Constraint-based sequential pattern mining: the pattern-growth methods

Constraints are essential for many sequential pattern mining applications. However, there is no systematic study on constraint-based sequential pattern mining. In this paper, we investigate this issue and point out that the framework developed for constrained frequent-pattern mining does not fit our mission well. An extended framework is developed based on a sequential pattern growth methodology. Our study shows that constraints can be effectively and efficiently pushed deep into the sequential pattern mining under this new framework. Moreover, this framework can be extended to constraint-based structured pattern mining as well. This research is supported in part by NSERC Grant 312194-05, NSF Grants IIS-0308001, IIS-0513678, BDI-0515813 and National Science Foundation of China (NSFC) grants No. 60303008 and 69933010. All opinions, findings, conclusions and recommendations in this paper are those of the authors and do not necessarily reflect the views of the funding agencies.     

From sequential pattern mining to structured pattern mining: A pattern-growth approach

Sequential pattern mining is an important data mining problem with broad applications. However,it is also a challenging problem since the mining may have to generate or examine a combinatorially explosivenumber of intermediate subsequences. Recent studies have developed two major classes of sequential patternmining methods: (1) a candidate generation-and-test approach, represented by (i) GSP, a horizontal format-basedsequential pattern mining method, and (ii) SPADE, a vertical format-based method; and (2) a pattern-growthmethod, represented by PrefixSpan and its further extensions, such as gSpan for mining structured patterns. In this study, we perform a systematic introduction and presentation of the pattern-growth methodologyand study its principles and extensions. We first introduce two interesting pattern-growth algorithms, FreeSpanand PrefixSpan, for efficient sequential pattern mining. Then we introduce gSpan for mining structured patternsusing the same methodology. Their relative performance in l     

Mining sequential patterns from data streams: a centroid approach

In recent years, emerging applications introduced new constraints for data mining methods. These constraints are typical of a new kind of data: the data streams. In data stream processing, memory usage is restricted, new elements are generated continuously and have to be considered in a linear time, no blocking operator can be performed and the data can be examined only once. At this time, only a few methods has been proposed for mining sequential patterns in data streams. We argue that the main reason is the combinatory phenomenon related to sequential pattern mining. In this paper, we propose an algorithm based on sequences alignment for mining approximate sequential patterns in Web usage data streams. To meet the constraint of one scan, a greedy clustering algorithm associated to an alignment method is proposed. We will show that our proposal is able to extract relevant sequences with very low thresholds.     

Mining interval sequential patterns

The main task of mining sequential patterns is to analyze the transaction database of a company in order to find out the priorities of items that most customers take when consuming. In this article, we propose a new method—the ISP Algorithm. With this method, we can find out not only the order of consumer items of each customer, but also offer the periodic interval of consumer items of each customer. Compared with other previous periodic association rules, the difference is that the period the algorithm provides is not the repeated purchases in a regular time, but the possible repurchases within a certain time frame. The algorithm utilizes the transaction time interval of individual customers and that of all the customers to find out when and who will buy goods, and what items of goods they will buy. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 359–373, 2005.     

Mining conjunctive sequential patterns

In this paper we aim at extending the non-derivable condensed representation in frequent itemset mining to sequential pattern mining. We start by showing a negative example: in the context of frequent sequences, the notion of non-derivability is meaningless. Therefore, we extend our focus to the mining of conjunctions of sequences. Besides of being of practical importance, this class of patterns has some nice theoretical properties. Based on a new unexploited theoretical definition of equivalence classes for sequential patterns, we are able to extend the notion of a non-derivable itemset to the sequence domain. We present a new depth-first approach to mine non-derivable conjunctive sequential patterns and show its use in mining association rules for sequences. This approach is based on a well known combinatorial theorem: the Möbius inversion. A performance study using both synthetic and real datasets illustrates the efficiency of our mining algorithm. These new introduced patterns have a high-potential for real-life applications, especially for network monitoring and biomedical fields with the ability to get sequential association rules with all the classical statistical metrics such as confidence, conviction, lift etc.     

