Christophe Rigotti

A condensed representation to find frequent patterns

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.

Approximation of Frequency Queris by Means of Free-Sets

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.

Constraint-based mining of episode rules and optimal window sizes

Episode rules are patterns that can be extracted from a large event sequence, to suggest to experts possible dependencies among occurrences of event types. The corresponding mining approaches have been designed to find rules under a temporal constraint that specifies the maximum elapsed time between the first and the last event of the occurrences of the patterns (i.e., a window size constraint). In some applications the appropriate window size is not known, and furthermore, this size is not the same for different rules. To cope with this class of applications, it has been recently proposed in [2] to specifying the maximal elapsed time between two events (i.e., a maximum gap constraint) instead of a window size constraint. Unfortunately, we show that the algorithm proposed to handle the maximum gap constraint is not complete. In this paper we present a sound and complete algorithm to mine episode rules under the maximum gap constraint, and propose to find, for each rule, the window size corresponding to a local maximum of confidence. We show that the extraction can be efficiently performed in practice on real and synthetic datasets. Finally the experiments show that the notion of local maximum of confidence is significant in practice, since no local maximum are found in random datasets, while they can be found in real ones.

Unsupervised Spatiotemporal Mining of Satellite Image Time Series Using Grouped Frequent Sequential Patterns

An important aspect of satellite image time series is the simultaneous access to spatial and temporal information. Various tools allow end users to interpret these data without having to browse the whole data set. In this paper, we intend to extract, in an unsupervised way, temporal evolutions at the pixel level and select those covering at least a minimum surface and having a high connectivity measure. To manage the huge amount of data and the large number of potential temporal evolutions, a new approach based on data-mining techniques is presented. We have developed a frequent sequential pattern extraction method adapted to that spatiotemporal context. A successful application to crop monitoring involving optical data is described. Another application to crustal deformation monitoring using synthetic aperture radar images gives an indication about the generic nature of the proposed approach.

DBC: a condensed representation of frequent patterns for efficient mining

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-bordered condensation (DBC), 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 the DBCcan be extracted very efficiently even in difficult cases and that this extraction and the regeneration of the frequent patterns is much more efficient than the direct extraction of the frequent patterns themselves. We compared the DBC with another representation of frequent patterns previously investigated in the literature called frequent closed sets. In nearly all experiments we have run, the DBC have been extracted much more efficiently than frequent closed sets. In the other cases, the extraction times are very close.

Constraint-Based Mining of Sequential Patterns over Datasets with Consecutive Repetitions

Constraint-based mining of sequential patterns is an active research area motivated by many application domains. In practice, the real sequence datasets can present consecutive repetitions of symbols (e.g., DNA sequences, discretized stock market data) that can lead to a very important consumption of resources during the extraction of patterns that can turn even efficient algorithms to become unusable. We propose a constraint-based mining algorithm using an approach that enables to compact these consecutive repetitions, reducing drastically the amount of data to process and speeding-up the extraction time. The technique introduced in this paper allows to retain the advantages of existing state-of-the-art algorithms based on the notion of occurrence lists, while permitting to extend their application fields to datasets containing consecutive repetitions. We analyze the benefits obtained using synthetic datasets, and show that the approach is of practical interest on real datasets.

Finding collections of k -clique percolated components in attributed graphs

In this paper, we consider graphs where a set of Boolean attributes is associated to each vertex, and we are interested in k -clique percolated components (components made of overlapping cliques) in such graphs. We propose the task of finding the collections of homogeneous k -clique percolated components, where homogeneity means sharing a common set of attributes having value true. A sound and complete algorithm based on subgraph enumeration is proposed. We report experiments on two real databases (a social network of scientific collaborations and a network of gene interactions), showing that the extracted patterns capture meaningful structures.

GO-SPADE: mining sequential patterns over datasets with consecutive repetitions

Databases of sequences can contain consecutive repetitions of items. This is the case in particular when some items represent discretized quantitative values. We show that on such databases, a typical algorithm like the SPADE algorithm tends to loose its efficiency. SPADE is based on the used of lists containing the localization of the occurrences of a pattern in the sequences and these lists are not appropriated in the case of data with repetitions. We introduce the concept of generalized occurrences and the corresponding primitive operators to manipulate them. We present an algorithm called GO-SPADE that extends SPADE to incorporate generalized occurrences. Finally we present experiments showing that GO-SPADE can handle sequences containing consecutive repetitions at nearly no extra cost.

Automatic generation of CHR constraint solvers

In this paper, we present a framework for automatic generation of CHR solvers given the logical specification of the constraints. This approach takes advantage of the power of tabled resolution for constraint logic programming, in order to check the validity of the rules. Compared to previous work (Apt and Monfroy 1999; Ringeissen and Monfroy 2000; Abdennadher and Rigotti 2000; Abdennadher and Rigotti 2001a), where different methods for automatic generation of constraint solvers have been proposed, our approach enables the generation of more expressive rules (even recursive and splitting rules) that can be used directly as CHR solvers.

Automatic generation of rule-based constraint solvers over finite domains

A general approach to implement propagation and simplification of constraints consists of applying rules over these constraints. However, a difficulty that arises frequently when writing a constraint solver is to determine the constraint propagation algorithm. In this article, we propose a method for generating propagation and simplification rules for constraints over finite domains defined extensionally by, for example, a truth table or their tuples. The generation of rules is performed in two steps. First, propagation rules are generated. Propagation rules do not rewrite constraints but add new ones. Thus, the constraint store may contain superfluous constraints. Removing these constraints not only allows saving of space but also decreases the cost of constraint solving. Constraints can be removed using simplification rules. Thus, in a second step, some propagation rules are transformed into simplification rules.Furthermore, we show that our approach performs well on various examples, including Boolean constraints, multivalued logic, and Allens qualitative approach to temporal logic. Moreover, an application taken from the field of digital circuit design shows that our approach is of practical use.