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In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. Such cubes are also successfully used for multidimensional analysis of data streams. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. In this paper, we introduce the concept of convex cube which captures all the tuples satisfying a monotone and/or antimonotone constraint combination. It can be represented in a very compact way in order to optimize both computation time and required storage space. The convex cube is not an additional structure appended to the list of cube variants but we propose it as a unifying structure that we use to characterize, in a simple, sound and homogeneous way, the other quoted types of cubes. [ABSTRACT FROM AUTHOR]

In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. Such cubes are also successfully used for multidimensional analysis of data streams. In this paper, we address the issue of performing cube comparisons in order to exhibit trend reversals between two cubes. Mining such trend changes provides users with a novel and specially interesting knowledge. For capturing the latter, we introduce the concept of emerging cube. Moreover, we provide a condensed representation of emerging cubes which avoids to compute two underlying cubes. Finally, we study an algorithmic way to achieve our representation using cube maximals and cube transversals. [ABSTRACT FROM AUTHOR]

Datacubes are specially useful for answering efficiently queries on data warehouses. Nevertheless the amount of generated aggregated data is incomparably more voluminous than the initial data which is itself very large. Recently, research work has addressed the issue of a concise representation of datacubes in order to reduce their size. The approach presented in this paper fits in a similar trend. We propose a concise representation, called Partition Cube, based on the concept of partition and define an algorithm to compute it. Various experiments are performed in order to compare our approach with methods fitting in the same trend. This comparison relates to the efficiency of algorithms computing the representations, the main memory requirements, and the storage space which is necessary. [ABSTRACT FROM AUTHOR]

The extraction of frequent patterns often yields extremely voluminous results which are difficult to handle. Computing a concise representation or cover of the frequent pattern set is thus an interesting alternative investigated by various approaches. The work presented in this article fits in such a trend. We introduce the concept of essential pattern and propose a new cover based on this concept. Such a cover makes it possible to decide whether a pattern is frequent or not, to compute its frequency and, in contrast with related work, to infer its disjunction and negation frequencies. A levelwise algorithm with a pruning step which uses the maximal frequent patterns for computing the essential patterns is proposed. Experiments show that when the number of frequent patterns is very high (strongly correlated data), the defined cover is significantly more reduced than the cover considered until now as minimal: the frequent closed patterns. [ABSTRACT FROM AUTHOR]