加权频繁模式挖掘算法研究
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摘要
随着信息技术尤其是网络技术的快速发展,人们收集、存储和传输数据的能力不断提高,各类应用领域的数据量大量产生,数据挖掘日益成为数据分析和决策支持的一种重要工具。频繁模式挖掘是数据挖掘领域内的一个基本问题,它被广泛应用到多种领域和挖掘任务中,例如Web挖掘、零售业数据挖掘、科学研究、关联规则挖掘、序列模式挖掘、路径分析等。
在传统的频繁模式挖掘方法中,事务数据库(Transaction Database,TDB)中的每个项都被看成是同等重要的,而在实际应用中,每个项通常具有不同的重要性。为解决这个问题,本文研究了加权频繁模式挖掘(Weighted Frequent Pattern Mining,WFPM)问题,其主要特征就是在挖掘过程中通过给TDB中各个项目赋予不同的权值来体现它们的重要性不同。经过十几年的研究,已经奠定了较成熟的频繁模式挖掘算法理论基础,但对于加权频繁模式挖掘算法及其应用的研究工作尚处在初始阶段,值得深入研究和探讨。在加权事例中,加权支持度度量不再满足向下闭合特性(亦称反单调性(Antimonotonicity)),传统的频繁模式挖掘算法已经不再适用,因此在加权频繁模式算法中,研究的主要关注点是如何使加权支持度或兴趣度度量满足向下闭合特性(Downward Closure Property),以便高效地剪枝搜索空间。本文主要以基于Web频繁遍历路径模式挖掘和零售业数据挖掘为实例,详细阐述了基于加权有向图(Weighted Directed Graph,WDG)的加权频繁遍历模式挖掘和加权强相关频繁模式挖掘的有关思想。
图遍历模式挖掘一直是数据挖掘研究的热点之一,图及其遍历可广泛地模拟现实世界的多种数据访问形式,比较有代表性的实例就是Web路径访问,Web结构可被抽象为一个加权有向图:顶点代表网页或站点,有向边代表网页间的网页或站点间的超级链接,权值代表Web结构元素的不同重要性,然而传统的遍历模式挖掘算法仅仅考虑了非加权的遍历模式挖掘。为解决加权遍历模式挖掘问题,本文主要从以下几个方面做了深入研究:
归纳了加权频繁遍历模式挖掘(Weighted Frequent Traversai Pattern Mining,WFTPM)的种类,将Web加权频繁遍历模式挖掘,从用户类型角度分为个体加权频繁遍历模式挖掘(IndividualWFTPM,IWFTPM)和整体加权频繁遍历模式挖掘(Holistic WFTPM,HWFTPM);从采取的挖掘方法角度分为普通遍历模式挖掘和序列遍历模式挖掘。
提出了加权有向图模型,总结了加权有向图的种类,提出了两类加权有向图——顶点加权有向图(Vertex-Weighted Directed Graph,VWDG)和边加权有向图(Edge-Weighted Directed Graph,EWDG),并详细阐述了两类WDG间的转换方法,简化了基于加权有向图的频繁遍历模式挖掘问题,完善了基于图遍历的模式挖掘问题的理论基础。
基于加权有向图模型,本文做了以下几方面工作。
针对挖掘IWFTPM问题,提出了加权遍历模式间的一种新颖特性——可拓展特性,把对候选模式的剪枝问题转化为判断候选模式的可扩展性问题。基于加权模式间的可拓展特性,提出了一种基于加权有向图结构的频繁遍历模式挖掘算法——WFTPMiner(Weighted Frequent Traversal PatternMiner)算法,并提出了实现该算法的两种策略——EGTG(Evaluated by Global Topology of Graph)策略和ELTG(Evaluated by Local Topology of Graph)策略。
当最小支持度阈值较小时,用算法WFTPMiner挖掘加权频繁模式将导致效率低下,为克服以上不足,提出了一种修订的加权支持度表示法,然后利用加权FP-tree模式增长方法,提出了两种高效的基于加权有向图的频繁遍历模式挖掘算法:CWFTPMiner(Closed Weighted Frequent TraversalPattern Miner)和WTMaxMiner(Weighted Traversal-based Maximal frequent pattern Miner),前者用于挖掘闭合加权频繁遍历模式,后者用于挖掘最大加权频繁遍历模式。此外,在实现这两种算法的过程中,详细分析了闭合约束和加权约束的不同结合顺序可能造成的信息丢失现象,提出了两种约束的正确结合顺序。
对加权FP-tree模式增长算法的弊端和遍历路径中相关项目的连续性特点,把遍历模式看作是序列模式,提出了一种基于图遍历的加权序列模式挖掘算法WTSPMiner(Weighted Traversal-basedSequential Pattern Miner),该算法采用一种改进的加权前缀投影模式增长方法,运用分而治之策略,把挖掘原来加权序列数据库的任务分解成一组挖掘局部加权投影数据库的小任务,通过将加权约束添加到挖掘过程中,实现加权频繁序列遍历模式的挖掘。
为解决HWFTP挖掘问题,提出了一种挖掘基于统计理论的加权频繁遍历模式挖掘算法SWFTPMiner(Statistical theory-based Weighted Frequent Traversal Pattern Miner),该算法利用统计理论中的置信度概念,首先清除掉原始遍历数据库T中带有噪声权值的“异常点”(Outlier),从而得到能反映整体绝大多数用户遍历行为的修订加权有向图G_r及遍历数据库T_r,然后具体提出了两种从修订的T_r中挖掘WFTPs的策略方法——逐层挖掘策略和分而治之挖掘策略。
此外,本文以零售业为例,提出了一种加权强相关频繁模式挖掘算法WHFPMiner(WeightedHighly-correlated Frequent Pattern Miner),在算法中,提出了一种新的目标兴趣度度量标准——加权h-置信度,通过采用修订的加权支持度,证明了加权h-置信度具有反单调性和交叉加权支持性,最终基于加权FP-tree模式增长方法,利用加权h-置信度的两种特性快速地挖掘出包含有相似加权支持度水平的项目的加权频繁模式。
