Efficient Graph-Based Algorithms for Discovering and Maintaining Association Rules in Large Databases

In this paper, we study the issues of mining and maintaining association rules in a large database of customer transactions. The problem of mining association rules can be mapped into the problems of finding large itemsets which are sets of items brought together in a sufficient number of transactions. We revise a graph-based algorithm to further speed up the process of itemset generation. In addition, we extend our revised algorithm to maintain discovered association rules when incremental or decremental updates are made to the databases. Experimental results show the efficiency of our algorithms. The revised algorithm is a significant improvement over the original one on mining association rules. The algorithms for maintaining association rules are more efficient than re-running the mining algorithms for the whole updated database and outperform previously proposed algorithms that need multiple passes over the database. Received 4 August 1999 / Revised 18 March 2000 / Accepted in revised form 18 October 2000     

典型关联规则挖掘算法的分析与比较

关联规则的发现是数据挖掘的一个重要方面,目前许多研究人员正致力于关联规则的快速开采算法的研究。文中介绍了几种典型的开采大型事务数据库中所有关联规则的算法,特别针对算法过程中产生候选频繁项集的大小和所需扫描事务数据库的次数这两个影响关联规则挖掘效率的关键问题,分析各个算法采用的解决策略及相应的局限性,并比较它们的时间效率和空间效率。最后展望了关联规则挖掘算法的研究方向。     

A graph-based approach for discovering various types of associationrules

Mining association rules is an important task for knowledge discovery. We can analyze past transaction data to discover customer behaviors such that the quality of business decisions can be improved. Various types of association rules may exist in a large database of customer transactions. The strategy of mining association rules focuses on discovering large item sets, which are groups of items which appear together in a sufficient number of transactions. We propose a graph-based approach to generate various types of association rules from a large database of customer transactions. This approach scans the database once to construct an association graph and then traverses the graph to generate all large item sets. Empirical evaluations show that our algorithms outperform other algorithms which need to make multiple passes over the database     

基于矩阵的加权关联规则挖掘算法

关联规则挖掘是数据挖掘中的一个重要模型。传统的关联规则挖掘算法需要多次扫描数据库,生成大量候选项集,并且把数据库中各个项目按平等一致的方法对待,算法复杂且与实际情况不符。为此提出一种基于矩阵的加权关联规则挖掘算法,它只需扫描一次数据库,不生成候选项目集,可以快速挖掘出频率小但重要性高的项目。     

A fast algorithm for mining association rules

In this paper,the problem of discovering association rules between items in a large database of sales transactions is discussed.and a novel algorithm,BitMatrix,is proposed.The proposed algorithm is fundamentally different from the known algorithms Apriori and AprioriTid.Empirical evaluation shows that the algorithm outperforms the known ones for large databases.Scale-up experiments show that the algorithm scales linearly with the number of transactions.     

一种矩阵和排序索引关联规则数据挖掘算法

在关联规则挖掘算法中,Apriori由于多次对数据库进行扫描会产生较多的候选集,在多次扫描数据库的情况下容易产生I/O开销问题,并引起数据挖掘效率低。矩阵关联规则在数据挖掘过程中没有删除非频繁项集,致使存在较多的无效扫描,对于挖掘效率的提高也不明显。该文提出了一种改进的矩阵和排序索引关联规则数据挖掘算法,首先,删除不需要的事务和项,通过矩阵相乘和查找表获得频繁的二项式集合,结合排序索引得到剩下的频繁k-项集。与矩阵关联规则算法和Apriori算法进行比较,提出的算法可以直接查找频繁项集并对数据库进行扫描,当产生频繁项集比较多或者数据库需要进行动态更新时,该算法具有较好的可行性和执行效率。实验表明,提出的矩阵排序索引算法很好地降低了内存的使用率和I/O的开销,提高了数据挖掘的效率且具有较好的可扩展性。     

一种基于BUC的水平加权关联规则挖掘算法

关联规则挖掘可以从大量数据中发现项集间潜在而有趣的相互联系。针对用户对每个项目感兴趣的程度不同,一些学者提出了水平加权关联规则。然而每次生成新候选集后对整个数据库事物的扫描成为算法效率的一大瓶颈。为进一步提高加权关联规则的挖掘效率,在原有的水平加权关联规则算法的基础上,采取了深度优先的策略,提出了一种基于BUC的水平加权关联规则挖掘算法——BUc—MINWAL。改进算法可以大大减少对数据库的扫描范围。实验结果表明,改进的算法有更好的执行效率。     