Mining hybrid sequential patterns and sequential rules

The problem addressed in this paper is to discover the frequently occurred sequential patterns from databases. Basically, the existing studies on finding sequential patterns can be roughly classified into two main categories. In the first category, the discovered patterns are continuous patterns, where all the elements in the pattern appear in consecutive positions in transactions. The second category is to mine discontinuous patterns, where the adjacent elements in the pattern need not appear consecutively in transactions. Although there are many researches on finding either kind of patterns, no previous researches can find both of them. Neither can they find the discontinuous patterns formed of several continuous sub-patterns. Therefore, we define a new kind of patterns, called hybrid pattern, which is the combination of continuous patterns and discontinuous patterns. In this paper, two algorithms are developed to mine hybrid patterns, where the first algorithm is easy but slow while the second complicated but much faster than the first one. Finally, the simulation result shows that our second algorithm is as fast as the currently best algorithm for mining sequential patterns.     

TSP: Mining top-k closed sequential patterns

Sequential pattern mining has been studied extensively in the data mining community. Most previous studies require the specification of a min_support threshold for mining a complete set of sequential patterns satisfying the threshold. However, in practice, it is difficult for users to provide an appropriate min_support threshold. To overcome this difficulty, we propose an alternative mining task: mining top-k frequent closed sequential patterns of length no less than min_, where k is the desired number of closed sequential patterns to be mined and min_ is the minimal length of each pattern. We mine the set of closed patterns because it is a compact representation of the complete set of frequent patterns. An efficient algorithm, called TSP, is developed for mining such patterns without min_support. Starting at (absolute) min_support=1, the algorithm makes use of the length constraint and the properties of top-k closed sequential patterns to perform dynamic support raising and projected database pruning. Our extensive performance study shows that TSP has high performance. In most cases, it outperforms the efficient closed sequential pattern-mining algorithm, CloSpan, even when the latter is running with the best tuned min_support threshold. Thus, we conclude that, for sequential pattern mining, mining top-k frequent closed sequential patterns without min_support is more preferable than the traditional min_support-based mining.     

Mining non-redundant time-gap sequential patterns

Mining sequential patterns is to discover sequential purchasing behaviors for most of the customers from a large amount of customer transactions. An example of such a pattern is that most of the customers purchased item B after purchasing item A, and then they purchased item C after using item B. The manager can use this information to promote item B and item C when a customer purchased item A and item B, respectively. However, the manager cannot know what time the customers will need these products if we only discover the sequential patterns without any extra information. In this paper, we develop a new algorithm to discover not only the sequential patterns but also the time interval between any two items in the pattern. We call this information the time-gap sequential patterns. An example of time-gap sequential pattern is that most of the customers purchased item A, and then they bought item B after m to n days, and then after p to q days, they bought item C. When a customer bought item A, the information about item B can be sent to this customer after m to n days, that is, we can provide the product information in which the customer is interested on the appropriate date.     

去冗余Top-k对比序列模式挖掘

对比序列模式可以用来表征不同类别数据集之间的差异。在生物信息、物流管理、电子商务等领域,对比序列模式有着广泛的应用。Top-k对比序列模式挖掘的目标是发现数据集中对比度最高的前k个序列模式。在Top-k对比序列模式挖掘中,可能挖掘出冗余的序列模式。目前,虽然有Top-k对比序列模式发现算法被提出,但这些算法并未考虑冗余序列模式的问题。为此,本文提出了基于广度优先生成树的去冗余Top-k对比序列模式挖掘算法BFM（breadth-first miner）。使用BFM算法可以有效地解决冗余问题,得到去冗余的Top-k对比序列模式。在BFM算法的基础上,提出了性能更好的算法PBFM（pruning breadth-first miner）。通过在真实数据集上的实验分析与对比 ,验证了本文算法的有效性。     

带数据项约束的序列模式挖掘

传统的数据挖掘方法会生成大量的模式和规则,且难以理解,而实际上用户感兴趣的只是其中的一小部分.针对该问题,在挖掘序列模式的PrefixSpan算法基础上提出一种带数据项约束的序列模式挖掘方法,通过数据项约束,减少了搜索空间.实验结果表明,该方法可以有效地挖掘出满足数据项约束的序列模式.     

