Reductions for Frequency-Based Data Mining Problems

Studying the computational complexity of problems is one of the - if not the - fundamental questions in computer science. Yet, surprisingly little is known about the computational complexity of many central problems in data mining. In this paper we study frequency-based problems and propose a new type of reduction that allows us to compare the complexities of the maximal frequent pattern mining problems in different domains (e.g. graphs or sequences). Our results extend those of Kimelfeld and Kolaitis [ACM TODS, 2014] to a broader range of data mining problems. Our results show that, by allowing constraints in the pattern space, the complexities of many maximal frequent pattern mining problems collapse. These problems include maximal frequent subgraphs in labelled graphs, maximal frequent itemsets, and maximal frequent subsequences with no repetitions. In addition to theoretical interest, our results might yield more efficient algorithms for the studied problems.Comment: This is an extended version of a paper of the same title to appear in the Proceedings of the 17th IEEE International Conference on Data Mining (ICDM'17

Revisiting Numerical Pattern Mining with Formal Concept Analysis

In this paper, we investigate the problem of mining numerical data in the framework of Formal Concept Analysis. The usual way is to use a scaling procedure --transforming numerical attributes into binary ones-- leading either to a loss of information or of efficiency, in particular w.r.t. the volume of extracted patterns. By contrast, we propose to directly work on numerical data in a more precise and efficient way, and we prove it. For that, the notions of closed patterns, generators and equivalent classes are revisited in the numerical context. Moreover, two original algorithms are proposed and used in an evaluation involving real-world data, showing the predominance of the present approach

Flexible constrained sampling with guarantees for pattern mining

Pattern sampling has been proposed as a potential solution to the infamous pattern explosion. Instead of enumerating all patterns that satisfy the constraints, individual patterns are sampled proportional to a given quality measure. Several sampling algorithms have been proposed, but each of them has its limitations when it comes to 1) flexibility in terms of quality measures and constraints that can be used, and/or 2) guarantees with respect to sampling accuracy. We therefore present Flexics, the first flexible pattern sampler that supports a broad class of quality measures and constraints, while providing strong guarantees regarding sampling accuracy. To achieve this, we leverage the perspective on pattern mining as a constraint satisfaction problem and build upon the latest advances in sampling solutions in SAT as well as existing pattern mining algorithms. Furthermore, the proposed algorithm is applicable to a variety of pattern languages, which allows us to introduce and tackle the novel task of sampling sets of patterns. We introduce and empirically evaluate two variants of Flexics: 1) a generic variant that addresses the well-known itemset sampling task and the novel pattern set sampling task as well as a wide range of expressive constraints within these tasks, and 2) a specialized variant that exploits existing frequent itemset techniques to achieve substantial speed-ups. Experiments show that Flexics is both accurate and efficient, making it a useful tool for pattern-based data exploration.Comment: Accepted for publication in Data Mining & Knowledge Discovery journal (ECML/PKDD 2017 journal track

Testing Interestingness Measures in Practice: A Large-Scale Analysis of Buying Patterns

Understanding customer buying patterns is of great interest to the retail industry and has shown to benefit a wide variety of goals ranging from managing stocks to implementing loyalty programs. Association rule mining is a common technique for extracting correlations such as "people in the South of France buy ros\'e wine" or "customers who buy pat\'e also buy salted butter and sour bread." Unfortunately, sifting through a high number of buying patterns is not useful in practice, because of the predominance of popular products in the top rules. As a result, a number of "interestingness" measures (over 30) have been proposed to rank rules. However, there is no agreement on which measures are more appropriate for retail data. Moreover, since pattern mining algorithms output thousands of association rules for each product, the ability for an analyst to rely on ranking measures to identify the most interesting ones is crucial. In this paper, we develop CAPA (Comparative Analysis of PAtterns), a framework that provides analysts with the ability to compare the outcome of interestingness measures applied to buying patterns in the retail industry. We report on how we used CAPA to compare 34 measures applied to over 1,800 stores of Intermarch\'e, one of the largest food retailers in France