Incrementally building frequent closed itemset lattice

A concept lattice is an ordered structure between concepts. It is particularly effective in mining association rules. However, a concept lattice is not efficient for large databases because the lattice size increases with the number of transactions. Finding an efficient strategy for dynamically updating the lattice is an important issue for real-world applications, where new transactions are constantly inserted into databases. To build an efficient storage structure for mining association rules, this study proposes a method for building the initial frequent closed itemset lattice from the original database. The lattice is updated when new transactions are inserted. The number of database rescans over the entire database is reduced in the maintenance process. The proposed algorithm is compared with building a lattice in batch mode to demonstrate the effectiveness of the proposed algorithm.     

基于频繁模式树的负关联规则挖掘算法

典型的正关联规则仅考虑事务中所列举的项目。负关联规则不但要考虑事务中所包含的项目集，还必需考虑事务中所不包含的项目，它包含了非常有价值的信息。然而，对于负关联规则的研究却很少，仅有的几种算法也存在一定的局限性。为此，该文提出了一种基于FP-tree的负关联规则挖掘算法，该算法不但可以发现事务数据库中所有的负关联规则，而且整个过程只需扫描事务数据库两次，算法是有效和可行的。     

Maintaining the discovered high-utility itemsets with transaction modification

Most approaches for discovering frequent itemsets derive association rules from a binary database. Profit, cost, and quantity are not considered in traditional association-rule mining. Utility mining was proposed to measure the utilities of purchase products to derive highutility itemsets (HUIs). Many algorithms have been proposed to efficiently find HUIs from a static database. In real-world applications, transactions are inserted, deleted, or modified in dynamic situations. Existing batch approaches have to re-process the updated database since previously discovered HUIs are not maintained. In this paper, a Fast UPdated (FUP) strategy with utility measure and a maintenance algorithm, called FUP-HUI-MOD, are developed to efficiently maintain and update discovered HUIs. When transactions are modified, the proposed algorithm partitions the transactions before and after the modification into two parts, creating four cases. Each case is maintained using a specific procedure to update the discovered HUIs. Based on the designed FUP-HUI-MOD algorithm, the original database is not required to be rescanned each time compared to the state-of-the-art high-utility itemset mining algorithms in batch mode. Experiments are conducted to show that the proposed algorithm outperforms batch algorithms in maintaining HUIs.     

基于频繁模式树的关联规则增量式更新算法

研究了大型事务数据库中关联规则的增量式更新总是，提出了一种基于频繁模式树的关联规则增量式更新算法，以处理最小支持度或事务数据库发生变化后相应关联规则的更新问题，并对其性能进行了分析。     

约束性相联规则发现方法及算法

文中研究了在大型事务７库中发现有约束条件的相联规则问题,提出了有效实现约束性相联规则发现的两种方法,过滤数据库算法Ｆｉｌｔｅｒｉｎｇ和频繁项集生成算法Ｓｅｐａｒａｔｅ,这两种可以同时并有物方法比已有算法运算效率有显著性提高。     

一种基于矩阵的强关联规则生成算法*

针对Apriori算法扫描数据库的I/O代价和候选项集数目较多等问题,提出一种基于矩阵的强关联规则生成算法,算法通过将事务数据库转化为0-1矩阵后对项集按照支持度计数非递减顺序排列,从而减少候选项集的产生,同时实现置信度的高效计算。通过对实例和大数据量数据库的分析表明,该方法是有效的。     

Efficient algorithms for distortion and blocking techniques in association rule hiding

Data mining provides the opportunity to extract useful information from large databases. Various techniques have been proposed in this context in order to extract this information in the most efficient way. However, efficiency is not our only concern in this study. The security and privacy issues over the extracted knowledge must be seriously considered as well. By taking this into consideration, we study the procedure of hiding sensitive association rules in binary data sets by blocking some data values and we present an algorithm for solving this problem. We also provide a fuzzification of the support and the confidence of an association rule in order to accommodate for the existence of blocked/unknown values. In addition, we quantitatively compare the proposed algorithm with other already published algorithms by running experiments on binary data sets, and we also qualitatively compare the efficiency of the proposed algorithm in hiding association rules. We utilize the notion of border rules, by putting weights in each rule, and we use effective data structures for the representation of the rules so as (a) to minimize the side effects created by the hiding process and (b) to speed up the selection of the victim transactions. Finally, we study the overall security of the modified database, using the C4.5 decision tree algorithm of the WEKA data mining tool, and we discuss the advantages and the limitations of blocking.     