广泛的实验性能分析表明,本文提出的算法是高效的和可伸缩的,能够有效的完成各自的加权频繁挖掘任务。更重要的是,本文中提到的很多算法具有广阔的应用领域,例如,基于加权有向图的频繁遍历模式挖掘算法可以很方便地应用到很多能够被建模为加权有向图的实际应用中。
With the development of information technology, especially emerging of the network technology, our, abilities to collect, store and transfer data have been improved dramatically, and the great amount of data from diverse fields has been generated. Data mining technology has increasingly become an essential tool for data analysis and decision support. Frequent pattern mining is an important problem in the data mining area with a wide range of applications and mining tasks such as Web mining, retailing data mining, association rules mining, sequential pattern mining, path analysis, and so on.
Traditional methods for mining frequent patterns treat each item in TDB (Transaction Database) uniformly, while each item has usually different importance in the real applications. To solve this problem, this paper studies the problem of WFPM (Weighted Frequent Pattern Mining) whose principal characteristic is to assign each item of TDB a weight to reflect its importance in the mining process. In the last decade, the FPM algorithms have achieved a more mature theoretical foundation, however the WFPM and its applications are at an early stage of development, and it is worthy of in-depth study and exploration. The downward closure property (i.e., antimonotonicity) of the unweighted support measure in the weighted case no longer exists and previous algorithms cannot be applied directly. So the main focus in the WFPM algorithms is how to let weighted support or interesting measure satisfy the downward closure property so as to prune the search space efficiently. Taking Web-based frequent traversal path mining and the data mining in retailing for examples, this dissertation sets forth the related methods about mining weighted frequent traversal pattern based on WDG (Weighted Directed Graph) and weighted highly-correlated frequent pattern thoroughly.
Data mining on graph traversals has been an active research during recent years. Graph and traversals on it are widely used to model several classes of accessing data in the real world, and the most representative example is Web path accessing. The structure of Web can be simulated by a WDG, in which the vertices represent the related web pages or websites, and every directed edge between two wertices stands for the hyperlink from one vertex to another one, and the weights of vertices or edges reflect their own different importance. However, traditional traversal patterns mining algorithms hardly considered weighted traversals. To solve the problem of weighted traversal pattern mining, the dissertation makes an intensive study as follows.
