CFP-tree: A compact disk-based structure for storing and querying frequent itemsets

Frequent itemset mining is an important problem in the data mining area with a wide range of applications. Many decision support systems need to support online interactive frequent itemset mining, which is a challenging task because frequent itemset mining is a computation intensive repetitive process. One solution is to precompute frequent itemsets. In this paper, we propose a compact disk-based data structure—CFP-tree to store precomputed frequent itemsets on a disk to support online mining requests. The CFP-tree structure effectively utilizes the redundancy in frequent itemsets to save space. The compressing ratio of a CFP-tree can be as high as several thousands or even higher. Efficient algorithms for retrieving frequent itemsets from a CFP-tree, as well as efficient algorithms to construct and maintain a CFP-tree, are developed. Our performance study demonstrates that with a CFP-tree, frequent itemset mining requests can be responded to promptly.     

基于DiffNodeset结构的最大频繁项集挖掘算法

在数据挖掘中,通过挖掘最大频繁项集来代替挖掘频繁项集可以大大地提升系统的运行效率。针对现有的最大频繁项集挖掘算法的运行时间消耗仍然很大的问题,提出了一种基于DiffNodeset结构的最大频繁项集挖掘（DNMFIM）算法。首先,采用了一种新的数据结构DiffNodeset来实现求交集以及支持度的快速计算;其次,引入一种新的线性复杂度的连接方法来降低两个DiffNodeset在连接过程中的复杂度,避免了多次的无效计算;然后,将集合枚举树作为搜索空间,同时采用多种优化剪枝策略来缩小搜索空间;最后,再结合最大频繁项集挖掘算法（MAFIA）中所使用的超集检测技术来有效地提高算法的准确性。实验结果表明,DNMFIM算法在时间效率方面性能优于MAFIA与基于N-list的MAFIA（NB-MAFIA）,该算法在不同类型数据集中进行最大频繁项集挖掘时均有良好的效果。     

最大频繁项目集的快速更新

挖掘最大频繁项目集是多种数据挖掘应用中的关键问题．为克服基于Apriori的最大频繁项目集挖掘算法存在的不足,DMFIA采用FP-tree存储结构及自顶向下的搜索策略,有效地提高了最大频繁项目集的挖掘效率．但对于频繁项目多而最大频繁项目集维数相对较小的情况,DMFIA要经过多层搜索且在每一层产生大量的候选项目集,因而影响算法的执行效率．为此,该文提出了DMFIA的改进算法IDMFIA(the Improved algorithm of DMFIA)．IDMFIA采用自顶向下和自底向上双向搜索策略,可尽早修剪掉较短最大频繁项目集的超集和较长最大频繁项目集的子集．另外,该文还提出最大频繁项目集更新算法FUMFIA(Fast Updating Maximum Frequent Itemsets Algorithm),该算法充分利用已建立的FP-tree和已挖掘的最大频繁项目集,可对已挖掘的最大频繁项目集进行高效维护．实验结果表明,IDMFIA和FUMFIA可有效提高最大频繁项目集的挖掘和更新效率．     

Mining itemset utilities from transaction databases

The rationale behind mining frequent itemsets is that only itemsets with high frequency are of interest to users. However, the practical usefulness of frequent itemsets is limited by the significance of the discovered itemsets. A frequent itemset only reflects the statistical correlation between items, and it does not reflect the semantic significance of the items. In this paper, we propose a utility based itemset mining approach to overcome this limitation. The proposed approach permits users to quantify their preferences concerning the usefulness of itemsets using utility values. The usefulness of an itemset is characterized as a utility constraint. That is, an itemset is interesting to the user only if it satisfies a given utility constraint. We show that the pruning strategies used in previous itemset mining approaches cannot be applied to utility constraints. In response, we identify several mathematical properties of utility constraints. Then, two novel pruning strategies are designed. Two algorithms for utility based itemset mining are developed by incorporating these pruning strategies. The algorithms are evaluated by applying them to synthetic and real world databases. Experimental results show that the proposed algorithms are effective on the databases tested.     

