SAT-Based Data Mining

Itemset mining is an important subfield of data mining, which consists of discovering interesting and useful patterns in transaction databases. The traditional task of frequent itemset mining is to discover groups of items (itemsets) that appear frequently together in transactions made by customers. Although itemset mining was designed for market basket analysis, it can be viewed more generally as the task of discovering groups of attribute values frequently cooccurring in databases. Because of its numerous applications in domains such as bioinformatics, text mining, product recommendation, e‐learning, and web click stream analysis, itemset mining has become a popular research area. This study provides an up‐to‐date survey that can serve both as an introduction and as a guide to recent advances and opportunities in the field. The problem of frequent itemset mining and its applications are described. Moreover, main approaches and strategies to solve itemset mining problems are presented, as well as their characteristics are provided. Limitations of traditional frequent itemset mining approaches are also highlighted, and extensions of the task of itemset mining are presented such as high‐utility itemset mining, rare itemset mining, fuzzy itemset mining, and uncertain itemset mining. This study also discusses research opportunities and the relationship to other popular pattern mining problems, such as sequential pattern mining, episode mining, subgraph mining, and association rule mining. Main open‐source libraries of itemset mining implementations are also briefly presented.WIREs Data Mining Knowl Discov2017, 7:e1207. doi: 10.1002/widm.1207This article is categorized under:Algorithmic Development > Association RulesTechnologies > Association Rules

Mining frequent itemsets from transactional datasets is a well known problem. Thus, various methods have been studied to deal with this issue. Recently, original proposals have emerged from the cross-fertilization between data mining and artificial intelligence. In these declarative approaches, the itemset mining problem is modeled either as a constraint network or a propositional formula whose models correspond to the patterns of interest. In this paper, we focus on the propositional satisfiability based itemset mining framework. Our main goal is to enhance the efficiency of SAT model enumeration algorithms. This issue is particularly crucial for the scalability and competitiveness of such declarative itemset mining approaches. In this context, we deeply analyse the effect of the different SAT solver components on the efficiency of the model enumeration problem. Our analysis includes the main components of modern SAT solvers such as restarts, activity based variable ordering heuristics and clauses learning mechanism. Through extensive experiments, we show that these classical components play an essential role in such procedure to improve the performance by pushing forward the efficiency of SAT solvers. More precisely, our experimental evaluation includes a comparative study in enumerating all the models corresponding to the closed frequent itemsets. Additionally, our experimental analysis is extended to include the Top-k itemset mining problem.

Knowledge discovery in databases and data mining aim at semiautomatic tools for the analysis of large data sets. We consider some methods used in data mining, concentrating on levelwise search for all frequently occurring patterns. We show how this technique can be used in various applications. We also discuss possibilities for compiling data mining queries into algorithms, and look at the use of sampling in data mining. We conclude by listing several open research problems in data mining and knowledge discovery.

Assessing the quality of discovered results is an important open problem in data mining. Such assessment is particularly vital when mining itemsets, since commonly many of the discovered patterns can be easily explained by background knowledge. The simplest approach to screen uninteresting patterns is to compare the observed frequency against the independence model. Since the parameters for the independence model are the column margins, we can view such screening as a way of using the column margins as background knowledge. In this paper we study techniques for more flexible approaches for infusing background knowledge. Namely, we show that we can efficiently use additional knowledge such as row margins, lazarus counts, and bounds of ones. We demonstrate that these statistics describe forms of data that occur in practice and have been studied in data mining. To infuse the information efficiently we use a maximum entropy approach. In its general setting, solving a maximum entropy model is infeasible, but we demonstrate that for our setting it can be solved in polynomial time. Experiments show that more sophisticated models fit the data better and that using more information improves the frequency prediction of itemsets.

SufRec, an algorithm for mining association rules: Recursivity and task parallelism