Mining frequent itemsets a perspective from operations research

Many papers on frequent itemsets have been published. Besides somecontests in this field were held. In the majority of the papers the focus ison speed. Ad hoc algorithms and datastructures were introduced. Inthis paper we put most of the algorithms in one framework, usingclassical Operations Research paradigms such as backtracking, depth-first andbreadth-first search, and branch-and-bound. Moreover we presentexperimental results where the different algorithms are implementedunder similar designs.data mining;operation research;Frequent itemsets

Improved Methods for Extracting Frequent Itemsets from Interim-Support Trees

Mining association rules in relational databases is a significant computational task with lots of applications. A fundamental ingredient of this task is the discovery of sets of attributes (itemsets) whose frequency in the data exceeds some threshold value. In previous work [9] we have introduced an approach to this problem which begins by carrying out an efficient partial computation of the necessary totals, storing these interim results in a set-enumeration tree. This work demonstrated that making ∗ Aris Pagourtzis and Dora Souliou were partially supported for this research by “Pythagoras

Using Answer Set Programming for pattern mining

Serial pattern mining consists in extracting the frequent sequential patterns from a unique sequence of itemsets. This paper explores the ability of a declarative language, such as Answer Set Programming (ASP), to solve this issue efficiently. We propose several ASP implementations of the frequent sequential pattern mining task: a non-incremental and an incremental resolution. The results show that the incremental resolution is more efficient than the non-incremental one, but both ASP programs are less efficient than dedicated algorithms. Nonetheless, this approach can be seen as a first step toward a generic framework for sequential pattern mining with constraints.Comment: Intelligence Artificielle Fondamentale (2014

Frequent Itemset Mining for Big Data

Traditional data mining tools, developed to extract actionable knowledge from data, demonstrated to be inadequate to process the huge amount of data produced nowadays. Even the most popular algorithms related to Frequent Itemset Mining, an exploratory data analysis technique used to discover frequent items co-occurrences in a transactional dataset, are inefficient with larger and more complex data. As a consequence, many parallel algorithms have been developed, based on modern frameworks able to leverage distributed computation in commodity clusters of machines (e.g., Apache Hadoop, Apache Spark). However, frequent itemset mining parallelization is far from trivial. The search-space exploration, on which all the techniques are based, is not easily partitionable. Hence, distributed frequent itemset mining is a challenging problem and an interesting research topic. In this context, our main contributions consist in an (i) exhaustive theoretical and experimental analysis of the best-in-class approaches, whose outcomes and open issues motivated (ii) the development of a distributed high-dimensional frequent itemset miner. The dissertation introduces also a data mining framework which takes strongly advantage of distributed frequent itemset mining for the extraction of a specific type of itemsets (iii). The theoretical analysis highlights the challenges related to the distribution and the preliminary partitioning of the frequent itemset mining problem (i.e. the search-space exploration) describing the most adopted distribution strategies. The extensive experimental campaign, instead, compares the expectations related to the algorithmic choices against the actual performances of the algorithms. We run more than 300 experiments in order to evaluate and discuss the performances of the algorithms with respect to different real life use cases and data distributions. The outcomes of the review is that no algorithm is universally superior and performances are heavily skewed by the data distribution. Moreover, we were able to identify a concrete lack as regards frequent pattern extraction within high-dimensional use cases. For this reason, we have developed our own distributed high-dimensional frequent itemset miner based on Apache Hadoop. The algorithm splits the search-space exploration into independent sub-tasks. However, since the exploration strongly benefits of a full-knowledge of the problem, we introduced an interleaving synchronization phase. The result is a trade-off between the benefits of a centralized state and the ones related to the additional computational power due to parallelism. The experimental benchmarks, performed on real-life high-dimensional use cases, show the efficiency of the proposed approach in terms of execution time, load balancing and reliability to memory issues. Finally, the dissertation introduces a data mining framework in which distributed itemset mining is a fundamental component of the processing pipeline. The aim of the framework is the extraction of a new type of itemsets, called misleading generalized itemsets