Mining sequential patterns with itemset constraints

Mining sequential patterns is used to discover all the frequent sequences in a sequence database. However, the mining may return a huge number of patterns, while the users are only interested in a particular subset of these. In this paper, we consider the problem of mining sequential patterns with itemset constraints. In order to solve this problem, we propose a new algorithm named MSPIC-DBV, which is a pattern-growth algorithm that uses prefixes and dynamic bit vectors. This algorithm prunes the search space at the beginning and during the mining process. Moreover, it reduces the number of candidates that need to be checked. The experimental results show that the proposed algorithm outperforms the previous methods.     

Mining sequential patterns from probabilistic databases

Knowledge and Information Systems - This paper considers the problem of sequential pattern mining (SPM) in probabilistic databases. Specifically, we consider SPM in situations where there is...     

Mining interesting sequential patterns for intelligent systems

Mining sequential patterns means to discover sequential purchasing behaviors of most customers from a large number of customer transactions. Past transaction data can be analyzed to discover customer purchasing behaviors such that the quality of business decisions can be improved. However, the size of the transaction database can be very large. It is very time consuming to find all the sequential patterns from a large database, and users may be only interested in some sequential patterns. Moreover, the criteria of the discovered sequential patterns for user requirements may not be the same. Many uninteresting sequential patterns for user requirements can be generated when traditional mining methods are applied. Hence, a data mining language needs to be provided such that users can query only knowledge of interest to them from a large database of customer transactions. In this article, a data mining language is presented. From the data mining language, users can specify the items of interest and the criteria of the sequential patterns to be discovered. Also, an efficient data mining technique is proposed to extract the sequential patterns according to the users' requests. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 73–87, 2005.     

Mining sequential patterns from multidimensional sequence data

The problem addressed in This work is to discover the frequently occurred sequential patterns from databases. Although much work has been devoted to this subject, to the best of our knowledge, no previous research was able to find sequential patterns from d-dimensional sequence data, where d>2. Without such a capability, many practical data would be impossible to mine. For example, an online stock-trading site may have a customer database, where each customer may visit a Web site in a series of days; each day takes a series of sessions and each session visits a series of Web pages. Then, the data for each customer forms a 3-dimensional list, where the first dimension is days, the second is sessions, and the third is visited pages. To mine sequential patterns from this kind of sequence data, two efficient algorithms have been developed in This work.     

Mining sequential patterns with periodic wildcard gaps

Mining frequent patterns with periodic wildcard gaps is a critical data mining problem to deal with complex real-world problems. This problem can be described as follows: given a subject sequence, a pre-specified threshold, and a variable gap-length with wildcards between each two consecutive letters. The task is to gain all frequent patterns with periodic wildcard gaps. State-of-the-art mining algorithms which use matrices or other linear data structures to solve the problem not only consume a large amount of memory but also run slowly. In this study, we use an Incomplete Nettree structure (the last layer of a Nettree which is an extension of a tree) of a sub-pattern P to efficiently create Incomplete Nettrees of all its super-patterns with prefix pattern P and compute the numbers of their supports in a one-way scan. We propose two new algorithms, MAPB (Mining sequentiAl Pattern using incomplete Nettree with Breadth first search) and MAPD (Mining sequentiAl Pattern using incomplete Nettree with Depth first search), to solve the problem effectively with low memory requirements. Furthermore, we design a heuristic algorithm MAPBOK (MAPB for tOp-K) based on MAPB to deal with the Top-K frequent patterns for each length. Experimental results on real-world biological data demonstrate the superiority of the proposed algorithms in running time and space consumption and also show that the pattern matching approach can be employed to mine special frequent patterns effectively.     

带有间隔约束的多序列模式挖掘

研究这样一个问题：给定多序列、支持度阈值和间隔约束,从多序列中挖掘所有出现次数不小于支持度阈值的频繁序列模式,这里要求模式中任意两个相邻元素在序列中的出现都要满足用户自定义的间隔约束,并且模式在序列中的出现要满足one-off条件。在解决该问题上,已有算法M-OneOffMine在计算模式的支持度时,只考虑模式的每个字符在序列中的首次出现,导致计算的模式支持度远小于其真实支持度,以致许多频繁的模式没有被挖掘出来。为此,设计了一个有效的带有间隔约束的多序列模式挖掘算法--MMSP算法：首先,通过采用二维表保存模式的候选位置;然后,根据候选位置采用最左最优的思想选择匹配位置。通过生物DNA序列进行实验,多序列中元素序列数目不变而序列长度变化时,MMSP挖掘出的频繁模式总数是同类算法M-OneOffMine的3.23倍;在元素序列个数变化时,MMSP挖掘出的频繁模式个数平均是M-OneOffMine的4.11倍;这两种情况下MMSP都有更好的时间性能。在模式长度变化时,MMSP挖掘出的频繁模式个数分别平均是M-OneOffMine的2.21倍和MPP的5.24倍。同时还验证了M-OneOffMine挖掘到的模式是MMSP挖掘到的频繁的子集。实验结果表明,MMSP算法不仅可以挖掘到更多的频繁模式,而且时间花费更少,更适合于实际的应用。     