Over the past few decades, numerous optimization-based methods have been proposed for solving the classification problem in data mining. Classic optimization-based methods do not consider attribute interactions toward classification. Thus, a novel learning machine is needed to provide a better understanding on the nature of classification when the interaction among contributions from various attributes cannot be ignored. The interactions can be described by a non-additive measure while the Choquet integral can serve as the mathematical tool to aggregate the values of attributes and the corresponding values of a non-additive measure. As a main part of this research, a new nonlinear classification method with non-additive measures is proposed. Experimental results show that applying non-additive measures on the classic optimization-based models improves the classification robustness and accuracy compared with some popular classification methods. In addition, motivated by well-known Support Vector Machine approach, we transform the primal optimization-based nonlinear classification model with the signed non-additive measure into its dual form by applying Lagrangian optimization theory and Wolfes dual programming theory. As a result, 2n – 1 parameters of the signed non-additive measure can now be approximated with m (number of records) Lagrangian multipliers by applying necessary conditions of the primal classification problem to be optimal. This method of parameter approximation is a breakthrough for solving a non-additive measure practically when there are relatively small number of training cases available (mn－1). Furthermore, the kernel-based learning method engages the nonlinear classifiers to achieve better classification accuracy. The research produces practically deliverable nonlinear models with the non-additive measure for classification problem in data mining when interactions among attributes are considered.

This study is concerned with the Boolean satisfiability (SAT) problem and its solution in setting a hybrid computational intelligence environment of genetic and fuzzy computing. In this framework, fuzzy sets realize an embedding principle meaning that original two-valued (Boolean) functions under investigation are extended to their continuous counterparts resulting in the form of fuzzy (multivalued) functions. In the sequel, the SAT problem is reformulated for the fuzzy functions and solved using a genetic algorithm (GA). It is shown that a GA, especially its recursive version, is an efficient tool for handling multivariable SAT problems. Thorough experiments revealed that the recursive version of the GA can solve SAT problems with more than 1000 variables.

This dissertation is to illustrate the current state of the art of DNA computing achievements, especially of new approaches to solve theoretical 3-SAT problems and the hitting-set problem. Beginning with Adleman’s breakthrough which is an molecular algorithm for the solution of a NP-complete, combinatorial problem, the directed Hamiltonian path problem (HPP). Today, many researchers all over the world concentrate on proposing new methods to solve engineering or application problems with a DNA computing approach. Satisfiability problem is given a Boolean formula, and decide if a satisfying truth assignment exists. ( ) ( ) … ( ) ( ) is an example of Boolean formula. k-SAT problem means that each clause has exactly k literals. Not-All-Equal (NAE) 3-SAT problem and One-In-Three (1IN3) 3-SAT problem are both NP-complete problems. In this dissertation, we present molecular solutions to find all true assignments (3-SAT problem) and furthermore find Not-All-Equal (NAE) solutions and One-In-Three (1IN3) solutions in DNA-based Supercomputing. Hitting-set problem assume that there exists a collection C of subsets of a finite set S, and a positive integer K  |S|, and we need to know if there is a subset  S with | |  K such that contains at least one element of each subset in C. In other words, is the subset that intersects every subset in C and is called the hitting-set. In this dissertation, a DNA-based algorithm is proposed to solve the small hitting-set problem. A small hitting-set is a hitting-set with the smallest K value, i.e., the hitting-set with the smallest number of elements. Furthermore, an algorithm is introduced to find the number of ones from 2n combinations and minimum numbers of ones represents the small hitting-set since K is expected to be as small as possible. The complexity of all the presented DNA-based algorithms is also discussed. We describe time complexity and volume complexity of three Algorithms, numbers of test tube used and the longest library strand in solution space of all three Algorithms. Finally, the simulated experiment is applied to verify correctness of the proposed DNA-based algorithm for solving the One-In-Three (1IN3) 3-SAT problem, and simulation of Not-All-Equal (NAE) 3-SAT problem is similar. Also, another simulated experiment is applied to our proposed DNA-based algorithm 6-2, in order to solve the well-known hitting-set problem. This research has been motivated by the benefit and the application of DNA computing and gives new methods to solve two 3-SAT problems and the hitting-set problem which are NP-complete.

With the popularity of the Internet and the development of information technology, hundreds of millions of information and data that are so close to our human kind are recorded. In recent decades, as an interdisciplinary, data science has had a vigorous development. This paper mainly discusses two core problems in data science, that are data analysis and data mining. Beginning with the data analysis based on statistics, this paper discusses and reviews data mining based on traditional machine learning and that based on neural network. Then it discusses the common problems in data mining. Each part summarizes the corresponding application and research. Through the discussion of the basic contents in data analysis and data mining, this paper provides a powerful help for the future research in this field.

