用于图分类的频繁子结构挖掘算法研究
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摘要
随着计算机与信息技术的发展,数据挖掘技术已经广泛应用到人工智能、模式识别、生物信息等许多领域。当前,复杂类型数据的挖掘需求上升,专家学者开始关注这方面的新应用和理论研究,并试图利用结构化数据挖掘方面的经验和方法来帮助解决新问题。
在计算机科学领域,图具有直观的表达形式,它能够表达更加丰富的语义,同时,图也是最复杂的数据结构之一,与一般的数据相比,这种丰富的语义也增加了数据结构的复杂性和挖掘令人感兴趣的图结构的难度。因此,图挖掘需要综合应用图论知识与数据挖掘的技术。图的挖掘无论在研究领域还是在商业领域都有着广泛的应用,例如:CAD电路分析、分子模型分析、Web浏览中的用户兴趣点的挖掘以及数据的压缩等等。在图挖掘中频繁子图挖掘又是图分类和图聚类的基础,如何从大量的图中挖掘出令人感兴趣的频繁子图模式成为国内数据挖掘领域研究的热点之一。本文的主要内容如下。
首先,本文介绍了图的相关概念、图挖掘方法的类型和经典的频繁子图挖掘算法,并对现有的经典算法进行了全面的综合分析、归纳和总结,重点指出了有代表性的算法的优缺点以及图挖掘存在的主要问题,为下一步的研究指明了方向。其次,针对基于模式增长算法gSpan所存在的扩展频繁子图时产生冗余的问题,提出了一种改进的算法CSGM。用ADI++存储结构来代替原算法的邻接链表的存储结构,同时还提出了有效的删除非最小DFS编码的方法,保证算法在扩展频繁子图时每一次均能够生成图的标准编码,避免对标准编码不必要的判断以及非标准编码的支持度计算。另外,在挖掘中使用Hash表存储同构图的Hash地址,来计算频繁子图的支持度,避免了对图集的重复扫描,也相应地减少了子图同构判断的次数。在实际数据集和人工合成的模拟数据集上做了全面的实验,对算法的正确性、处理大规模图集的能力以及运行时间上进行了验证。
再次,以频繁子图挖掘结果作为特征候选集,选取特征来生成一个有辨别力的频繁模式的小集合用作分类特征,本文又提出了一种特征模式选取算法。通过引入信息熵、信息增益这种有判别力的度量手段给出了目标函数,说明了如何选取分类特征的方法。同时,为了缩减图模式的搜索空间和提高挖掘效率,还给出了垂直剪枝和水平剪枝两种剪枝策略。通过实验验证了挖掘结果的质量及算法的运行效率。
最后,提出了一种基于频繁模式的图分类算法。先从理论上分析了模式的预测能力和支持度之间的关系,给出了最小支持度阈值的设置策略。进一步采用有判别力的频繁子图作为特征图模式来构造分类规则,通过关联分类的方法来训练分类器,识别新图的类别。通过实验对分类器的性能进行了验证。
With the development of computer science and information technology,data mining technology has been widely applied to artificial intelligence,pattern recognition,bioinformatics and many other fields.The demand of mining on complex data is rising now. Experts have paid attention to these fields and tried to solve the problems by virtue of the experience of structured data mining.
In computer science, the graph is one of the most complicated data structures. Its’rich semantic increases more complexity of the data structure and more difficulty for mining the interesting graph structures. The graph theory is often used together with various technologies in graph data mining. Graph can be intuitively presented and has a wide variety of applications both in research and business, e.g. CAD circuit analysis, molecular model analysis, finding user’s interest in Web browsing and data compression. About graph mining, frequent subgraph mining is the foundation of graph classification and graph clustering. Accordingly, how to derive the frequent subgraph patterns from the great volume of graph-structured data became one of the hottest issues in data mining field. This is also the focus of this paper.
Firstly, in this paper the basic concept of graph, the type of graph mining approaches and the classic frequent subgraph mining algorithm are introduced. Then the existing classic graph mining algorithms are analysed and pointed out the excellence and the inferior aspects. The problems of graph mining are also introduced in this section, the direction for future research is given.