频繁项集挖掘的研究进展及主流方法

关联分析作为数据挖掘的主要研究模块之一,主要用于发现隐藏在大型数据集中的强关联特征。而多数关联规则挖掘任务可分为频繁模式(频繁项集、频繁序列、频繁子图)的产生和规则的产生。前者发现数据集中满足最小支持度阈值的项集、序列与子图;后者从上一步发现的频繁模式中提取高置信度的规则。频繁项集挖掘是许多数据挖掘任务中的关键问题,也是关联规则挖掘算法的核心。十几年来,学者们致力于提高频繁项集的生成效率,从不同的角度进行改进以提高算法效率,大量的高效可伸缩性算法被提出。文中对频繁项集挖掘进行深入分析,对完全频繁项集、闭频繁项集、极大频繁项集的典型算法进行介绍和评述,最后对频繁项集挖掘算法的研究方向进行简要分析。     

快速挖掘全局最大频繁项目集

挖掘最大频繁项目集是多种数据挖掘应用中的关键问题.现行可用的最大频繁项目集挖掘算法大多基于单机环境,针对分布式环境下的全局最大频繁项目集挖掘尚不多见.若将基于单机环境的最大频繁项目集挖掘算法运用于分布式环境,或运用分布式环境下的全局频繁项目集挖掘算法来挖掘全局最大频繁项目集,均会产生大量的候选频繁项目集,且网络通信代价高.为此,提出了快速挖掘全局最大频繁项目集算法FMGMFI(fast mining global maximum frequent itemsets),该算法采用FP-tree存储结构,可方便地从各局部FP-tree的相关路径中得到项目集的频度,同时采用自顶向下和自底向上的双向搜索策略,可有效地降低网络通信代价.实验结果表明,FMGMF算法是有效、可行的.     

Meta itemset: a new concise representation of frequent itemset

The sheer size of all frequent itemsets is one challenging problem in data mining research. Based on both closed itemset and maximal itemset, meta itemset which is a new concise representation of frequent itemset is proposed. It is proved that both closed itemset and maximal itemset are special cases of meta itemset. The set of all closed itemsets and the set of all maximal itemsets form the upper bound and the lower bound of the set of all meta itemsets. Then, property and pruning strategies of meta itemset are discussed. Finally, an efficient algorithm for mining meta itemset is proposed. Experimental results show that the proposed algorithm is effective and efficient.     

Non-derivable itemset mining

All frequent itemset mining algorithms rely heavily on the monotonicity principle for pruning. This principle allows for excluding candidate itemsets from the expensive counting phase. In this paper, we present sound and complete deduction rules to derive bounds on the support of an itemset. Based on these deduction rules, we construct a condensed representation of all frequent itemsets, by removing those itemsets for which the support can be derived, resulting in the so called Non-Derivable Itemsets (NDI) representation. We also present connections between our proposal and recent other proposals for condensed representations of frequent itemsets. Experiments on real-life datasets show the effectiveness of the NDI representation, making the search for frequent non-derivable itemsets a useful and tractable alternative to mining all frequent itemsets.     

MAXFP-M iner: 利用FP- tree 快速挖掘最大频繁项集

为提高频繁项集的挖掘效率，提出了最大频繁项集树的概念和基于FP-tree的最大频繁项集挖掘算法MAXFP-Miner，首先建立了FP-tree，在此基础上建立最大频繁项集树MAXFP-tree，MAXFP-tree中包含了所有最大频繁项集，缩小了搜索空间，提高了算法的效率，算法分析和实验表明，该算法特别适合于挖掘稠密型及具有长频繁项集的数据集。     

一种支持在线数据挖掘的存储结构

数据挖掘是一个庞大的计算过程,频繁项集挖掘是教据挖掘中很重要的一部分。本文提出一种基于数据挖掘的存储频繁项集结构——BFp-tree,对频繁项集进行预处理,并将其存储在磁盘上,以支持在线挖掘要求。BFp-tree利用共享前缀和后缀的特点节省存储空间,对稠密的数据集压缩效率较高。     

