Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential pattern mining that rely on a multi-valued decision diagram representation of the database. Specifically, our representation can accommodate multiple item attributes and various constraint types, including a number of non-monotone constraints. To evaluate the applicability of our approach, we develop an MDD-based prefix-projection algorithm and compare its performance against a typical generate-and-check variant, as well as a state-of-the-art constraint-based sequential pattern mining algorithm. Results show that our approach is competitive with or superior to these other methods in terms of scalability and efficiency.
Research in CSPM has primarily focused on exploiting special properties of constraints, such as monotonicity or anti-monotonicity, to guarantee the feasibility of pattern extensions in the mining algorithm @cite_6 @cite_28 @cite_10 @cite_26 @cite_21 @cite_0 @cite_4 @cite_15 @cite_8 . Constraint types that do not possess such properties remain a challenge for CSPM algorithms, although some of these have been successfully incorporated in more general item-set mining on databases where events have no specific order @cite_18 @cite_1 @cite_5 @cite_12 @cite_2 , as well as in CSPM when items and attributes are interchangeable @cite_0 .
@cite_18 @cite_26 @cite_4 @cite_8 @cite_28 @cite_21 @cite_1 @cite_6 @cite_0 @cite_2 @cite_5 @cite_15 @cite_10 @cite_12
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From the standpoint of supporting human-centered discovery of knowledge, the present-day model of mining association rules suffers from the following serious shortcomings: (i) lack of user exploration and control, (ii) lack of focus, and (iii) rigid notion of relationships. In effect, this model functions as a black-box, admitting little user interaction in between. We propose, in this paper, an architecture that opens up the black-box, and supports constraint-based, human-centered exploratory mining of associations. The foundation of this architecture is a rich set of constraint constructs, including domain, class, and SQL-style aggregate constraints, which enable users to clearly specify what associations are to be mined. We propose constrained association queries as a means of specifying the constraints to be satisfied by the antecedent and consequent of a mined association. In this paper, we mainly focus on the technical challenges in guaranteeing a level of performance that is commensurate with the selectivities of the constraints in an association query. To this end, we introduce and analyze two properties of constraints that are critical to pruning: anti-monotonicity and succinctness . We then develop characterizations of various constraints into four categories, according to these properties. Finally, we describe a mining algorithm called CAP, which achieves a maximized degree of pruning for all categories of constraints. Experimental results indicate that CAP can run much faster, in some cases as much as 80 times, than several basic algorithms. This demonstrates how important the succinctness and anti-monotonicity properties are, in delivering the performance guarantee. Sequential pattern mining (SPM) under gap constraint is a challenging task. Many efficient specialized methods have been developed but they are all suffering from a lack of genericity. The Constraint Programming (CP) approaches are not so effective because of the size of their encodings. In[7], we have proposed the global constraint Prefix-Projection for SPM which remedies to this drawback. However, this global constraint cannot be directly extended to support gap constraint. In this paper, we propose the global constraint GAP-SEQ enabling to handle SPM with or without gap constraint. GAP-SEQ relies on the principle of right pattern extensions. Experiments show that our approach clearly outperforms both CP approaches and the state-of-the-art cSpade method on large datasets. A lot of works address the mining of patterns under constraints. The search space is reduced by taking advantage of pruning conditions on patterns, typically by using anti-monotone and monotone properties. In this paper, we introduce two virtual patterns in order to automatically deduce pruning conditions from any constraint coming from the primitive-based framework which gathers a large set of varied constraints. These virtual patterns enable us to provide negative and positive pruning conditions according to the generalization and the specialization of patterns. We show that these pruning conditions are monotone or anti-monotone and can be pushed into usual constraint mining algorithms. Experiments carried on several contexts show that our proposals improve the mining. Currently, there is tremendous interest in providing ad-hoc mining capabilities in database management systems. As a first step towards this goal, in [15] we proposed an architecture for supporting constraint-based, human-centered, exploratory mining of various kinds of rules including associations, introduced the notion of constrained frequent set queries (CFQs), and developed effective pruning optimizations for CFQs with 1-variable (1-var) constraints. While 1-var constraints are useful for constraining the antecedent and