zhao F, Liu H Q, Jiao L.C. Spectral clustering with fuzzy similarity measure[J]. DigitalSignal Processing,2011,21(6):701-709.
[76] Mirkin B, Nascimento S. Additive spectral method for fuzzy cluster analysis of similaritydata including community structure and affinity matrices[J]. Information Sciences,2012,183(1):16-34.
[77] Pawlak Z. Rough sets[J]. International Journal of Information and ComputerSciences,1982,11(5):145-172.
[78] Herawan T, Deris M M, Abawajy J.H. A rough set approach for selecting clusteringattribute[J]. Knowledge-Based Systems,2010,23(3):220-231.
[79]刘少辉，胡斐，贾自艳,史忠植.一种基于Rough集的层次聚类算法[J].计算机研究与发展,2004,41(4):552-557.
[80] Malyszko D, Stepaniuk J. Adaptive multilevel rough entropy evolutionary thresholding[J].Information Sciences,2010,180(7):1138-1158.
[81] Malyszko D, Stepaniuk J. Rough Entropy Hierarchical Agglomerative Clustering in ImageSegmentation[J]. Transactions on Rough Sets XIII,2011,6499:89-103.
[82] Yanto I T R, Herawan T, Deris M M. Data clustering using variable precision rough set[J].Intelligent Data Analysis,2011,15(4):465-482.
[83] Chen M, Miao D Q. Interval set clustering[J]. Expert Systems with Applications,2011,38(4):2923-2932.
[84] Mitra S, Pedrycz W, Barman B. Shadowed c-means: Integrating fuzzy and rough clustering[J].Pattern Recognition,2010,43(4):1282-1291.
[85] Xue Z X, Shang Y L, Feng A.F. Semi-supervised outlier detection based on fuzzy roughC-means clustering[J]. Mathematics and Computers in Simulation,2010,80(9):1911-1921.
[86] Maji P. Fuzzy-Rough Supervised Attribute Clustering Algorithm and Classification ofMicroarray Data[J]. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics,2011,41(1):222-233.
[87] Zhou J, Pedrycz W, Miao D.Q.. Shadowed sets in the characterization of rough-fuzzyclustering[J]. Pattern Recognition,2011,44(8):1738-1749.
[88] Deng Z H, Choi K S, Chung F L, Wang S T. Enhanced soft subspace clustering integratingwithin-cluster and between-cluster information[J]. Pattern Recognition,2010,43(3):767-781.
[89] Ahmad A, Dey L. A k-means type clustering algorithm for subspace clustering of mixednumeric and categorical datasets[J]. Pattern Recognition Letters,2011,32(7):1062-1069.
[90] Peng L Q, Zhang J Y. An entropy weighting mixture model for subspace clustering ofhigh-dimensional data[J]. Pattern Recognition Letters,2011,32(8):1154-1161.
[91] Bai L, Liang J Y, Dang C Y, Cao F Y. A novel attribute weighting algorithm for clusteringhigh-dimensional categorical data[J]. Pattern Recognition,2011,44(12):2843-2861.
[92] Boongoen T, Shang C J, Iam-On N, Shen Q. Extending Data Reliability Measure to a FilterApproach for Soft Subspace Clustering[J]. IEEE Transactions on Systems Man andCybernetics Part B-Cybernetics,2011,41(6):1705-1714.
[93] Chen X J, Ye Y M, Xu X F, Huang J Z. A feature group weighting method for subspaceclustering of high-dimensional data[J]. Pattern Recognition,2012,45(1):434-446.
[94] Frey J, Dueck D. Clustering by passing messages between data points[J]. Science,2007,315(5814):972-976.
[95] Zadeh L A. Fuzzy sets and information granularity[G]//Gupta M, Ragade R, Yager R.Advances in Fuzzy Set Theory and Applications, North-Holland, Amsterdam,1979:3-18.
[96] Lin T Y. Granular computing[G]//Announcement of the BBISC Special Interest Group onGranular Computing,1997.
[97]丁世飞,朱红,许新征,史忠植.基于熵的模糊信息测度研究[J].计算机学报,2012,4(4):796-801
[98] Viktor Mayer Sch nberger. Delete: The Virtue of Forgetting in the Digital Age[M]. PrincetonUniversity Press,2009.
[99] Skowron A, Raus zer C. The Discernibility Matrices and Functions in Informat ion[C].Intelligent Decision Support Handbook of Applications and Advances of the Rough SetsTheory,1992:331-338.
[100] Pawlak z，Grzymala busse J，Slowinski，et a1．Rough Set[J]．Communications of the ACM,1995,38(11):89-95
[101]张文修,昊伟志,粱吉业,李德玉.粗糙集理论与方法[M].北京：科学出版社．2001
[102]陈洁,张燕平,张铃等.基于信息粒度的聚类分析及其应用[J].中国图像图形学报,2007,12(1):87-91
[103]王伦文.聚类的粒度分析[J].计算机工程与应用,2006,42(5):29-31.
[104] Dunn J C. A fuzzy relative of the ISODATA process and its use in detecting compact wellseparated cluster[J]. J Cybernet,1974,3:32-57
[105] Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms[M]. New York:Plenum Press,1981
[106] Li R P, Mukaidon M. A maximum entropy approach to fuzzy clustering[C]. In: Proc. of the4th IEEE Int’l Conf. on Fuzzy System. Yokohama: IEEE,1995.2227~2232.