Propositional Satisfiability (SAT) is a keystone in the history of computer science. SAT was the first problem shown to be NP-complete in 1971 by Stephen Cook. Having passed more than 40 years from then, SAT is now a lively research field where theory and practice have a natural intermixing. In this talk, we overview the use of SAT in practical domains, where SAT is thought in a broad sense, i.e. including SAT extensions such as Maximum Satisfiability (MaxSAT), Pseudo-Boolean Optimization (PBO) and Quantified Boolean Formulas (QBF).

Advances in methods for solving Boolean satisfiability (SAT) for large problems have motivated recent attempts to recast physical design problems as Boolean SAT problems. One persistent criticism of these approaches is their inability to supply partial solutions, i.e., to satisfy most but not all of the constraints cast in the SAT style. In this paper, we present a formulation for "subset satisfiable" Boolean SAT: we transform a "strict" SAT problem with N constraints into a new, "relaxed" SAT problem which is satisfiable just if not more than k/spl Lt/N of these constraints cannot be satisfied in the original problem. We describe a transformation based on explicit thresholding and counting for the necessary SAT relaxation. Examples from field-programmable gate-array routing show how we can determine efficiently when we can satisfy "almost all" of our geometric constraints.

Quantum annealing device has shown a great potential in solving discrete problems that are theoretically and empirically hard. Boolean Satisfiability (SAT) problem, determining if there is an assignment of variables that satisfies a given Boolean function, is the first proven NP-complete problem widely used in various domains. Here, we present a novel mapping of the SAT problem to the quadratic unconstrained binary optimization problem (QUBO), and further develop a tool flow embedding the proposed QUBO to the architecture of the commercialized quantum computer D-Wave. By leveraging electronic design automation techniques including synthesis, placement and routing, this is not only the first work providing the detail flow that embeds the QUBO, but also a technique scalable for real world applications and some hard SAT problems with over 6000 variables in QUBO. Based on our results, we discuss the challenges in solving SAT using the current generation of annealing device, and explore the problem solving capability of future quantum annealing computers.

Data mining is nontrivial extraction of implicit, previously unknown and potential useful information from the data. For a database with number of records and for a set of classes such that each record belongs to one of the given classes, the problem of classification is to decide the class to which the given record belongs. The classification problem is also to generate a model for each class from given data set. We are going to make use of supervised classification in which we have training dataset of record, and for each record the class to which it belongs is known. There are many approaches to supervised classification. Decision tree is attractive in data mining environment as they represent rules. Rules can readily expressed in natural languages and they can be even mapped o database access languages. Now a days classification based on decision trees is one of the important problems in data mining which has applications in many areas. Now a days database system have become highly distributed, and we are using many paradigms. we consider the problem of inducing decision trees in a large distributed network of highly distributed databases. The classification based on decision tree can be done on the existence of distributed databases in healthcare and in bioinformatics, human computer interaction and by the view that these databases are soon to contain large amounts of data, characterized by its high dimensionality. Current decision tree algorithms would require high communication bandwidth, memory, and they are less efficient and scalability reduces when executed on such large volume of data. So there are some approaches being developed to improve the scalability and even approaches to analyse the data distributed over a network.[keywords: Data mining, Decision tree, decision tree induction, distributed data, classification]

Constraint Programming is becoming competitive for solving certain data-mining problems largely due to the development of global constraints. We introduce the CoverSize constraint for itemset mining problems, a global constraint for counting and constraining the number of transactions covered by the itemset decision variables. We show the relation of this constraint to the well-known table constraint, and our filtering algorithm internally uses the reversible sparse bitset data structure recently proposed for filtering table. Furthermore, we expose the size of the cover as a variable, which opens up new modelling perspectives compared to an existing global constraint for (closed) frequent itemset mining. For example, one can constrain minimum frequency or compare the frequency of an itemset in different datasets as is done in discriminative itemset mining. We demonstrate experimentally on the frequent, closed and discriminative itemset mining problems that the CoverSize constraint with reversible sparse bitsets allows to outperform other CP approaches.

Frequent itemset mining (FIM) is a useful task for discovering frequent co-occurring items. Since its inception, a number of significant FIM algorithms have been developed to speed up mining performances. Unfortunately, for huge dataset, scalability remains an important issue. In this work, we propose a new propositional satisfiability (SAT) parallel approach, called PSATCFIM, to deal with closed frequent itemsets mining problem. It is designed to run on multicore machines and uses a divide and conquer approach to partition the enumeration process. Such partitioning based on guiding paths eliminates computational overlap between cores. Through empirical study, we demonstrate that PSATCFIM can achieve significant performance improvements with respect to the sequential based version.