consequent separately, many natural examples of CFQs illustrate the need for constraining the antecedent and consequent jointly, for which 2-variable (2-var) constraints are indispensable. Developing pruning optimizations for CFQs with 2-var constraints is the subject of this paper. But this is a difficult problem because: (i) in 2-var constraints, both variables keep changing and, unlike 1-var constraints, there is no fixed target for pruning; (ii) as we show, “conventional” monotonicity-based optimization techniques do not apply effectively to 2-var constraints. The contributions are as follows. (1) We introduce a notion of quasi-succinctness , which allows a quasi-succinct 2-var constraint to be reduced to two succinct 1-var constraints for pruning. (2) We characterize the class of 2-var constraints that are quasi-succinct. (3) We develop heuristic techniques for non-quasi-succinct constraints. Experimental results show the effectiveness of all our techniques. (4) We propose a query optimizer for CFQs and show that for a large class of constraints, the computation strategy generated by the optimizer is ccc-optimal , i.e., minimizing the effort incurred w.r.t. constraint checking and support counting. Sequential pattern mining (SPM) is an important data mining problem with broad applications. SPM is a hard problem due to the huge number of intermediate subsequences to be considered. State of the art approaches for SPM (e.g., PrefixSpan 2001) are largely based on the pattern-growth approach, where for each frequent prefix subsequence, only its related suffix subsequences need to be considered, and the database is recursively projected into smaller ones. Many authors have promoted the use of constraints to focus on the most promising patterns according to the interests of the end user. The top-k SPM problem is also used to cope with the difficulty of thresholding and to control the number of solutions. State of the art methods developed for SPM and top-k SPM, though efficient, are locked into a rather rigid search strategy, and suffer from the lack of declarativity and flexibility. Indeed, adding new constraints usually amounts to changing the data-structures used in the core of the algorithm, and combining these new constraints often require new developments. Recent works (e.g. 2014; Negrevergne and Guns 2015) have investigated the use of Constraint Programming (CP) for SPM. However, despite their nice declarative aspects, all these modelings have scaling problems, due to the huge size of their constraint networks. To address this issue, we propose the Prefix-Projection global constraint, which encapsulates both the subsequence relation as well as the frequency constraint. Its filtering algorithm relies on the principle of projected databases which allows to keep in the variables domain, only values leading to a frequent pattern in the database. Prefix-Projection filtering algorithm enforces domain consistency on the variable succeeding the current frequent prefix in polynomial time. This global constraint also allows for a straightforward implementation of additional constraints such as size, item membership, regular expressions and any combination of them. Experimental results show that our approach clearly outperforms existing CP approaches and competes well with the state-of-the-art methods on large datasets for mining frequent sequential patterns, sequential patterns under various constraints, and top-k sequential patterns. Unlike existing CP methods, our approach achieves a better scalability. We consider the problem of makespan minimization on m unrelated machines in the context of algorithmic mechanism design, where the machines are the strategic players. This is a multidimensional scheduling domain, and the only known positive results for makespan minimization in such a domain are O(m)-approximation truthful mechanisms [22, 20]. We study a well-motivated special case of this problem, where the processing time of a job on each machine may either be "low" or "high", and the low and high values are public and job-dependent. This preserves the multidimensionality of the domain, and generalizes the restricted-machines (i.e., pj,∞ ) setting in scheduling. We give a general technique to convert any c-approximation algorithm to a 3c-approximation truthful-in-expectation mechanism. This is one of the few known results that shows how to export approximation algorithms for a multidimensional problem into truthful mechanisms in a black-box fashion. When the low and high values are the same for all jobs, we devise a deterministic 2-approximation truthful mechanism. These are the first truthful mechanisms with non-trivial performance guarantees for a multidimensional scheduling domain. Our constructions are novel in two respects. First, we do not utilize or rely on explicit price definitions to prove truthfulness; instead we design algorithms that satisfy cycle monotonicity. Cycle monotonicity [23] is a necessary and sufficient condition for truthfulness, is a generalization of value monotonicity for multidimensional domains. However, whereas value monotonicity has been used extensively and successfully to design truthful mechanisms in single-dimensional domains, ours is the first work that leverages