CLS-Miner: efficient and effective closed high-utility itemset mining

High-utility itemset mining (HUIM) is a popular data mining task with applications in numerous domains. However, traditional HUIM algorithms often produce a very large set of high-utility itemsets (HUIs). As a result, analyzing HUIs can be very time consuming for users. Moreover, a large set of HUIs also makes HUIM algorithms less efficient in terms of execution time and memory consumption. To address this problem, closed high-utility itemsets (CHUIs), concise and lossless representations of all HUIs, were proposed recently. Although mining CHUIs is useful and desirable, it remains a computationally expensive task. This is because current algorithms often generate a huge number of candidate itemsets and are unable to prune the search space effectively. In this paper, we address these issues by proposing a novel algorithm called CLS-Miner. The proposed algorithm utilizes the utility-list structure to directly compute the utilities of itemsets without producing candidates. It also introduces three novel strategies to reduce the search space, namely chain-estimated utility co-occurrence pruning, lower branch pruning, and pruning by coverage. Moreover, an effective method for checking whether an itemset is a subset of another itemset is introduced to further reduce the time required for discovering CHUIs. To evaluate the performance of the proposed algorithm and its novel strategies, extensive experiments have been conducted on six benchmark datasets having various characteristics. Results show that the proposed strategies are highly efficient and effective, that the proposed CLS-Miner algorithmoutperforms the current state-ofthe- art CHUD and CHUI-Miner algorithms, and that CLSMiner scales linearly.     

Parallel Algorithms for Discovery of Association Rules

Discovery of association rules is an important data mining task. Several parallel and sequential algorithms have been proposed in the literature to solve this problem. Almost all of these algorithms make repeated passes over the database to determine the set of frequent itemsets (a subset of database items), thus incurring high I/O overhead. In the parallel case, most algorithms perform a sum-reduction at the end of each pass to construct the global counts, also incurring high synchronization cost. In this paper we describe new parallel association mining algorithms. The algorithms use novel itemset clustering techniques to approximate the set of potentially maximal frequent itemsets. Once this set has been identified, the algorithms make use of efficient traversal techniques to generate the frequent itemsets contained in each cluster. We propose two clustering schemes based on equivalence classes and maximal hypergraph cliques, and study two lattice traversal techniques based on bottom-up and hybrid search. We use a vertical database layout to cluster related transactions together. The database is also selectively replicated so that the portion of the database needed for the computation of associations is local to each processor. After the initial set-up phase, the algorithms do not need any further communication or synchronization. The algorithms minimize I/O overheads by scanning the local database portion only twice. Once in the set-up phase, and once when processing the itemset clusters. Unlike previous parallel approaches, the algorithms use simple intersection operations to compute frequent itemsets and do not have to maintain or search complex hash structures. Our experimental testbed is a 32-processor DEC Alpha cluster inter-connected by the Memory Channel network. We present results on the performance of our algorithms on various databases, and compare it against a well known parallel algorithm. The best new algorithm outperforms it by an order of magnitude.     

关联规则中基于降维的最大频繁模式挖掘算法

基于FP-tree的最大频繁模式挖掘算法是目前较为高效的频繁模式挖掘算法,针对这些算法需要递归生成条件FP-tree、产生大量候选最大频繁项集等问题,在分析FPMax、DMFIA算法的基础上,提出基于降维的最大频繁模式挖掘算法(BDRFI)。该算法改传统的FP-tree为数字频繁模式树DFP-tree,提高了超集检验的效率;采用的预测剪枝策略减少了挖掘的次数;基于降低项集维度的挖掘方式,减少了候选项的数目,避免了递归地产生条件频繁模式树,提高了算法的效率。实验结果表明,BDRFI的效率是同类算法的2~8倍。     

Mining itemset utilities from transaction databases

The rationale behind mining frequent itemsets is that only itemsets with high frequency are of interest to users. However, the practical usefulness of frequent itemsets is limited by the significance of the discovered itemsets. A frequent itemset only reflects the statistical correlation between items, and it does not reflect the semantic significance of the items. In this paper, we propose a utility based itemset mining approach to overcome this limitation. The proposed approach permits users to quantify their preferences concerning the usefulness of itemsets using utility values. The usefulness of an itemset is characterized as a utility constraint. That is, an itemset is interesting to the user only if it satisfies a given utility constraint. We show that the pruning strategies used in previous itemset mining approaches cannot be applied to utility constraints. In response, we identify several mathematical properties of utility constraints. Then, two novel pruning strategies are designed. Two algorithms for utility based itemset mining are developed by incorporating these pruning strategies. The algorithms are evaluated by applying them to synthetic and real world databases. Experimental results show that the proposed algorithms are effective on the databases tested.     

