Abstract. Solving inductive queries which have to return complete collections of patterns satisfying a given predicate has been studied extensively the last few years. The specific problem of frequent set mining from potentially huge boolean matrices has given rise to tens of efficient solvers. Frequent sets are indeed useful for many data mining tasks, including the popular association rule mining task but also feature construction, association-based classification, clustering, etc. The research in this area has been boosted by the fascinating concept of condensed representations w.r.t. frequency queries. Such representations can be used to support the discovery of every frequent set and its support without looking back at the data. Interestingly, the size of condensed representations can be several orders of magnitude smaller than the size of frequent set collections. Most of the proposals concern exact representations while it is also possible to consider approximated ones, i.e., to trade computational complexity with a bounded approximation on the computed support values. This paper surveys the core concepts used in the recent works on condensed representation for frequent sets. 1

Abstract. Inductive databases (IDBs) have been proposed to afford the problem of knowledge discovery from huge databases. With an IDB the user/analyst performs a set of very different operations on data using a query language, powerful enough to perform all the required elaborations, such as data preprocessing, pattern discovery and pattern postprocessing. We present a synthetic view on important concepts that have been studied within the cInQ European project when considering the pattern domain of itemsets. Mining itemsets has been proved useful not only for association rule mining but also feature construction, classification, clustering, etc. We introduce the concepts of pattern domain, evaluation functions, primitive constraints, inductive queries and solvers for itemsets. We focus on simple high-level definitions that enable to forget about technical details that the interested reader will find, among others, in cInQ publications. 1

Abstract. Closed sets are being successfully applied in the context of compacted data representation for association rule learning. However, their use is mainly descriptive. This paper shows that, when considering labeled data, closed sets can be adapted for prediction and discrimination purposes by conveniently contrasting covering properties on positive and negative examples. We formally justify that these sets characterize the space of relevant combinations of features for discriminating the target class. In practice, identifying relevant/irrelevant combinations of features through closed sets is useful in many applications. Here we apply it to compacting emerging patterns and essential rules and to learn descriptions for subgroup discovery. 1

Abstract. Clustering or bi-clustering techniques have been proved quite useful in many application domains. A weakness of these techniques remains the poor support for grouping characterization. We consider eventually large Boolean data sets which record properties of objects and we assume that a bi-partition is available. We introduce a generic cluster characterization technique which is based on collections of bi-sets (i.e., sets of objects associated to sets of properties) which satisfy some userdefined constraints, and a measure of the accuracy of a given bi-set as a bi-cluster characterization pattern. The method is illustrated on both formal concepts (i.e., “maximal rectangles of true values”) and the new type of δ-bi-sets (i.e., “rectangles of true values with a bounded number of exceptions per column”). The added-value is illustrated on benchmark data and two real data sets which are intrinsically noisy: a medical data about meningitis and Plasmodium falciparum gene expression data. 1

Abstract. Emerging patterns (EPs) are associations of features whose frequencies increase significantly from one class to another. They have been proven useful to build powerful classifiers and to help establishing diagnosis. Because of the huge search space, mining and representing EPs is a hard and complex task for large datasets. Thanks to the use of recent results on condensed representations of frequent closed patterns, we propose here an exact condensed representation of EPs (i.e., all EPs and their growth rates). From this condensed representation, we give a method to provide interesting EPs, in fact those with the highest growth rates. We call strong emerging patterns (SEPs) these EPs. We also highlight a property characterizing the jumping emerging patterns. Experiments quantify the interests of SEPs (smaller number, ability to extract longer and less frequent patterns) and show their usefulness (in collaboration with the Philips company, SEPs successfully enabled to identify the failures of a production chain of silicon plates). These concepts of condensed representation and “strong patterns ” with respect to a measure are generalized to other interestingness measures based on frequencies.

Abstract. Mining patterns under constraints in large data (also called fat data) is an important task to benefit from the multiple uses of the patterns embedded in these data sets. It is a difficult task due to the exponential growth of the search space according to the number of attributes. From such contexts, closed patterns can be extracted by using the properties of the Galois connections. But, from the best of our knowledge, there is no approach to extract interesting patterns like δ-free patterns which are on the core of a lot of relevant rules. In this paper, we propose a new method based on an efficient way to compute the extension of a pattern and a pruning criterion to mine frequent δ-free patterns in large databases. We give an algorithm (FTminer)for the practical use of this method. We show the efficiency of this approach by means of experiments on benchmarks and on gene expression data.

Clustering or co-clustering techniques have been proved useful in many application domains. A weakness of these techniques remains the poor support for grouping characterization. As a result, interpreting clustering results and discovering knowledge from them can be quite hard. We consider potentially large Boolean data sets which record properties of objects and we assume the availability of a bi-partition which has to be characterized by means of a symbolic description. Our generic approach exploits collections of local patterns which satisfy some user-defined constraints in the data, and a measure of the accuracy of a given local pattern as a bi-cluster characterization pattern. We consider local patterns which are bi-sets, i.e., sets of objects associated to sets of properties. Two concrete examples are formal concepts (i.e., associated closed sets) and the so-called δ-bi-sets (i.e., an extension of formal concepts towards faulttolerance). We introduce the idea of characterizing query which can be used by experts to support knowledge discovery from bi-partitions thanks to available local patterns. The added-value is illustrated on benchmark data and three real data sets: a medical data set and two gene expression data sets. 1

Abstract. The large amount of association rules resulting from a KDD process makes the exploitation of the patterns embedded in the database difficult even impossible. In order to address this problem, various interestingness measures were proposed for selecting the most relevant rules. Nevertheless, the choice of an appropriate measure remains a hard task and the use of several measures may lead to conflicting information. In this paper, we propose a unified framework for a set of interestingness measures M and prove that most of the usual objective measures behave in a similar way. In the context of classification rules, we show that each measure of M admits a lower bound on condition that a minimal frequency threshold and a maximal number of exceptions are considered. Furthermore, our framework enables to characterize the whole collection of the rules simultaneously optimizing all the measures of M. We finally provide a method to mine a rule cover of this collection. 1

Learning classifiers has been studied extensively the last two decades. Recently, various approaches based on patterns (e.g., association rules) that hold within labeled data have been considered. In this paper, we propose a novel associative classification algorithm that combines rules and a decision tree structure. In a so-called δ-PDT (δ-Pattern Decision Tree), nodes are made of selected disjunctive δstrong classification rules. Such rules are generated from collections of δ-free patterns that can be computed efficiently. These rules have a minimal body, they are nonredundant and they avoid classification conflicts under a sensible condition on δ. We show that they also capture the discriminative power of emerging patterns. Our approach is empirically evaluated by means of a comparison to stateof-the-art proposals. 1.

Abstract. Feature construction has been studied extensively, including for 0/1 data samples. Given the recent breakthrough in closedness-related constraint-based mining, we are considering its impact on feature construction for classification tasks. We investigate the use of condensed representations of frequent itemsets (closure equivalence classes) as new features. These itemset types have been proposed to avoid set counting in difficult association rule mining tasks. However, our guess is that their intrinsic properties (say the maximality for the closed itemsets and the minimality for the δ-free itemsets) might influence feature quality. Understanding this remains fairly open and we discuss these issues thanks to itemset properties on the one hand and an experimental validation on various data sets on the other hand. 1