cycle monotonicity in the multidimensional setting. Second, our randomized mechanisms are obtained by first constructing a fractional truthful mechanism for a fractional relaxation of the problem, and then converting it into a truthful-in-expectation mechanism. This builds upon a technique of [16], and shows the usefulness of fractional mechanisms in truthful mechanism design. Sequential pattern mining is advantageous for several applications. For example, it finds out the sequential purchasing behavior of majority customers from a large number of customer transactions. However, the existing researches in the field of discovering sequential patterns are based on the concept of frequency and presume that the customer purchasing behavior sequences do not fluctuate with change in time, purchasing cost and other parameters. To acclimate the sequential patterns to these changes, constraint are integrated with the traditional sequential pattern mining approach. It is possible to discover more user)centered patterns by integrating certain constraints with the sequential mining process. Thus in this paper, monetary and compactness constraints in addition to frequency and length are included in the sequential mining process for discovering pertinent sequential patterns from sequential databases. Also, a CFML)PrefixSpan algorithm is proposed by integrating these constraints with the original PrefixSpan algorithm, which allows discovering all CFML sequential patterns from the sequential database. The proposed CFML)PrefixSpan algorithm has been validated on synthetic sequential databases. The experimental results ensure that the efficacy of the sequential pattern mining process is further enhanced in view of the fact that the purchasing cost, time duration and length are integrated with the sequential pattern mining process. Recent work has highlighted the importance of the constraint based mining paradigm in the context of frequent itemsets, associations, correlations, sequential patterns, and many other interesting patterns in large databases. The authors study constraints which cannot be handled with existing theory and techniques. For example, avg(S) spl theta spl nu , median(S) spl theta spl nu , sum(S) spl theta spl nu (S can contain items of arbitrary values) ( spl theta spl isin spl ges , spl les ), are customarily regarded as "tough" constraints in that they cannot be pushed inside an algorithm such as a priori. We develop a notion of convertible constraints and systematically analyze, classify, and characterize this class. We also develop techniques which enable them to be readily pushed deep inside the recently developed FP-growth algorithm for frequent itemset mining. Results from our detailed experiments show the effectiveness of the techniques developed. Constraint-based pattern discovery is at the core of numerous data mining tasks. Patterns are extracted with respect to a given set of constraints (frequency, closedness, size, etc). In the context of sequential pattern mining, a large number of devoted techniques have been developed for solving particular classes of constraints. The aim of this paper is to investigate the use of Constraint Programming (CP) to model and mine sequential patterns in a sequence database. Our CP approach offers a natural way to simultaneously combine in a same framework a large set of constraints coming from various origins. Experiments show the feasibility and the interest of our approach. Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel subsequence interleaving model based on a probabilistic model of the sequence database, which allows us to search for the most compressing set of patterns without designing a specific encoding scheme. Our proposed algorithm is able to efficiently mine the most relevant sequential patterns and rank them using an associated measure of interestingness. The efficient inference in our model is a direct result of our use of a structural expectation-maximization framework, in which the expectation-step takes the form of a submodular optimization problem subject to a coverage constraint. We show on both synthetic and real world datasets that our model mines a set of sequential patterns with low spuriousness and redundancy, high interpretability and usefulness in real-world applications. Furthermore, we demonstrate that the quality of the patterns from our approach is comparable to, if not better than, existing state of the art sequential pattern mining algorithms. The application of frequent patterns in classification has demonstrated its power in recent studies. It often adopts a two-step approach: frequent pattern (or classification rule) mining followed by feature selection (or rule ranking). However, this two-step process could be computationally expensive, especially when the problem scale is large or the minimum support is low. It was observed that frequent pattern mining usually produces a huge number of "patterns" that could not only slow down the mining process but also make feature selection hard to complete. In this paper, we propose a direct discriminative pattern mining approach, DDPMine, to tackle the efficiency issue arising from the two-step approach. DDPMine performs a branch-and-bound search for directly mining discriminative