The dissertation generalizes the categories of WFTPM (Weighted Frequent Traversal Pattern Mining). From the user-type perspective, Web weighted frequent traversal pattern mining can be divided into two classes: one is the IWFTPM (Individual WFTPM), the other is HWFTPM (Holistic WFTPM), and from the mining methods, into common TPM and sequential TPM.
In addition, this dissertation proposes the WDG model and divides the categories of WDG into two types, i.e., VWDG (Vertex-Weighted Directed Graph) and EWDG (Edge-Weighted Directed Graph). Moreover, the transformational methods between VWDG and EWDG are presented in detail, which simplifies the problem of WFTPM based on WDG traversals and improves the theoretical basis of patterns mining based on graph traversals.
Based on the WDG model, the thesis accomplishes the several following contributions.
For the problem of IWFTPM, the dissertation devises a novel property among the weighted traversal patterns—scalable property, and converts candidate patterns' pruning problem into corresponding patterns' scalability-checking problem. Based on the scalable property among the weighed patterns, the paper puts forward a WDG structure-based frequent traversal pattern mining algorithm named WFTPMiner (Weighted Frequent Traversal Pattern Miner), and presents two strategies to implement the algorithm—strategy EGTG (Evaluated by Global Topology of Graph ) and strategy ELTG (Evaluated by Local Topology of Graph).
When the minimum support threshold is lower, algorithm WFTPMiner is inefficient to mine weighted frequent patterns. To overcome this deficiency of WFTPMiner, a revised expression of weighted support is presented. Then, based on the weighted FP-tree pattern growth method, two efficient algorithms—CWFTPMiner (Closed Weighted Frequent Traversal Pattern Miner) and WTMaxMiner (Weighted Traversal-based Maximal frequent pattern Miner) is devised, among which the former is used to mine closed WFTPs and the latter is used to mine maximal WFTPs. In addition, in the process of implementing above two algorithms, the thesis analyzes the possible information loss case resulting from the wrong order of incorporating the closure constraint with weight constraint, and brings forward the right sequence of combination between two above-mentioned constraints.
By analyzing the shortcoming of weighed FP-tree pattern growth method and the continuity property of the items in the traversal path, the paper regards a traversal pattern as a sequence pattern. Based on the above fact, a WDG-based weighted sequential pattern mining algorithm named WTSPMiner (Weighted Traversal-based Sequential Pattern Miner) is presented. This algorithm adopts an improved weighted prefix-projected pattern growth approach to decompose the task of mining original sequence database with weight constraint into a series of smaller tasks of mining locally weighted projected database with a 'divide-and-conquer' strategy. The algorithm pushes the weight constraint into the mining process to accomplish the mining of weighted frequent sequence traversal patterns.
To solve the problem of HWFTPM, an algorithm called SWFTPMiner (Statistical theory-based Weighted Frequent Traversal Pattern Miner) is devised. Adopting the notion of confidence level in statistical theory, the algorithm first eliminates the outliers with noisy weights from the original traversal database T to get the revised WDG G_r and traversal database T_r which reflect the most users' traversal behaviors of the holistic. Then, based on the revised G_r and T_r, two mining strategies, respectively called level-wise mining strategy and divide-and-conquer mining strategy, are presented to mine the WFTPs from T_r in detail.
In addition, taking the retailing as a example, the thesis brings forward an algorithm called WHFPMiner (Weighted Highly-correlated Frequent Pattern Miner), in which a new objective interesting measure called weighted h-confidence is developed to mine weighted frequent patterns with strong correlation. Adopting the revised weighted support, we prove that the weighted h-confidence has two properties, i.e., anti-monotone property and cross weighted support property. Based on the weighted FP-tree pattern growth method, the algorithm applies two properties of weighted h-confidence to mine the weighted frequent patterns involving items with similar level of weighted support quickly and effectively.
