Survey on Sequential Pattern Mining Algorithms
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paper_title: Data Mining Concepts and Techniques

paper_content:

Understand the need for analyses of large, complex, information-rich data sets. Identify the goals and primary tasks of the data-mining process. Describe the roots of data-mining technology. Recognize the iterative character of a data-mining process and specify its basic steps. Explain the influence of data quality on a data-mining process. Establish the relation between data warehousing and data mining. Data mining is an iterative process within which progress is defined by discovery, through either automatic or manual methods. Data mining is most useful in an exploratory analysis scenario in which there are no predetermined notions about what will constitute an "interesting" outcome. Data mining is the search for new, valuable, and nontrivial information in large volumes of data. It is a cooperative effort of humans and computers. Best results are achieved by balancing the knowledge of human experts in describing problems and goals with the search capabilities of computers. In practice, the two primary goals of data mining tend to be prediction and description. Prediction involves using some variables or fields in the data set to predict unknown or future values of other variables of interest. Description, on the other hand, focuses on finding patterns describing the data that can be interpreted by humans. Therefore, it is possible to put data-mining activities into one of two categories: Predictive data mining, which produces the model of the system described by the given data set, or Descriptive data mining, which produces new, nontrivial information based on the available data set.
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paper_title: Web usage mining for Web site evaluation

paper_content:

An electrical connector having means providing a signal when the connector members are fully interengaged. The signal means includes a pair of contacts in the two connector members which are axially spaced apart a distance greater than that of the power contacts in the two members so that the power contacts will become electrically coupled prior to the signal contacts when the connector members are mated. The signal contacts are preferably fixedly mounted in the connector insulators and conductors are releasably coupled to the rear portions of such contacts.
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paper_title: Modified Web Access Pattern (mWAP) Approach for Sequential Pattern Mining

paper_content:

With the explosive growth of data available on the World Wide Web, discovery and analysis of useful information from the World Wide Web becomes a practical necessity. Web access pattern, which is the sequence of accesses pursued by users frequently, is a kind of interesting and useful knowledge in practice. Sequential Pattern mining is the process of applying data mining techniques to a sequential database for the purposes of discovering the correlation relationships that exist among an ordered list of events. Web access pattern tree (WAP-tree) mining is a sequential pattern mining technique for web log access sequences, which first stores the original web access sequence database on a prefix tree, similar to the frequent pattern tree (FP -tree) for storing non-sequential data. WAP-tree algorithm then, mines the frequent sequences from the WAP -tree by recursively re-constructing intermediate trees, starting with suffix sequences and ending with prefix sequences. An attempt has been made to modify WAP tree approach for improving efficiency. mWAP totally eliminates the need to engage in numerous re - construction of intermediate WAP-trees during mining and considerably reduces execution time.
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paper_title: The PSP Approach for Mining Sequential Patterns

paper_content:

In this paper, we present an approach, called PSP, for mining sequential patterns embedded in a database. Close to the problem of discovering association rules, mining sequential patterns requires handling time constraints. Originally introduced in [3], the issue is addressed by the GSP approach [10]. Our proposal resumes the general principles of GSP but it makes use of a different intermediary data structure which is proved to be more efficient than in GSP.
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paper_title: A new algorithm for gap constrained sequence mining

paper_content:

The sequence mining problem consists in finding frequent sequential patterns in a database of time-stamped events. Several application domains require limiting the maximum temporal gap between events occurring in the input sequences. However pushing down such constraint is critical for most sequence mining algorithms.In this paper we describe CCSM (Cache-based Constrained Sequence Miner), a new level-wise algorithm that overcomes the troubles usually related to this kind of constraints. CCSM adopts an innovative approach based on k-way intersections of idlists to compute the support of candidate sequences. Our k-way intersection method is enhanced by the use of an effective cache that stores intermediate idlists for future reuse. The reuse of intermediate results entails a surprising reduction in the actual number of join operations performed on idlists.CCSM has been experimentally compared with cSPADE, a state of the art algorithm, on several synthetically generated datasets, obtaining better or similar results in most cases.
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paper_title: Incremental Mining of Sequential Patterns in Large Databases

paper_content:

The database used in mining for knowledge discovery is dynamic in nature. Data may be updated and new transactions may be added over time. As a result, the knowledge discovered from such databases is also dynamic. Incremental mining techniques have been developed to speed up the knowledge discovery process by avoiding re-learning of rules from the old data. To maintain the large itemsets against the incoming dataset, we adopt the idea of negative border to help reduce the number of scans over the original database and discover new itemsets in the updated database. A lot of effort in the re-computation of negative border can be saved, and the minimal candidate set of large itemsets and negative border in the updated database can be obtained efficiently. Simulation results have shown that our method runs faster than other incremental mining techniques, especially when the large itemsets in the updated database are significantly different from those in the original database.
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paper_title: Mining sequential patterns

paper_content:

We are given a large database of customer transactions, where each transaction consists of customer-id, transaction time, and the items bought in the transaction. We introduce the problem of mining sequential patterns over such databases. We present three algorithms to solve this problem, and empirically evaluate their performance using synthetic data. Two of the proposed algorithms, AprioriSome and AprioriAll, have comparable performance, albeit AprioriSome performs a little better when the minimum number of customers that must support a sequential pattern is low. Scale-up experiments show that both AprioriSome and AprioriAll scale linearly with the number of customer transactions. They also have excellent scale-up properties with respect to the number of transactions per customer and the number of items in a transaction. >
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paper_title: Interactive sequence discovery by incremental mining

paper_content:

Sequential pattern mining has become a challenging task in data mining due to its complexity. Essentially, the mining algorithms discover all the frequent patterns meeting the user specified minimum support threshold. However, it is very unlikely that the user could obtain the satisfactory patterns in just one query. Usually the user must try various support thresholds to mine the database for the final desirable set of patterns. Consequently, the time-consuming mining process has to be repeated several times. However, current approaches are inadequate for such interactive mining due to the long processing time required for each query. In order to reduce the response time for each query during the interactive process, we propose a knowledge base assisted mining algorithm for interactive sequence discovery. The proposed approach utilizes the knowledge acquired from each mining process, accumulates the counting information to facilitate efficient counting of patterns, and speeds up the whole interactive mining process. Furthermore, the knowledge base makes possible the direct generation of new candidate sets and the concurrent support counting of variable sized candidates. Even for some queries, due to the pattern information already kept in the knowledge base, database access is not required at all. The conducted experiments show that our approach outperforms GSP, a state-of-the-art sequential pattern mining algorithm, by several order of magnitudes for interactive sequence discovery.
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paper_title: Scalable Data Mining for Rules

paper_content:

Data mining is the process of automatic extraction of novel, useful, and understandable patterns in very large databases. High-performance scalable and parallel computing is crucial for ensuring system scalability and inter-activity as datasets grow inexorably in size and complexity. This thesis deals with both the algorithmic and systems aspects of scalable and parallel data mining algorithms applied to massive databases. The algorithmic aspects focus on the design of efficient, scalable, disk-based parallel algorithms for three key rule discovery techniques---association rules, sequence discovery, and decision tree classification. The systems aspects deal with the scalable implementation of these methods on both sequential machines and popular parallel hardware ranging from shared-memory systems (SMP) to hybrid hierarchical clusters of networked SMP workstations. .pp The association and sequence mining algorithms use lattice-theoretic combinatorial properties to decompose the original problem into small independent sub-problems that can be solved in main memory. Using efficient search techniques and simple intersection operations all frequent patterns are enumerated in a few database scans. The parallel algorithms are asynchronous, requiring no communication or synchronization after an initial set-up phase. Furthermore, the algorithms are based on a hierarchical parallelization, utilizing both shared-memory and message-passing primitives. In classification rule mining, we present disk-based parallel algorithms on shared-memory multiprocessors, the first such study. Extensive experiments have been conducted for all three problems, showing immense improvement over previous approaches, with linear scalability in database size.
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paper_title: RuleGrowth: mining sequential rules common to several sequences by pattern-growth

paper_content:

Mining sequential rules from large databases is an important topic in data mining fields with wide applications. Most of the relevant studies focused on finding sequential rules appearing in a single sequence of events and the mining task dealing with multiple sequences were far less explored. In this paper, we present RuleGrowth, a novel algorithm for mining sequential rules common to several sequences. Unlike other algorithms, RuleGrowth uses a pattern-growth approach for discovering sequential rules such that it can be much more efficient and scalable. We present a comparison of RuleGrowth's performance with current algorithms for three public datasets. The experimental results show that RuleGrowth clearly outperforms current algorithms for all three datasets under low support and confidence threshold and has a much better scalability.
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paper_title: An incremental mining algorithm for maintaining sequential patterns using pre-large sequences

paper_content:

Highlights? In this paper, we propose an incremental mining algorithm for maintaining sequential patterns based on the concept of pre-large sequences to reduce the need for rescanning original databases. ? The proposed algorithm does not require rescanning original databases until the accumulative amount of newly added customer sequences exceeds a safety bound, which depends on database size. ? The proposed approach becomes increasingly efficient as databases grow. Mining useful information and helpful knowledge from large databases has evolved into an important research area in recent years. Among the classes of knowledge derived, finding sequential patterns in temporal transaction databases is very important since it can help model customer behavior. In the past, researchers usually assumed databases were static to simplify data-mining problems. In real-world applications, new transactions may be added into databases frequently. Designing an efficient and effective mining algorithm that can maintain sequential patterns as a database grows is thus important. In this paper, we propose a novel incremental mining algorithm for maintaining sequential patterns based on the concept of pre-large sequences to reduce the need for rescanning original databases. Pre-large sequences are defined by a lower support threshold and an upper support threshold that act as gaps to avoid the movements of sequences directly from large to small and vice versa. The proposed algorithm does not require rescanning original databases until the accumulative amount of newly added customer sequences exceeds a safety bound, which depends on database size. Thus, as databases grow larger, the numbers of new transactions allowed before database rescanning is required also grow. The proposed approach thus becomes increasingly efficient as databases grow.
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paper_title: A General Model for Sequential Pattern Mining with a Progressive Database

paper_content:

Although there have been many recent studies on the mining of sequential patterns in a static database and in a database with increasing data, these works, in general, do not fully explore the effect of deleting old data from the sequences in the database. When sequential patterns are generated, the newly arriving patterns may not be identified as frequent sequential patterns due to the existence of old data and sequences. Even worse, the obsolete sequential patterns that are not frequent recently may stay in the reported results. In practice, users are usually more interested in the recent data than the old ones. To capture the dynamic nature of data addition and deletion, we propose a general model of sequential pattern mining with a progressive database while the data in the database may be static, inserted, or deleted. In addition, we present a progressive algorithm Pisa, which stands for progressive mining of sequential patterns, to progressively discover sequential patterns in defined time period of interest (POI). The POI is a sliding window continuously advancing as the time goes by. Pisa utilizes a progressive sequential tree to efficiently maintain the latest data sequences, discover the complete set of up-to-date sequential patterns, and delete obsolete data and patterns accordingly. The height of the sequential pattern tree proposed is bounded by the length of POI, thereby effectively limiting the memory space required by Pisa that is significantly smaller than the memory needed by the alternative method, direct appending (DirApp). Note that the sequential pattern mining with a static database and with an incremental database are special cases of the progressive sequential pattern mining. By changing start time and end time of the POI, Pisa can easily deal with a static database or an incremental database as well. Complexity of algorithms proposed is analyzed. The experimental results show that Pisa not only significantly outperforms the prior methods in execution time by orders of magnitude but also possesses graceful scalability.
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paper_title: Mining sequential patterns by pattern-growth: the PrefixSpan approach

paper_content:

Sequential pattern mining is an important data mining problem with broad applications. However, it is also a difficult problem since the mining may have to generate or examine a combinatorially explosive number of intermediate subsequences. Most of the previously developed sequential pattern mining methods, such as GSP, explore a candidate generation-and-test approach [R. Agrawal et al. (1994)] to reduce the number of candidates to be examined. However, this approach may not be efficient in mining large sequence databases having numerous patterns and/or long patterns. In this paper, we propose a projection-based, sequential pattern-growth approach for efficient mining of sequential patterns. In this approach, a sequence database is recursively projected into a set of smaller projected databases, and sequential patterns are grown in each projected database by exploring only locally frequent fragments. Based on an initial study of the pattern growth-based sequential pattern mining, FreeSpan [J. Han et al. (2000)], we propose a more efficient method, called PSP, which offers ordered growth and reduced projected databases. To further improve the performance, a pseudoprojection technique is developed in PrefixSpan. A comprehensive performance study shows that PrefixSpan, in most cases, outperforms the a priori-based algorithm GSP, FreeSpan, and SPADE [M. Zaki, (2001)] (a sequential pattern mining algorithm that adopts vertical data format), and PrefixSpan integrated with pseudoprojection is the fastest among all the tested algorithms. Furthermore, this mining methodology can be extended to mining sequential patterns with user-specified constraints. The high promise of the pattern-growth approach may lead to its further extension toward efficient mining of other kinds of frequent patterns, such as frequent substructures.
---
paper_title: Mining sequential patterns

paper_content:

We are given a large database of customer transactions, where each transaction consists of customer-id, transaction time, and the items bought in the transaction. We introduce the problem of mining sequential patterns over such databases. We present three algorithms to solve this problem, and empirically evaluate their performance using synthetic data. Two of the proposed algorithms, AprioriSome and AprioriAll, have comparable performance, albeit AprioriSome performs a little better when the minimum number of customers that must support a sequential pattern is low. Scale-up experiments show that both AprioriSome and AprioriAll scale linearly with the number of customer transactions. They also have excellent scale-up properties with respect to the number of transactions per customer and the number of items in a transaction. >
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paper_title: Frequent-subsequence-based prediction of outer membrane proteins

paper_content:

A number of medically important disease-causing bacteria (collectively called Gram-negative bacteria) are noted for the extra "outer" membrane that surrounds their cell. Proteins resident in this membrane (outer membrane proteins, or OMPs) are of primary research interest for antibiotic and vaccine drug design as they are on the surface of the bacteria and so are the most accessible targets to develop new drugs against. With the development of genome sequencing technology and bioinformatics, biologists can now deduce all the proteins that are likely produced in a given bacteria and have attempted to classify where proteins are located in a bacterial cell. However such protein localization programs are currently least accurate when predicting OMPs, and so there is a current need for the development of a better OMP classifier. Data mining research suggests that the use of frequent patterns has good performance in aiding the development of accurate and efficient classification algorithms. In this paper, we present two methods to identify OMPs based on frequent subsequences and test them on all Gram-negative bacterial proteins whose localizations have been determined by biological experiments. One classifier follows an association rule approach, while the other is based on support vector machines (SVMs). We compare the proposed methods with the state-of-the-art methods in the biological domain. The results demonstrate that our methods are better both in terms of accurately identifying OMPs and providing biological insights that increase our understanding of the structures and functions of these important proteins.
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paper_title: SPIRIT: Sequential Pattern Mining with Regular Expression Constraints

paper_content:

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 mining systems provide users with only a very restricted mechanism (based on minimum support) for specifying patterns of interest. In this paper, 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 tradeoffs that arise when constraints that do not subscribe to nice properties (like anti-monotonicity) are integrated into the mining process. A quantitative exploration of these tradeoffs is conducted through an extensive experimental study on synthetic and real-life data sets.
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paper_title: Web usage mining for Web site evaluation

paper_content:

An electrical connector having means providing a signal when the connector members are fully interengaged. The signal means includes a pair of contacts in the two connector members which are axially spaced apart a distance greater than that of the power contacts in the two members so that the power contacts will become electrically coupled prior to the signal contacts when the connector members are mated. The signal contacts are preferably fixedly mounted in the connector insulators and conductors are releasably coupled to the rear portions of such contacts.
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paper_title: PrefixSpan,: mining sequential patterns efficiently by prefix-projected pattern growth

paper_content:

Sequential pattern mining is an important data mining problem with broad applications. It is challenging since one may need to examine a combinatorially explosive number of possible subsequence patterns. Most of the previously developed sequential pattern mining methods follow the methodology of A priori which may substantially reduce the number of combinations to be examined. Howeve6 Apriori still encounters problems when a sequence database is large andor when sequential patterns to be mined are numerous ano we propose a novel sequential pattern mining method, called Prefixspan (i.e., Prefix-projected - Ettern_ mining), which explores prejxprojection in sequential pattern mining. Prefixspan mines the complete set of patterns but greatly reduces the efforts of candidate subsequence generation. Moreover; prefi-projection substantially reduces the size of projected databases and leads to efJicient processing. Our performance study shows that Prefixspan outperforms both the Apriori-based GSP algorithm and another recently proposed method; Frees pan, in mining large sequence data bases.
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paper_title: Constraint-based sequential pattern mining: the pattern-growth methods

paper_content:

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.
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paper_title: Discovering recency, frequency, and monetary (RFM) sequential patterns from customers' purchasing data

paper_content:

In response to the thriving development in electronic commerce (EC), many on-line retailers have developed Web-based information systems to handle enormous amounts of transactions on the Internet. These systems can automatically capture data on the browsing histories and purchasing records of individual customers. This capability has motivated the development of data-mining applications. Sequential pattern mining (SPM) is a useful data-mining method to discover customers' purchasing patterns over time. We incorporate the recency, frequency, and monetary (RFM) concept presented in the marketing literature to define the RFM sequential pattern and develop a novel algorithm for generating all RFM sequential patterns from customers' purchasing data. Using the algorithm, we propose a pattern segmentation framework to generate valuable information on customer purchasing behavior for managerial decision-making. Extensive experiments are carried out, using synthetic datasets and a transactional dataset collected by a retail chain in Taiwan, to evaluate the proposed algorithm and empirically demonstrate the benefits of using RFM sequential patterns in analyzing customers' purchasing data.
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paper_title: Frequent-subsequence-based prediction of outer membrane proteins

paper_content:

A number of medically important disease-causing bacteria (collectively called Gram-negative bacteria) are noted for the extra "outer" membrane that surrounds their cell. Proteins resident in this membrane (outer membrane proteins, or OMPs) are of primary research interest for antibiotic and vaccine drug design as they are on the surface of the bacteria and so are the most accessible targets to develop new drugs against. With the development of genome sequencing technology and bioinformatics, biologists can now deduce all the proteins that are likely produced in a given bacteria and have attempted to classify where proteins are located in a bacterial cell. However such protein localization programs are currently least accurate when predicting OMPs, and so there is a current need for the development of a better OMP classifier. Data mining research suggests that the use of frequent patterns has good performance in aiding the development of accurate and efficient classification algorithms. In this paper, we present two methods to identify OMPs based on frequent subsequences and test them on all Gram-negative bacterial proteins whose localizations have been determined by biological experiments. One classifier follows an association rule approach, while the other is based on support vector machines (SVMs). We compare the proposed methods with the state-of-the-art methods in the biological domain. The results demonstrate that our methods are better both in terms of accurately identifying OMPs and providing biological insights that increase our understanding of the structures and functions of these important proteins.
---
paper_title: PrefixSpan,: mining sequential patterns efficiently by prefix-projected pattern growth

paper_content:

Sequential pattern mining is an important data mining problem with broad applications. It is challenging since one may need to examine a combinatorially explosive number of possible subsequence patterns. Most of the previously developed sequential pattern mining methods follow the methodology of A priori which may substantially reduce the number of combinations to be examined. Howeve6 Apriori still encounters problems when a sequence database is large andor when sequential patterns to be mined are numerous ano we propose a novel sequential pattern mining method, called Prefixspan (i.e., Prefix-projected - Ettern_ mining), which explores prejxprojection in sequential pattern mining. Prefixspan mines the complete set of patterns but greatly reduces the efforts of candidate subsequence generation. Moreover; prefi-projection substantially reduces the size of projected databases and leads to efJicient processing. Our performance study shows that Prefixspan outperforms both the Apriori-based GSP algorithm and another recently proposed method; Frees pan, in mining large sequence data bases.
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paper_title: Discovering time-interval sequential patterns in sequence databases

paper_content:

Abstract Sequential pattern mining, which discovers frequent subsequences as patterns in a sequence database, in an important data-mining problem with broad applications. Although conventional sequential patterns can reveal the order of items, the time between items is not determined; that is, a sequential pattern does not include time intervals between successive items. Accordingly, this work addresses sequential patterns that include time intervals, called time-interval sequential patterns. This work develops two efficient algorithms for mining time-interval sequential patterns. The first algorithm is based on the conventional Apriori algorithm, while the second one is based on the PrefixSpan algorithm. The latter algorithm outperforms the former, not only in computing time but also in scalability with respect to various parameters.
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paper_title: Mining sequential patterns by pattern-growth: the PrefixSpan approach

paper_content:

Sequential pattern mining is an important data mining problem with broad applications. However, it is also a difficult problem since the mining may have to generate or examine a combinatorially explosive number of intermediate subsequences. Most of the previously developed sequential pattern mining methods, such as GSP, explore a candidate generation-and-test approach [R. Agrawal et al. (1994)] to reduce the number of candidates to be examined. However, this approach may not be efficient in mining large sequence databases having numerous patterns and/or long patterns. In this paper, we propose a projection-based, sequential pattern-growth approach for efficient mining of sequential patterns. In this approach, a sequence database is recursively projected into a set of smaller projected databases, and sequential patterns are grown in each projected database by exploring only locally frequent fragments. Based on an initial study of the pattern growth-based sequential pattern mining, FreeSpan [J. Han et al. (2000)], we propose a more efficient method, called PSP, which offers ordered growth and reduced projected databases. To further improve the performance, a pseudoprojection technique is developed in PrefixSpan. A comprehensive performance study shows that PrefixSpan, in most cases, outperforms the a priori-based algorithm GSP, FreeSpan, and SPADE [M. Zaki, (2001)] (a sequential pattern mining algorithm that adopts vertical data format), and PrefixSpan integrated with pseudoprojection is the fastest among all the tested algorithms. Furthermore, this mining methodology can be extended to mining sequential patterns with user-specified constraints. The high promise of the pattern-growth approach may lead to its further extension toward efficient mining of other kinds of frequent patterns, such as frequent substructures.
---
paper_title: Discovering time-interval sequential patterns in sequence databases

paper_content:

Abstract Sequential pattern mining, which discovers frequent subsequences as patterns in a sequence database, in an important data-mining problem with broad applications. Although conventional sequential patterns can reveal the order of items, the time between items is not determined; that is, a sequential pattern does not include time intervals between successive items. Accordingly, this work addresses sequential patterns that include time intervals, called time-interval sequential patterns. This work develops two efficient algorithms for mining time-interval sequential patterns. The first algorithm is based on the conventional Apriori algorithm, while the second one is based on the PrefixSpan algorithm. The latter algorithm outperforms the former, not only in computing time but also in scalability with respect to various parameters.
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Title: Survey on Sequential Pattern Mining Algorithms

Section 1: Introduction
Description 1: In this section, provide an overview of sequential pattern mining, its significance in data mining, and its applications.

Section 2: Literature Review
Description 2: Summarize recent research and developments in constraint-based and incremental mining of sequential patterns along with specific algorithm examples and their contributions.

Section 3: Comparison of Sequential Pattern Mining Algorithms
Description 3: Discuss general concerns in sequential pattern mining, including efficiency and extensions to other time-related patterns, and how various algorithms address these concerns.

Section 4: Apriori-Based Algorithms
Description 4: Detail key features, methodology, and examples of Apriori-based algorithms such as GSP, SPIRIT, SPADE, and SPAM, highlighting their merits and drawbacks.

Section 5: Pattern-Growth Algorithms
Description 5: Explain the principles of pattern-growth methods, highlighting algorithms like PrefixSpan and WAP-MINE, and their performance improvements over Apriori-based methods.

Section 6: Extensions of Sequential Pattern Mining to Other Time-Related Patterns
Description 6: Describe how sequential pattern mining has been extended to consider other time-related patterns and constraints, including specific examples and use cases.

Section 7: Comparative Study of Sequential Pattern Mining Algorithms
Description 7: Provide a comparative analysis of various sequential pattern mining algorithms based on features such as memory usage, time complexity, and scalability.

Section 8: Conclusion
Description 8: Summarize the state of sequential pattern mining, acknowledge advancements, and suggest areas for future research.