Secondly, to resolve the problem that gSpan algorithm will produce a lot of redundant subgraphs while extending frequent subgraphs, an improved algorithm CSGM is proposed, which using ADI++ storage structure instead of the adjacency list storage structure in gSpan, and meanwhile an approache of deleting the non-DFS code is also present. It can handle larger graph dataset and guarantee that a canonical code can be obtained at each extension. It not only avoids calculating the support of the non-canonical code graphs but also avoids the calculation of whether an input code is a canonical code or not, the new algorithm reduces the computation. Hash table is used to store graph’s hash address and calculate the support of frequent subgraphs during mining, it can avoid scanning the databases repeatly and reduce the counts of subgraph isomorphism judgment. The experiments have been done on the actual and simulate date sets to verify the correctness, the efficiency and the ability to handle large graph databases .
Afterwards, the result of frequent subgraphs mining is used as a feature candidate set, to select a small set of frequent and discriminative patterns for classification from it, an algorithm of selecting feature patterns is provided in this article. The objective function is given by introducing the discriminative measure of information entropy and information gain. The method for classification feature selection is explained. Meawhile, in order to reduce the searching space of graph patterns and improve the efficiency, both vertical pruning and horizontal pruning strategies are proposed. The qualityof mining results and running efficiency are verified by experiment.
Finally, an algorithm of graph classification based on frequent patterns is provided. By analyzing the relationship between pattern frequency and its predictive power, such a analysis suggests a strategy for setting min_sup. Furthermore,the discriminative frequent subgraphs are used as feature patterns to construct the classification rules, the classifier is trained by associative classification, and the new graph is distinguished. The performance of the classifier is verified by experiment.
在计算机科学领域,图具有直观的表达形式,它能够表达更加丰富的语义,同时,图也是最复杂的数据结构之一,与一般的数据相比,这种丰富的语义也增加了数据结构的复杂性和挖掘令人感兴趣的图结构的难度。因此,图挖掘需要综合应用图论知识与数据挖掘的技术。图的挖掘无论在研究领域还是在商业领域都有着广泛的应用,例如:CAD电路分析、分子模型分析、Web浏览中的用户兴趣点的挖掘以及数据的压缩等等。在图挖掘中频繁子图挖掘又是图分类和图聚类的基础,如何从大量的图中挖掘出令人感兴趣的频繁子图模式成为国内数据挖掘领域研究的热点之一。本文的主要内容如下。
首先,本文介绍了图的相关概念、图挖掘方法的类型和经典的频繁子图挖掘算法,并对现有的经典算法进行了全面的综合分析、归纳和总结,重点指出了有代表性的算法的优缺点以及图挖掘存在的主要问题,为下一步的研究指明了方向。其次,针对基于模式增长算法gSpan所存在的扩展频繁子图时产生冗余的问题,提出了一种改进的算法CSGM。用ADI++存储结构来代替原算法的邻接链表的存储结构,同时还提出了有效的删除非最小DFS编码的方法,保证算法在扩展频繁子图时每一次均能够生成图的标准编码,避免对标准编码不必要的判断以及非标准编码的支持度计算。另外,在挖掘中使用Hash表存储同构图的Hash地址,来计算频繁子图的支持度,避免了对图集的重复扫描,也相应地减少了子图同构判断的次数。在实际数据集和人工合成的模拟数据集上做了全面的实验,对算法的正确性、处理大规模图集的能力以及运行时间上进行了验证。
再次,以频繁子图挖掘结果作为特征候选集,选取特征来生成一个有辨别力的频繁模式的小集合用作分类特征,本文又提出了一种特征模式选取算法。通过引入信息熵、信息增益这种有判别力的度量手段给出了目标函数,说明了如何选取分类特征的方法。同时,为了缩减图模式的搜索空间和提高挖掘效率,还给出了垂直剪枝和水平剪枝两种剪枝策略。通过实验验证了挖掘结果的质量及算法的运行效率。
最后,提出了一种基于频繁模式的图分类算法。先从理论上分析了模式的预测能力和支持度之间的关系,给出了最小支持度阈值的设置策略。进一步采用有判别力的频繁子图作为特征图模式来构造分类规则,通过关联分类的方法来训练分类器,识别新图的类别。通过实验对分类器的性能进行了验证。
With the development of computer science and information technology,data mining technology has been widely applied to artificial intelligence,pattern recognition,bioinformatics and many other fields.The demand of mining on complex data is rising now. Experts have paid attention to these fields and tried to solve the problems by virtue of the experience of structured data mining.