The extensive performance analysis show that suggested approaches in this dissertation are efficient and scalable, and are competent for respective task of mining weighted frequent patterns. More importantly, most algorithms presented by the paper have a broad application fields, for example, WDG-based frequent pattern mining algorithms can be applied to various real applications whose characteristic can be simulated by the WDG model expediently.
在传统的频繁模式挖掘方法中,事务数据库(Transaction Database,TDB)中的每个项都被看成是同等重要的,而在实际应用中,每个项通常具有不同的重要性。为解决这个问题,本文研究了加权频繁模式挖掘(Weighted Frequent Pattern Mining,WFPM)问题,其主要特征就是在挖掘过程中通过给TDB中各个项目赋予不同的权值来体现它们的重要性不同。经过十几年的研究,已经奠定了较成熟的频繁模式挖掘算法理论基础,但对于加权频繁模式挖掘算法及其应用的研究工作尚处在初始阶段,值得深入研究和探讨。在加权事例中,加权支持度度量不再满足向下闭合特性(亦称反单调性(Antimonotonicity)),传统的频繁模式挖掘算法已经不再适用,因此在加权频繁模式算法中,研究的主要关注点是如何使加权支持度或兴趣度度量满足向下闭合特性(Downward Closure Property),以便高效地剪枝搜索空间。本文主要以基于Web频繁遍历路径模式挖掘和零售业数据挖掘为实例,详细阐述了基于加权有向图(Weighted Directed Graph,WDG)的加权频繁遍历模式挖掘和加权强相关频繁模式挖掘的有关思想。
图遍历模式挖掘一直是数据挖掘研究的热点之一,图及其遍历可广泛地模拟现实世界的多种数据访问形式,比较有代表性的实例就是Web路径访问,Web结构可被抽象为一个加权有向图:顶点代表网页或站点,有向边代表网页间的网页或站点间的超级链接,权值代表Web结构元素的不同重要性,然而传统的遍历模式挖掘算法仅仅考虑了非加权的遍历模式挖掘。为解决加权遍历模式挖掘问题,本文主要从以下几个方面做了深入研究:
归纳了加权频繁遍历模式挖掘(Weighted Frequent Traversai Pattern Mining,WFTPM)的种类,将Web加权频繁遍历模式挖掘,从用户类型角度分为个体加权频繁遍历模式挖掘(IndividualWFTPM,IWFTPM)和整体加权频繁遍历模式挖掘(Holistic WFTPM,HWFTPM);从采取的挖掘方法角度分为普通遍历模式挖掘和序列遍历模式挖掘。
提出了加权有向图模型,总结了加权有向图的种类,提出了两类加权有向图——顶点加权有向图(Vertex-Weighted Directed Graph,VWDG)和边加权有向图(Edge-Weighted Directed Graph,EWDG),并详细阐述了两类WDG间的转换方法,简化了基于加权有向图的频繁遍历模式挖掘问题,完善了基于图遍历的模式挖掘问题的理论基础。
基于加权有向图模型,本文做了以下几方面工作。
针对挖掘IWFTPM问题,提出了加权遍历模式间的一种新颖特性——可拓展特性,把对候选模式的剪枝问题转化为判断候选模式的可扩展性问题。基于加权模式间的可拓展特性,提出了一种基于加权有向图结构的频繁遍历模式挖掘算法——WFTPMiner(Weighted Frequent Traversal PatternMiner)算法,并提出了实现该算法的两种策略——EGTG(Evaluated by Global Topology of Graph)策略和ELTG(Evaluated by Local Topology of Graph)策略。
当最小支持度阈值较小时,用算法WFTPMiner挖掘加权频繁模式将导致效率低下,为克服以上不足,提出了一种修订的加权支持度表示法,然后利用加权FP-tree模式增长方法,提出了两种高效的基于加权有向图的频繁遍历模式挖掘算法:CWFTPMiner(Closed Weighted Frequent TraversalPattern Miner)和WTMaxMiner(Weighted Traversal-based Maximal frequent pattern Miner),前者用于挖掘闭合加权频繁遍历模式,后者用于挖掘最大加权频繁遍历模式。此外,在实现这两种算法的过程中,详细分析了闭合约束和加权约束的不同结合顺序可能造成的信息丢失现象,提出了两种约束的正确结合顺序。
对加权FP-tree模式增长算法的弊端和遍历路径中相关项目的连续性特点,把遍历模式看作是序列模式,提出了一种基于图遍历的加权序列模式挖掘算法WTSPMiner(Weighted Traversal-basedSequential Pattern Miner),该算法采用一种改进的加权前缀投影模式增长方法,运用分而治之策略,把挖掘原来加权序列数据库的任务分解成一组挖掘局部加权投影数据库的小任务,通过将加权约束添加到挖掘过程中,实现加权频繁序列遍历模式的挖掘。
为解决HWFTP挖掘问题,提出了一种挖掘基于统计理论的加权频繁遍历模式挖掘算法SWFTPMiner(Statistical theory-based Weighted Frequent Traversal Pattern Miner),该算法利用统计理论中的置信度概念,首先清除掉原始遍历数据库T中带有噪声权值的“异常点”(Outlier),从而得到能反映整体绝大多数用户遍历行为的修订加权有向图G_r及遍历数据库T_r,然后具体提出了两种从修订的T_r中挖掘WFTPs的策略方法——逐层挖掘策略和分而治之挖掘策略。
此外,本文以零售业为例,提出了一种加权强相关频繁模式挖掘算法WHFPMiner(WeightedHighly-correlated Frequent Pattern Miner),在算法中,提出了一种新的目标兴趣度度量标准——加权h-置信度,通过采用修订的加权支持度,证明了加权h-置信度具有反单调性和交叉加权支持性,最终基于加权FP-tree模式增长方法,利用加权h-置信度的两种特性快速地挖掘出包含有相似加权支持度水平的项目的加权频繁模式。