基于项集优化重组的频繁项集发现算法

发现频繁项集是关联规则挖掘的主要途径,也是关联规则挖掘算法研究的重点。关联规则挖掘的经典Apriori算法及其改进算法大致可以归为基于SQL和基于内存两类。为了提高挖掘效率,在仔细分析了基于内存算法存在效率瓶颈的基础上,提出了一种发现频繁项集的改进算法。该算法使用了一种快速产生和验证候选项集的方法,提高了生成项目集的速度。实验结果显示该算法能有效提高挖掘效率。     

Algorithms for computing association rules using a partial-support tree

This paper presents new algorithms for the extraction of association rules from binary databases. Most existing methods operate by generating “candidate” sets, representing combinations of attributes which may be associated, and then testing the database to establish the degree of association. This may involve multiple database passes, and is also likely to encounter problems when dealing with “dense” data due to the increase in the number of sets under consideration. Our method uses a single pass of the database to perform a partial computation of support for all sets encountered in the database, storing this in the form of a set enumeration tree. We describe algorithms for generating this tree and for using it to generate association rules.     

一种基于倒排索引树的增量更新关联挖掘算法

增量更新关联规则挖掘主要解决事务数据库中交易记录不断更新和最小支持度发生变化时关联规则的维护问题。针对目前诸多增量更新关联规则挖掘算法存在效率低、计算成本高、规则难以维护等问题,提出一种基于倒排索引树的增量更新关联挖掘算法。该算法有效地将倒排索引技术与树型结构相结合,使得交易数据库中的数据不断更新和最小支持度随应用环境不同而不断改变时,以实现无需扫描原始交易数据库和不产生候选项集的情况下生成频繁项集。实验结果表明,该算法只需占用较小的存储空间、且检索项集的效率较高,能高效地解决增量更新关联规则难以维护的问题。     

一种更新频繁项目集的快速算法

数据库的更新会引起数据库中的关联规则的更新,找出更新后的所有的频繁项目集,也就能生成更新后的关联规则,因此关联规则的更新就转化为频繁项目集的更新。UWEP算法 利用以前的挖掘结果来减少挖掘新的频繁项目集的开销,采用了一些优化技术来减少数据库的扫描次数和候选项目集的数量,但UWEP算法只能处理增加新事务的情况。本文提出 的UWEP2算法是UWEP算法的扩展,能处理数据库中事务的增加、删除、修改等情况。我们将它与另一种更新频繁项目集的算法FUP2比较,实验显示,UWEP2算法比FUP2算法生成的候选项目集要少,性能要高。     

模糊Horn子句规则挖掘算法研究

模糊关联规则可以用自然语言来表达人类知识,受到数据挖掘与知识发现研究人员的广泛关注。但是,目前大多数模糊关联规则挖掘方法仍然基于经典关联规则的支持度和可信度测度。从模糊蕴涵的观点出发,定义了模糊Horn子句规则、支持度、蕴涵强度以及相关概念,提出了模糊Horn子句规则挖掘算法。该算法可以分解为3个步骤。首先,将定量数据库转换为模糊数据库。其次,挖掘模糊数据库中所有支持度不小于指定最小支持度阂值的频繁项目集。一旦得到了所有频繁项目集,就可以用一种直接的方法生成所有蕴涵强度不小于指定最小蕴涵强度阂值的模糊Horn子句规则。     

An effective mining approach for up-to-date patterns

Mining association rules is most commonly seen among the techniques for knowledge discovery from databases (KDD). It is used to discover relationships among items or itemsets. Furthermore, temporal data mining is concerned with the analysis of temporal data and the discovery of temporal patterns and regularities. In this paper, a new concept of up-to-date patterns is proposed, which is a hybrid of the association rules and temporal mining. An itemset may not be frequent (large) for an entire database but may be large up-to-date since the items seldom occurring early may often occur lately. An up-to-date pattern is thus composed of an itemset and its up-to-date lifetime, in which the user-defined minimum-support threshold must be satisfied. The proposed approach can mine more useful large itemsets than the conventional ones which discover large itemsets valid only for the entire database. Experimental results show that the proposed algorithm is more effective than the traditional ones in discovering such up-to-date temporal patterns especially when the minimum-support threshold is high.