Abstract Knowledge discovery systems are nowadays supposed to store and process very large data. When working with big time series, multivariate prediction becomes more and more complicated because the use of all the variables does not allow to have the most accurate predictions and poses certain problems for classical prediction models. In this article, we present a scalable prediction process for large time series prediction, including a new algorithm for identifying time series predictors, which analyses the dependencies between time series using the mutual reinforcement principle between Hubs and Authorities of the Hits (Hyperlink-Induced Topic Search) algorithm. The proposed framework is evaluated on 3 real datasets. The results show that the best predictions are obtained using a very small number of predictors compared to the initial number of variables. The proposed feature selection algorithm shows promising results compared to widely known algorithms, such as the classic and the kernel principle component analysis, factor analysis, and the fast correlation-based filter method, and improves the prediction accuracy of many time series of the used datasets.

The Skyline concept has been introduced in order to exhibit the best objects according to all the criterion combinations and makes it possible to analyze the relationships between Skyline objects. Like the data cube, the Skycube groups all the multidimensional Skylines and it is so voluminous that reduction approaches are a necessity. In this paper, we define an approach which partially materializes the Skycube. The underlying idea is to discard from the representation the Skycuboids which can be computed again easily. To meet this reduction objective, we characterize a formal framework: the Agree Concept Lattice. It provides a formal framework which makes it possible to improve computation time, reduce representation and easily navigate through the Hasse diagram in order to focus on the most relevant skycuboids. This structure is generic, applies to various database analysis problems and combines both formal concept analysis and database theory. It makes use of the concepts of agree set and database partition. They are associated to define the Agree Concept of a database relation. The set of all the Agree Concepts is organized within the Agree Concept Lattice. From this structure, we derive the Skyline concept lattice which is one of its constrained instances for efficient multidimensional Skyline analysis. The strong points of our approach are: (i) it is attribute oriented; (ii) it provides a boundary for the number of lattice nodes; (iii) it facilitates the navigation within the Skycuboids.

A general assumption in all existing algorithms permitting to mine functional dependencies is that the database is static. However, real life databases are frequently updated. To the best of our knowledge, the discovery of functional dependencies in

In this paper we propose a lattice-based approach intended for extracting semantics from datacubes: borders of version spaces for supervised classification, closed cube lattice to summarize the semantics of datacubes w.r.t. COUNT, SUM, and covering graph of the quotient cube as a visualization tool of minimal multidimensional associations. With this intention, we introduce two novel concepts: the cube transversals and the cube closures over the cube lattice of a categorical database relation. We propose a levelwise merging algorithm for mining minimal cube transversals with a single database scan. We introduce the cube connection, show that it is a Galois connection and derive a closure operator over the cube lattice. Using cube transversals and closures, we define a new characterization of boundary sets which provide a condensed representation of version spaces used to enhance supervised classification. The algorithm designed for computing such borders improves the complexity of previous proposals. We also introduce the concept of closed cube lattice and show that it is isomorph to on one hand the Galois lattice and on the other hand the quotient cube w.r.t. COUNT, SUM. Proposed in [16], the quotient cube is a succinct summary of a datacube preserving the Rollup/Drilldown semantics. We show that the quotient cube w.r.t. COUNT, SUM and the closed cube lattice have a similar expression power but the latter has the smallest possible size. Finally we focus on the multidimensional association issue and introduce the covering graph of the quotient cube which provides the user with a visualization tool of minimal multidimensional associations.

Constrained multidimensional patterns differ from the well-known frequent patterns from a conceptual and logical points of view because they are provided with a common structure and support various types of constraints. Classical data mining techniques are based on the power set lattice of binary attributes and, even extended, are not suitable when addressing the discovery of constrained multidimensional patterns. In this paper we propose a foundation for various multidimensional data mining problems by introducing a new algebraic structure called cube lattice which characterizes the search space to be explored. We take into consideration monotone and/or antimonotone constraints enforced when mining multidimensional patterns. In addition, we propose condensed representations of the constrained cube lattice which is a convex space. Finally, we place emphasis on advantages of the cube lattice when compared to the power set lattice of binary attributes used for multidimensional data mining.

In this article, we deal with the functional and approximate dependency inference problem by pointing out some relationships between relational database theory and formal concept analysis (FCA). More precisely, the notion of functional dependency in database is compared to the notion of implication in FCA. We propose a framework and several algorithms for mining these dependencies from large database relations. The common data centric step of this framework is the discovery of agree sets, which are closed sets with respect to the closure operator for functional dependency. Two approaches for discovering agree sets from database relations are proposed: the former is a database approach based on SQL queries and the latter is a data mining approach based on partitions. Experiments were performed in order to compare the two proposed methods.

The authors propose a framework for a broad class of data mining algorithms for understanding existing databases: functional and approximate dependency inference, minimal key inference, example relation generation and normal form tests. We point out that the common data centric step of these algorithms is the discovery of agree sets. A set-oriented approach for discovering agree sets from database relations based on SQL queries is proposed. Experiments have been performed in order to compare the proposed approach with a data mining approach. We also present a novel way to extract approximate functional dependencies having minimal errors from agree sets.

We address the problem of the usefulness and the relevance of the set of discovered association rules. Using the frequent closed itemset groundwork, we propose to generate bases for association rules, that are non-redundant generating sets for all association rules.