In computer science, the graph is one of the most complicated data structures. Its’rich semantic increases more complexity of the data structure and more difficulty for mining the interesting graph structures. The graph theory is often used together with various technologies in graph data mining. Graph can be intuitively presented and has a wide variety of applications both in research and business, e.g. CAD circuit analysis, molecular model analysis, finding user’s interest in Web browsing and data compression. About graph mining, frequent subgraph mining is the foundation of graph classification and graph clustering. Accordingly, how to derive the frequent subgraph patterns from the great volume of graph-structured data became one of the hottest issues in data mining field. This is also the focus of this paper.
Firstly, in this paper the basic concept of graph, the type of graph mining approaches and the classic frequent subgraph mining algorithm are introduced. Then the existing classic graph mining algorithms are analysed and pointed out the excellence and the inferior aspects. The problems of graph mining are also introduced in this section, the direction for future research is given.
Secondly, to resolve the problem that gSpan algorithm will produce a lot of redundant subgraphs while extending frequent subgraphs, an improved algorithm CSGM is proposed, which using ADI++ storage structure instead of the adjacency list storage structure in gSpan, and meanwhile an approache of deleting the non-DFS code is also present. It can handle larger graph dataset and guarantee that a canonical code can be obtained at each extension. It not only avoids calculating the support of the non-canonical code graphs but also avoids the calculation of whether an input code is a canonical code or not, the new algorithm reduces the computation. Hash table is used to store graph’s hash address and calculate the support of frequent subgraphs during mining, it can avoid scanning the databases repeatly and reduce the counts of subgraph isomorphism judgment. The experiments have been done on the actual and simulate date sets to verify the correctness, the efficiency and the ability to handle large graph databases .
Afterwards, the result of frequent subgraphs mining is used as a feature candidate set, to select a small set of frequent and discriminative patterns for classification from it, an algorithm of selecting feature patterns is provided in this article. The objective function is given by introducing the discriminative measure of information entropy and information gain. The method for classification feature selection is explained. Meawhile, in order to reduce the searching space of graph patterns and improve the efficiency, both vertical pruning and horizontal pruning strategies are proposed. The qualityof mining results and running efficiency are verified by experiment.
Finally, an algorithm of graph classification based on frequent patterns is provided. By analyzing the relationship between pattern frequency and its predictive power, such a analysis suggests a strategy for setting min_sup. Furthermore,the discriminative frequent subgraphs are used as feature patterns to construct the classification rules, the classifier is trained by associative classification, and the new graph is distinguished. The performance of the classifier is verified by experiment.
引文
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90 Zou Zhaonian, Li Jianzhong, Gao Hong and Zhang Shuo. Finging top-k maximal cliques in an uncertain graph. Proc. of the ICDE 2010. Long Beach, California, USA, 2010:649-652
91韩蒙,张炜,李建中. RAKING:一种高效的不确定图K-极大频繁模式挖掘算法.计算机学报, 2010,33(8):1387-1395
92 Liu Y, Li.J, Gao H. Summarizing graph patterns. Proc. of the 24th IEEE International Conference on Data Engineering Cancun, Mexico, 2008:903-912
93刘勇,高宏,李建中.基于联合意义度量的Top-K图模式挖掘.计算机学报, 2010,33(2):215-230
94刘勇,李建中,朱敬华.一种新的基于闭显露模式的图分类方法,计算机研究与发展. 2007,44(7):1169-1176
95 Zhiping Zeng, Jianyong Wang, Jun Zhang, Lizhu Zhou. FOGGER: an algorithm for graph generator discovery.EDBT 2009:517-528.