广泛的实验性能分析表明,本文提出的算法是高效的和可伸缩的,能够有效的完成各自的加权频繁挖掘任务。更重要的是,本文中提到的很多算法具有广阔的应用领域,例如,基于加权有向图的频繁遍历模式挖掘算法可以很方便地应用到很多能够被建模为加权有向图的实际应用中。
With the development of information technology, especially emerging of the network technology, our, abilities to collect, store and transfer data have been improved dramatically, and the great amount of data from diverse fields has been generated. Data mining technology has increasingly become an essential tool for data analysis and decision support. Frequent pattern mining is an important problem in the data mining area with a wide range of applications and mining tasks such as Web mining, retailing data mining, association rules mining, sequential pattern mining, path analysis, and so on.
Traditional methods for mining frequent patterns treat each item in TDB (Transaction Database) uniformly, while each item has usually different importance in the real applications. To solve this problem, this paper studies the problem of WFPM (Weighted Frequent Pattern Mining) whose principal characteristic is to assign each item of TDB a weight to reflect its importance in the mining process. In the last decade, the FPM algorithms have achieved a more mature theoretical foundation, however the WFPM and its applications are at an early stage of development, and it is worthy of in-depth study and exploration. The downward closure property (i.e., antimonotonicity) of the unweighted support measure in the weighted case no longer exists and previous algorithms cannot be applied directly. So the main focus in the WFPM algorithms is how to let weighted support or interesting measure satisfy the downward closure property so as to prune the search space efficiently. Taking Web-based frequent traversal path mining and the data mining in retailing for examples, this dissertation sets forth the related methods about mining weighted frequent traversal pattern based on WDG (Weighted Directed Graph) and weighted highly-correlated frequent pattern thoroughly.
Data mining on graph traversals has been an active research during recent years. Graph and traversals on it are widely used to model several classes of accessing data in the real world, and the most representative example is Web path accessing. The structure of Web can be simulated by a WDG, in which the vertices represent the related web pages or websites, and every directed edge between two wertices stands for the hyperlink from one vertex to another one, and the weights of vertices or edges reflect their own different importance. However, traditional traversal patterns mining algorithms hardly considered weighted traversals. To solve the problem of weighted traversal pattern mining, the dissertation makes an intensive study as follows.