[107]杨涛,李龙澍.一种基于粗糙集聚类的数据约简算法[J].系统仿真学报,2004,16（10）
[108] Zhang L, Zhang B. Quotient space based cluster analysis[C]. In Proceedings of Foundationsand Novel Approaches in Data Mining.2006:259-269.
[109]严莉莉,张燕平,胡必云.一种基于商空间粒度的覆盖聚类算法[J].计算机应用研究,2008,25(1):47-49.
[110]张铃,张钹,殷海风.多层前向网络的交叉覆盖设计算法[J].软件学报,1999,10(7):737-742.
[111]赵姝,张燕平,张铃,等.覆盖聚类算法[J].安徽大学学报:自然科学版,2005,29(2):28-32.
[112]徐峰,张铃,王伦文.基于商空间理论的模糊粒度计算方法[J].模式识别与人工智能,2004,17(4):425-429.
[113] Tang X Q, Zhu P, Cheng J X. Cluster Analysis Based on Fuzzy Quotient Space[J]. Journal ofSoftware,2008,19(4):861-868.
[114] Agrawal R, Gehrke J, Gunopulos D, Raghavan P. Automatic subspace clustering of highdimensionating data for data mining applications[C]. Proceedings of the1998ACMSIGMOD international conference on Management of data. ACM Press,1998:94-105.
[115] Aggarwal C C, et al. Fast algorithms for projected clustering[C]. Proceedings of the1999ACM SIGMOD international conference on Management of data. ACM Press,1999:61-72.
[116] Woo K G, Lee J H. FINDIT: a fast and intelligent subspace clustering algorithm usingdimension Voting[C]. PhD thesis, Korea Advanced Institute of Science and Technology,Taejon, Korea,2002.
[117] Frigui H, Nasraoui O. Simultaneous clustering and attribute discrimination[C]. Proceedingof the9thIEEE International Conference on Fuzzy Systems,2000.
[118] Huang Z, Ng M, Rong H. Automated variable weighting in k-means type clustering[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(5):657-668.
[119] Jing L, Michael K, Ng, and Joshua Zhexue H. An entropy weigh K-means algorithm forsubspace clustering of highdimensional sparse data[J]. IEEE Transactions on Knowledge andData Engineering,2007,19(8):1-16.
[120] Agrawal R, Gehrke J, Gunopulos D,et al. Automatic subspace clustering of highDimensional data[J]. Data Mining and Knowledge Discovery,2005,11:5-33.
[121] Jia S, Qian Y t, and Ji Z. Band selection for hyperspectral imagery using affinityPropagation[C]. Proceedings of the2008Digital Image Computing:Techniques andApplications, Canberra, ACT: IEEE,2008:137-141.
[122] Li G, Guo L, and Liu T M, et al. Grouping of brain MR images via affinity propagation[C].IEEE International Symposium on Circuits and Systems,2009(ISCAS2009), Taipei: IEEE,2009:2425-2428.
[123] Dueck D, Frey B J, and Jojic N, et al. Constructing treatment portfolios using affinitypropagation[C]. Proceedings of12th Annual International Conference, RECOMB2008,Berlin: Springer,2008:360-371.
[124] Kelly K． Afinity Program Slashes Computing Times[EB/OL].(2007-02-15).http://www.news.utoronto.ca/bin6/070215-2952.asp．
[125]王珏,王任,苗夺谦等.基于Rough Set理论的“数据浓缩”[J].计算机学报,1998,21(5):393-399
[126]肖大伟,王国胤,胡峰．一种基于粗糙集理论的快速并行属性约简算法[J].计算机科学2009,36(3):208-211
[127] Hu F, Wang G Y, Xia Y. Attribute Core Comput ationBased on Divide and ConquerMethod[C]. RSEISP '07Proceedings of the international conference on Rough Sets andIntelligent Systems Paradigms, Berlin: Springer,2007:310-319
[128]胡峰,王国胤.属性序下的快速约简算法[J].计算机学报,2007,30(6):1429-1435
[129]洪功冰．细粒度并行与多线程计算[J].计算机研究与发展,1996,33(6):473-480.
[130]夏飞,窦勇,徐佳庆等.基于FPGA的存储优化的细粒度并行Zuker算法加速器研究[J].计算机研究与发展,2011,48(4):709-719.
[131] Yu L, Liu Z Y. Study on Fine-grained Synchronization in Many-Core Architecture[C].10thACIS International Conference on Software Engineering, Artificial Intelligences,Networking and Parallel/Distributed Computing, Washington: IEEE,2009:524-529.
[132]英特尔亚太研发有限公司,北京并行科技有限公司.释放多核潜能:英特尔ParallelStudio并行开发指南[M].北京:清华大学出版社,2010.
[133]肖宇,于剑.基于近邻传播算法的半监督聚[J].软件学报,2008,19(11):2803-2813.
[134]董俊,王锁萍,熊范纶.可变相似性度量的近邻传播聚类[J].电子与信息学报,2010,32(3):509-514.
[135] Zhao Z Q, Gao J. A matrix modular neural network based on task decomposition withsubspace division by adaptive affinity propagation clustering[J]. Applied MathematicalModelling,2010,34(3):3884-3895
[136] Frey B J. Affinity propagation FAQ-General questions[EB/OL].[2010-11-1].http://www.psi.toronto-edu/affinity propagation/faq.html