Formal Concept Analysis

In mining and integrating data from multiple sources, there are many privacy and security issues. In several different contexts, the security of the full privacy-preserving data mining protocol depends on the security of the underlying private scalar product protocol. We show that two of the private scalar product protocols, one of which was proposed in a leading data mining conference, are insecure. We then describe a provably private scalar product protocol that is based on homomorphic encryption and improve its efficiency so that it can also be used on massive datasets.

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On private scalar product computation for privacy-preserving data mining

The task of finding correlations between items in a dataset, association mining, has received considerable attention over the last decade. This article presents a survey of association mining fundamentals, detailing the evolution of association mining algorithms from the seminal to the state-of-the-art. This survey focuses on the fundamental principles of association mining, that is, itemset identification, rule generation, and their generic optimizations.

Association mining

Recent studies on frequent itemset mining algorithms resulted in significant performance improvements. However, if the minimal support threshold is set too low, or the data is highly correlated, the number of frequent itemsets itself can be prohibitively large. To overcome this problem, recently several proposals have been made to construct a concise representation of the frequent itemsets, instead of mining all frequent itemsets. The main goal of this paper is to identify redundancies in the set of all frequent itemsets and to exploit these redundancies in order to reduce the result of a mining operation. We present deduction rules to derive tight bounds on the support of candidate itemsets. We show how the deduction rules allow for constructing a minimal representation for all frequent itemsets. We also present connections between our proposal and recent proposals for concise representations and we give the results of experiments on real-life datasets that show the effectiveness of the deduction rules. In fact, the experiments even show that in many cases, first mining the concise representation, and then creating the frequent itemsets from this representation outperforms existing frequent set mining algorithms.

Mining All Non-Derivable Frequent Itemsets

Frequent itemsets play an essential role in many data mining tasks that try to find interesting patterns from databases, such as association rules, correlations, sequences, episodes, classifiers, clusters and many more of which the mining of association rules is one of the most popular problems. The original motivation for searching association rules came from the need to analyze so called supermarket transaction data, that is, to examine customer behavior in terms of the purchased products. Association rules describe how often items are purchased together. For example, an association rule “beer ⇒ chips (80%)” states that four out of five customers that bought beer also bought chips. Such rules can be useful for decisions concerning product pricing, promotions, store layout and many others. Since their introduction in 1993 by Argawal et al. [3], the frequent itemset and association rule mining problems have received a great deal of attention. Within the past decade, hundreds of research papers have been published presenting new algorithms or improvements on existing algorithms to solve these mining problems more efficiently. In this chapter, we explain the basic frequent itemset and association rule mining problems. We describe the main techniques used to solve these problems and give a comprehensive survey of the most influential algorithms that were proposed during the last decade.

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Survey on Frequent Pattern Mining

Given a large collection of transactions containing items, a basic common data mining problem is to extract the so-called frequent itemsets (i.e., sets of items appearing in at least a given number of transactions). In this paper, we propose a structure called free-sets, from which we can approximate any itemset support (i.e., the number of transactions containing the itemset) and we formalize this notion in the framework of e-adequate representations (H. Mannila and H. Toivonen, 1996. In Proc. of the Second International Conference on Knowledge Discovery and Data Mining (KDD'96), pp. 189–194). We show that frequent free-sets can be efficiently extracted using pruning strategies developed for frequent itemset discovery, and that they can be used to approximate the support of any frequent itemset. Experiments on real dense data sets show a significant reduction of the size of the output when compared with standard frequent itemset extraction. Furthermore, the experiments show that the extraction of frequent free-sets is still possible when the extraction of frequent itemsets becomes intractable, and that the supports of the frequent free-sets can be used to approximate very closely the supports of the frequent itemsets. Finally, we consider the effect of this approximation on association rules (a popular kind of patterns that can be derived from frequent itemsets) and show that the corresponding errors remain very low in practice.

Free-Sets: A Condensed Representation of Boolean Data for the Approximation of Frequency Queries

Given a large collection of transactions containing items, a basic common data mining problem is to extract the so-called frequent itemsets (i.e., set of items appearing in at least a given number of transactions). In this paper, we propose a structure called free-sets, from which we can approximate any itemset support (i.e., the number of transactions containing the itemset) and we formalize this notion in the framework of Ɛ-adequate representation [10]. We show that frequent free-sets can be efficiently extracted using pruning strategies developed for frequent item-set discovery, and that they can be used to approximate the support of any frequent itemset. Experiments run on real dense data sets show a significant reduction of the size of the output when compared with standard frequent itemsets extraction. Furthermore, the experiments show that the extraction of frequent free-sets is still possible when the extraction of frequent itemsets becomes intractable. Finally, we show that the error made when approximating frequent itemset support remains very low in practice.

/pdf/approximation-of-frequency-queris-by-means-of-free-sets-53r24bhzrs.pdf

Approximation of Frequency Queris by Means of Free-Sets

Given a large set of data, a common data mining problem is to extract the frequent patterns occurring in this set. The idea presented in this paper is to extract a condensed representation of the frequent patterns called disjunction-free sets, instead of extracting the whole frequent pattern collection. We show that this condensed representation can be used to regenerate all frequent patterns and their exact frequencies. Moreover, this regeneration can be performed without any access to the original data. Practical experiments show that this representation can be extracted very efficiently even in difficult cases. We compared it with another representation of frequent patterns previously investigated in the literature called frequent closed sets. In nearly all experiments we have run, the disjunction-free sets have been extracted much more efficiently than frequent closed sets.

A condensed representation to find frequent patterns

Frequent set discovery from binary data is an important problem in data mining. It concerns the discovery of a concise representation of large tables from which descriptive rules can be derived, e.g., the popular association rules. Our work concerns the study of two representations, namely frequent sets and frequent closures. N. Pasquier and colleagues designed the close algorithm that provides frequent sets via the discovery of frequent closures. When one mines highly correlated data, apriori-based algorithms clearly fail while close remains tractable. We discuss our implementation of close and the experimental evidence we got from two real-life binary data mining processes. Then, we introduce the concept of almost-closure (generation of every frequent set from frequent almost-closures remains possible but with a bounded error on frequency). To the best of our knowledge, this is a new concept and, here again, we provide some experimental evidence of its add-value.

Artur Bykowski

Papers

Free-Sets: A Condensed Representation of Boolean Data for the Approximation of Frequency Queries

Approximation of Frequency Queris by Means of Free-Sets

A condensed representation to find frequent patterns

Frequent Closures as a Concise Representation for Binary Data Mining

DBC: a condensed representation of frequent patterns for efficient mining