The dissertation generalizes the categories of WFTPM (Weighted Frequent Traversal Pattern Mining). From the user-type perspective, Web weighted frequent traversal pattern mining can be divided into two classes: one is the IWFTPM (Individual WFTPM), the other is HWFTPM (Holistic WFTPM), and from the mining methods, into common TPM and sequential TPM.
In addition, this dissertation proposes the WDG model and divides the categories of WDG into two types, i.e., VWDG (Vertex-Weighted Directed Graph) and EWDG (Edge-Weighted Directed Graph). Moreover, the transformational methods between VWDG and EWDG are presented in detail, which simplifies the problem of WFTPM based on WDG traversals and improves the theoretical basis of patterns mining based on graph traversals.
Based on the WDG model, the thesis accomplishes the several following contributions.
For the problem of IWFTPM, the dissertation devises a novel property among the weighted traversal patterns—scalable property, and converts candidate patterns' pruning problem into corresponding patterns' scalability-checking problem. Based on the scalable property among the weighed patterns, the paper puts forward a WDG structure-based frequent traversal pattern mining algorithm named WFTPMiner (Weighted Frequent Traversal Pattern Miner), and presents two strategies to implement the algorithm—strategy EGTG (Evaluated by Global Topology of Graph ) and strategy ELTG (Evaluated by Local Topology of Graph).
When the minimum support threshold is lower, algorithm WFTPMiner is inefficient to mine weighted frequent patterns. To overcome this deficiency of WFTPMiner, a revised expression of weighted support is presented. Then, based on the weighted FP-tree pattern growth method, two efficient algorithms—CWFTPMiner (Closed Weighted Frequent Traversal Pattern Miner) and WTMaxMiner (Weighted Traversal-based Maximal frequent pattern Miner) is devised, among which the former is used to mine closed WFTPs and the latter is used to mine maximal WFTPs. In addition, in the process of implementing above two algorithms, the thesis analyzes the possible information loss case resulting from the wrong order of incorporating the closure constraint with weight constraint, and brings forward the right sequence of combination between two above-mentioned constraints.
By analyzing the shortcoming of weighed FP-tree pattern growth method and the continuity property of the items in the traversal path, the paper regards a traversal pattern as a sequence pattern. Based on the above fact, a WDG-based weighted sequential pattern mining algorithm named WTSPMiner (Weighted Traversal-based Sequential Pattern Miner) is presented. This algorithm adopts an improved weighted prefix-projected pattern growth approach to decompose the task of mining original sequence database with weight constraint into a series of smaller tasks of mining locally weighted projected database with a 'divide-and-conquer' strategy. The algorithm pushes the weight constraint into the mining process to accomplish the mining of weighted frequent sequence traversal patterns.
To solve the problem of HWFTPM, an algorithm called SWFTPMiner (Statistical theory-based Weighted Frequent Traversal Pattern Miner) is devised. Adopting the notion of confidence level in statistical theory, the algorithm first eliminates the outliers with noisy weights from the original traversal database T to get the revised WDG G_r and traversal database T_r which reflect the most users' traversal behaviors of the holistic. Then, based on the revised G_r and T_r, two mining strategies, respectively called level-wise mining strategy and divide-and-conquer mining strategy, are presented to mine the WFTPs from T_r in detail.
In addition, taking the retailing as a example, the thesis brings forward an algorithm called WHFPMiner (Weighted Highly-correlated Frequent Pattern Miner), in which a new objective interesting measure called weighted h-confidence is developed to mine weighted frequent patterns with strong correlation. Adopting the revised weighted support, we prove that the weighted h-confidence has two properties, i.e., anti-monotone property and cross weighted support property. Based on the weighted FP-tree pattern growth method, the algorithm applies two properties of weighted h-confidence to mine the weighted frequent patterns involving items with similar level of weighted support quickly and effectively.
The extensive performance analysis show that suggested approaches in this dissertation are efficient and scalable, and are competent for respective task of mining weighted frequent patterns. More importantly, most algorithms presented by the paper have a broad application fields, for example, WDG-based frequent pattern mining algorithms can be applied to various real applications whose characteristic can be simulated by the WDG model expediently.
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