96周颖杰,胡光岷,贺伟淞.基于时间序列图挖掘的网络流量异常检测.计算机科学, 2009, 36 (1): 46-50
97刘俊侠.使用有向图挖掘时间间隔序列模式.计算机科学探索, 2007,2 (6): 666-672
98 Shrivastava Swapnil, Pa. Supriya. Graph mining framework for finding and visualizing substructures using graph database. Proc. of the 2009 International Conference on Advances in Social Network Analysis and Mining, ASONAM 2009,2: 379-380
99 Rakhshan, L.B. Holder, D.J. Cook. Structural Web Search Engine. FLAIRS Conference, Augustine, Florida, USA, 2003:319-324
100 L. Yang, H. Lee, W. Achary. Mning Frequent Query Patterns from XML Queries, Eighth International Conference on Database Systems for Adavanced Application, 2003: 355-363
101 Tatsuya Asai, Hiroki Arimura, Kenji Abe, Shinji Kawasoe, Setsuo Arikawa. Online Algorithms for Mining Semi-structured Data Stream. Proc. of ICDM’02, 2002:27-34
102王艳辉,吴斌,王柏.频繁子图挖掘算法综述.计算机科学, 2005, 32 (10): 193-196
103 David W. Williams, Jun Huan, Wei Wang. Graph database indexing using structured graph decomposition. Proc. of the 23rd IEEE, 2007:231-235
104李玉华,罗汉果,孙小林.一种基于Apriori思想的频繁子图发现算法.计算机工程与科学, 2007, 29 (4):84-87
105 West D.B.图论导引(第二版).李建中,骆吉洲译.北京:机械工业出版社,2007: 33-127
106 Ryuhei Uehara, Seinosuke Toda, Takayuki Nagoya. Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs. Discrete Applied Mathematics, 2005, 145 (3): 479-482
107周杨,王峰. FSM-基于子图同构和结构同构的频繁子图挖掘算法.计算机研究与发展, 2007, 44 (Suppl.): 296-301
108 L.P. Cordella, P. Foggia, C. Sansone, M. Vento. A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs. Transactions on Pattern Analysis and Machine Intelligence, 2004, 26 (10): 1367-1372
109 P.Tan, V.Kumar and J.Srivastava.Selecting the right interestingness measure for association patterns. Proc. of SIGKDD, 2002: 32-41
110 W.Geamsakul, T.Matsuda, T.Yoshida and etc. Classifier construction by graph-based induction for graph-structured data. Proc. of PAKDD’03, 2003:52-62
111吴卫江,王智广,张晶.两个经典频繁子图挖掘算法的对比与分析.内蒙古师范大学学报:自然科学版, 2009, 38 (2): 167-170
112 T. Scheer and S. Wrobel. Finding the most interesting patterns in a database quickly by using sequential sampling. J. of Machine Learning Research, 2002, 3:833-862
113 N. Lachiche, P. Flach. 1BC2: a True first-Order Bayesian Classifier. Proc.of the 12th International Conference on Inductive Logic Programming, Sydney, Australia, 2002:133-148
114 Ou Guobin, Murphey YiLu. Multi-class pattern classification using neural networks. Pattern Recognition, 2007,40(1): 4-18
115 X.Yin and J.Han. CPAR: Classification based on predictive association rules. Proc. of SDM, 2003:331-335
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76 B.Bringmann and A.Zimmermann. Tree2-decision trees for tree structured data. Proc. of 2005 European Symp.Principle of Data Mining and Knowledge Discovery, 2005:46-58
77 Zimmermann and B.Bringmann. CTC-correlating tree patterns for classification. Proc. of 2005 Int Conf. Data Mining (ICDM05), 2005:833-836
78 W.Fan, K.Zhang, H.Cheng, J.Gao, X.Yan, J.Han, P.S.Yu and O.Verscheure. Direct mining of discriminative and essential frenquent patterns via model-based search tree. KDD, ACM, 2008:230-238
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81汪卫,周皓峰,袁晴晴.基于图论的频繁模式挖掘.计算机研究与发展, 2005,42 (2): 230-235
82 Chen Wang, Wei Wang, Jian Pei, Yongtai Zhu, Baile Shi. Scalable mining of large disk-based graph databases. KDD’04,2004:316-325
83 Chen Wang, Yongtai Zhu, Tianyi Wu, Wei Wang, Beile Shi. Constraint-Based Graph Mining in Large Database. APWeb,2005:133-144
84 Chen Wang, Mingsheng Hong, Jian Pei, Haofeng Zhou, Wei Wang, Baile Shi. Efficient Pattern-Growth Methods for Frequent Tree Pattern Mining. PAKDD’04, 2004:441-451
85 Qingqing Yuan, Yubo Lou, Haofeng Zhou, Wei Wang, Baile Shi. Extract Frequent Pattern from Simple Graph Data. WAIM’02, 2002:158-169
86李先通,李建中,高宏.一种高效频繁子图挖掘算法.软件学报. 2007,18(10): 2469-2480
87张硕,高宏,李建中,邹兆年.不确定图数据库中高效查询处理,计算机学报, 2009, 32(10):2066-2079
88邹兆年,李建中,高宏,张硕.从不确定图中挖掘频繁子图模式.软件学报,2008,19(12):1-12
89 Zou Zhaonian, Li Jianzhong, Gao Hong and Zhang Shuo. Mining frenquent subgraph patterns from uncertain graph data. IEEE Transactions on Knowledge and Data Engineering, 2010,22(9):1203-1218
90 Zou Zhaonian, Li Jianzhong, Gao Hong and Zhang Shuo. Finging top-k maximal cliques in an uncertain graph. Proc. of the ICDE 2010. Long Beach, California, USA, 2010:649-652
91韩蒙,张炜,李建中. RAKING:一种高效的不确定图K-极大频繁模式挖掘算法.计算机学报, 2010,33(8):1387-1395
92 Liu Y, Li.J, Gao H. Summarizing graph patterns. Proc. of the 24th IEEE International Conference on Data Engineering Cancun, Mexico, 2008:903-912
93刘勇,高宏,李建中.基于联合意义度量的Top-K图模式挖掘.计算机学报, 2010,33(2):215-230
94刘勇,李建中,朱敬华.一种新的基于闭显露模式的图分类方法,计算机研究与发展. 2007,44(7):1169-1176
95 Zhiping Zeng, Jianyong Wang, Jun Zhang, Lizhu Zhou. FOGGER: an algorithm for graph generator discovery.EDBT 2009:517-528.