海量文本数据库中的高效并行频繁项集挖掘方法

针对大规模文本数据库中频繁项集挖掘的特殊要求,本文提出了一种新的并行挖掘算法parFIM。parFIM以一种简单的数据结构H-Struct为基础,对数据进行纵向划分从而实现并行挖掘。算法同时考虑了去除短模式和减少重复模式。实验结果表明,parFIM能够很好地适用于大规模文本数据库中的频繁项集挖掘任务。     

Mining top-k regular-frequent itemsets using database partitioning and support estimation

Temporal regularity of itemset appearance can be regarded as an important criterion for measuring the interestingness of itemsets in several applications. A frequent itemset can be said to be regular-frequent in a database if it appears at a regular period. Therefore, the problem of mining a complete set of regular-frequent itemsets requires the specification of a support and a regularity threshold. However, in practice, it is often difficult for users to provide an appropriate support threshold. In addition, the use of a support threshold tends to produce a large number of regular-frequent itemsets and it might be better to ask for the number of desired results. We thus propose an efficient algorithm for mining top-k regular-frequent itemsets without setting a support threshold. Based on database partitioning and support estimation techniques, the proposed algorithm also uses a best-first search strategy with only one database scan. We then compare our algorithm with the state-of-the-art algorithms for mining top-k regular-frequent itemsets. Our experimental studies on both synthetic and real data show that our proposal achieves high performance for small and large values of k.     

A new algorithm for fast mining frequent itemsets using N-lists

Mining frequent itemsets has emerged as a fundamental problem in data mining and plays an essential role in many important data mining tasks.In this paper,we propose a novel vertical data representation called N-list,which originates from an FP-tree-like coding prefix tree called PPC-tree that stores crucial information about frequent itemsets.Based on the N-list data structure,we develop an efficient mining algorithm,PrePost,for mining all frequent itemsets.Efficiency of PrePost is achieved by the following three reasons.First,N-list is compact since transactions with common prefixes share the same nodes of the PPC-tree.Second,the counting of itemsets’ supports is transformed into the intersection of N-lists and the complexity of intersecting two N-lists can be reduced to O(m + n) by an efficient strategy,where m and n are the cardinalities of the two N-lists respectively.Third,PrePost can directly find frequent itemsets without generating candidate itemsets in some cases by making use of the single path property of N-list.We have experimentally evaluated PrePost against four state-of-the-art algorithms for mining frequent itemsets on a variety of real and synthetic datasets.The experimental results show that the PrePost algorithm is the fastest in most cases.Even though the algorithm consumes more memory when the datasets are sparse,it is still the fastest one.     

一种新的频繁项集精简表示方法及其挖掘算法的研究

频繁项集挖掘是数据挖掘研究领域的一个基本问题,其瓶颈在于频繁项集全集的结果过多,冗余现象严重.主要的解决思路是只挖掘全体频繁项集中有代表性的子集,使得这种子集或者可满足应用的需要或者可由它们导出其他项集.最大项集和闭项集便是这类解决方案中两种最典型的子集形式.在最大项集和闭项集的基础上,提出了元项集这一新的频繁项集精简表示方法.首先,证明了最大项集和闭项集都是元项集的特例,且元项集所包含的项集数目介于二者之间;其次,讨论了元项集的性质.最后,通过在闭项集挖掘算法DCI-Closed-Index的基础上引入剪枝策略,设计了一个元项集挖掘算法.实验结果表明,所提出的挖掘算法是有效的和高效的.     

Fast mining frequent itemsets using Nodesets

Node-list and N-list, two novel data structure proposed in recent years, have been proven to be very efficient for mining frequent itemsets. The main problem of these structures is that they both need to encode each node of a PPC-tree with pre-order and post-order code. This causes that they are memory-consuming and inconvenient to mine frequent itemsets. In this paper, we propose Nodeset, a more efficient data structure, for mining frequent itemsets. Nodesets require only the pre-order (or post-order code) of each node, which makes it saves half of memory compared with N-lists and Node-lists. Based on Nodesets, we present an efficient algorithm called FIN to mining frequent itemsets. For evaluating the performance of FIN, we have conduct experiments to compare it with PrePost and FP-growth¹, two state-of-the-art algorithms, on a variety of real and synthetic datasets. The experimental results show that FIN is high performance on both running time and memory usage.     

逆向启发式开采最大频繁项目集

关联规则是当前数据挖掘研究的主要领域之一。发现频繁项目集是关联规则数据开采中的关键问题。该文提出了一种基于最夫频繁项目集的逆向开采算法IDMFI（inverse discovery maximum frequent itemsets)，该算法利用频繁项目集的有关特性作为启发信息，采用逆向(即自顶向下)的搜索策略，能够大大减少候选项目集的生成，从而显著地提高了开采效率。