Mining sequential patterns across multiple sequence databases

In this paper, given a set of sequence databases across multiple domains, we aim at mining multi-domain sequential patterns, where a multi-domain sequential pattern is a sequence of events whose occurrence time is within a pre-defined time window. We first propose algorithm Naive in which multiple sequence databases are joined as one sequence database for utilizing traditional sequential pattern mining algorithms (e.g., PrefixSpan). Due to the nature of join operations, algorithm Naive is costly and is developed for comparison purposes. Thus, we propose two algorithms without any join operations for mining multi-domain sequential patterns. Explicitly, algorithm IndividualMine derives sequential patterns in each domain and then iteratively combines sequential patterns among sequence databases of multiple domains to derive candidate multi-domain sequential patterns. However, not all sequential patterns mined in the sequence database of each domain are able to form multi-domain sequential patterns. To avoid the mining cost incurred in algorithm IndividualMine, algorithm PropagatedMine is developed. Algorithm PropagatedMine first performs one sequential pattern mining from one sequence database. In light of sequential patterns mined, algorithm PropagatedMine propagates sequential patterns mined to other sequence databases. Furthermore, sequential patterns mined are represented as a lattice structure for further reducing the number of sequential patterns to be propagated. In addition, we develop some mechanisms to allow some empty sets in multi-domain sequential patterns. Performance of the proposed algorithms is comparatively analyzed and sensitivity analysis is conducted. Experimental results show that by exploring propagation and lattice structures, algorithm PropagatedMine outperforms algorithm IndividualMine in terms of efficiency (i.e., the execution time).     

Mining sequential patterns with regular expression constraints

Discovering sequential patterns is an important problem in data mining with a host of application domains including medicine, telecommunications, and the World Wide Web. Conventional sequential pattern mining systems provide users with only a very restricted mechanism (based on minimum support) for specifying patterns of interest. As a consequence, the pattern mining process is typically characterized by lack of focus and users often end up paying inordinate computational costs just to be inundated with an overwhelming number of useless results. We propose the use of Regular Expressions (REs) as a flexible constraint specification tool that enables user-controlled focus to be incorporated into the pattern mining process. We develop a family of novel algorithms (termed SPIRIT-Sequential Pattern mining with Regular expression consTraints) for mining frequent sequential patterns that also satisfy user-specified RE constraints. The main distinguishing factor among the proposed schemes is the degree to which the RE constraints are enforced to prune the search space of patterns during computation. Our solutions provide valuable insights into the trade-offs that arise when constraints that do not subscribe to nice properties (like anti monotonicity) are integrated into the mining process     

Mining fuzzy sequential patterns from quantitative transactions

Many researchers in database and machine learning fields are primarily interested in data mining because it offers opportunities to discover useful information and important relevant patterns in large databases. Most previous studies have shown how binary valued transaction data may be handled. Transaction data in real-world applications usually consist of quantitative values, so designing a sophisticated data-mining algorithm able to deal with various types of data presents a challenge to workers in this research field. In the past, we proposed a fuzzy data-mining algorithm to find association rules. Since sequential patterns are also very important for real-world applications, this paper thus focuses on finding fuzzy sequential patterns from quantitative data. A new mining algorithm is proposed, which integrates the fuzzy-set concepts and the AprioriAll algorithm. It first transforms quantitative values in transactions into linguistic terms, then filters them to find sequential patterns by modifying the AprioriAll mining algorithm. Each quantitative item uses only the linguistic term with the maximum cardinality in later mining processes, thus making the number of fuzzy regions to be processed the same as the number of the original items. The patterns mined out thus exhibit the sequential quantitative regularity in databases and can be used to provide some suggestions to appropriate supervisors.