96周颖杰,胡光岷,贺伟淞.基于时间序列图挖掘的网络流量异常检测.计算机科学, 2009, 36 (1): 46-50
97刘俊侠.使用有向图挖掘时间间隔序列模式.计算机科学探索, 2007,2 (6): 666-672
98 Shrivastava Swapnil, Pa. Supriya. Graph mining framework for finding and visualizing substructures using graph database. Proc. of the 2009 International Conference on Advances in Social Network Analysis and Mining, ASONAM 2009,2: 379-380
99 Rakhshan, L.B. Holder, D.J. Cook. Structural Web Search Engine. FLAIRS Conference, Augustine, Florida, USA, 2003:319-324
100 L. Yang, H. Lee, W. Achary. Mning Frequent Query Patterns from XML Queries, Eighth International Conference on Database Systems for Adavanced Application, 2003: 355-363
101 Tatsuya Asai, Hiroki Arimura, Kenji Abe, Shinji Kawasoe, Setsuo Arikawa. Online Algorithms for Mining Semi-structured Data Stream. Proc. of ICDM’02, 2002:27-34
102王艳辉,吴斌,王柏.频繁子图挖掘算法综述.计算机科学, 2005, 32 (10): 193-196
103 David W. Williams, Jun Huan, Wei Wang. Graph database indexing using structured graph decomposition. Proc. of the 23rd IEEE, 2007:231-235
104李玉华,罗汉果,孙小林.一种基于Apriori思想的频繁子图发现算法.计算机工程与科学, 2007, 29 (4):84-87
105 West D.B.图论导引(第二版).李建中,骆吉洲译.北京:机械工业出版社,2007: 33-127
106 Ryuhei Uehara, Seinosuke Toda, Takayuki Nagoya. Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs. Discrete Applied Mathematics, 2005, 145 (3): 479-482
107周杨,王峰. FSM-基于子图同构和结构同构的频繁子图挖掘算法.计算机研究与发展, 2007, 44 (Suppl.): 296-301
108 L.P. Cordella, P. Foggia, C. Sansone, M. Vento. A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs. Transactions on Pattern Analysis and Machine Intelligence, 2004, 26 (10): 1367-1372
109 P.Tan, V.Kumar and J.Srivastava.Selecting the right interestingness measure for association patterns. Proc. of SIGKDD, 2002: 32-41
110 W.Geamsakul, T.Matsuda, T.Yoshida and etc. Classifier construction by graph-based induction for graph-structured data. Proc. of PAKDD’03, 2003:52-62
111吴卫江,王智广,张晶.两个经典频繁子图挖掘算法的对比与分析.内蒙古师范大学学报:自然科学版, 2009, 38 (2): 167-170
112 T. Scheer and S. Wrobel. Finding the most interesting patterns in a database quickly by using sequential sampling. J. of Machine Learning Research, 2002, 3:833-862
113 N. Lachiche, P. Flach. 1BC2: a True first-Order Bayesian Classifier. Proc.of the 12th International Conference on Inductive Logic Programming, Sydney, Australia, 2002:133-148
114 Ou Guobin, Murphey YiLu. Multi-class pattern classification using neural networks. Pattern Recognition, 2007,40(1): 4-18
115 X.Yin and J.Han. CPAR: Classification based on predictive association rules. Proc. of SDM, 2003:331-335