patterns without generating the complete pattern set. Instead of selecting best patterns in a batch, we introduce a "feature-centered" mining approach that generates discriminative patterns sequentially on a progressively shrinking FP-tree by incrementally eliminating training instances. The instance elimination effectively reduces the problem size iteratively and expedites the mining process. Empirical results show that DDPMine achieves orders of magnitude speedup without any downgrade of classification accuracy. It outperforms the state-of-the-art associative classification methods in terms of both accuracy and efficiency. Sequential pattern mining is an important problem in data mining. State of the art techniques for mining sequential patterns, such as frequent subsequences, are often based on the pattern-growth approach, which recursively projects conditional databases. Explicitly creating database projections is thought to be a major computational bottleneck, but we will show in this paper that it can be beneficial when the appropriate data structure is used. Our technique uses a canonical directed acyclic graph as the sequence database representation, which can be represented as a binary decision diagram (BDD). In this paper, we introduce a new type of BDD, namely a sequence BDD (SeqBDD), and show how it can be used for efficiently mining frequent subsequences. A novel feature of the SeqBDD is its ability to share results between similar intermediate computations and avoid redundant computation. We perform an experimental study to compare the SeqBDD technique with existing pattern growth techniques, that are based on other data structures such as prefix trees. Our results show that a SeqBDD can be half as large as a prefix tree, especially when many similar sequences exist. In terms of mining time, it can be substantially more efficient when the support is low, the number of patterns is large, or the input sequences are long and highly similar. A well known but incorrect piece of functional programming folklore is that ML expressions can be efficiently typed in polynomial time. In probing the truth of that folklore, various researchers, including Wand, Buneman, Kanellakis, and Mitchell, constructed simple counterexamples consisting of typable ML programs having length n , with principal types having O(2 cn ) distinct type variables and length O(2 2cn ). When the types associated with these ML constructions were represented as directed acyclic graphs, their sizes grew as O(2 cn ). The folklore was even more strongly contradicted by the recent result of Kanellakis and Mitchell that simply deciding whether or not an ML expression is typable is PSPACE-hard. We improve the latter result, showing that deciding ML typability is DEXPTIME-hard. As Kanellakis and Mitchell have shown containment in DEXPTIME, the problem is DEXPTIME-complete. The proof of DEXPTIME-hardness is carried out via a generic reduction: it consists of a very straightforward simulation of any deterministic one-tape Turing machine M with input k running in O ( c |k| ) time by a polynomial-sized ML formula P M,k , such that M accepts k iff P M,k is typable. The simulation of the transition function δ of the Turing Machine is realized uniquely through terms in the lambda calculus without the use of the polymorphic let construct. We use let for two purposes only: to generate an exponential amount of blank tape for the Turing Machine simulation to begin, and to compose an exponential number of applications of the ML formula simulating state transition. It is purely the expressive power of ML polymorphism to succinctly express function composition which results in a proof of DEXPTIME-hardness. We conjecture that lower bounds on deciding typability for extensions to the typed lambda calculus can be regarded precisely in terms of this expressive capacity for succinct function composition. To further understand this lower bound, we relate it to the problem of proving equality of type variables in a system of type equations generated from an ML expression with let-polymorphism. We show that given an oracle for solving this problem, deciding typability would be in PSPACE, as would be the actual computation of the principal type of the expression, were it indeed typable. One of the major problems in pattern mining is the explosion of the number of results. Tight constraints reveal only common knowledge, while loose constraints lead to an explosion in the number of returned patterns. This is caused by large groups of patterns essentially describing the same set of transactions. In this paper we approach this problem using the MDL principle: the best set of patterns is that set that compresses the database best. For this task we introduce the Krimp algorithm. Experimental evaluation shows that typically only hundreds of itemsets are returned; a dramatic reduction, up to seven orders of magnitude, in the number of frequent item sets. These selections, called code tables, are of high quality. This is shown with compression ratios, swap-randomisation, and the accuracies of the code table-based Krimp classifier, all obtained on a wide range of datasets. Further, we extensively evaluate the heuristic choices made in the design of the algorithm.