Cube Lattices: a Framework for Multidimensional Data Mining

Abstract

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.

Scalable Informative Rule Mining

“…Following the notations in multidimensional data mining, we further define the generalization/specialization order between rules to establish the structure of a cube lattice [9]. A rule r is an ancestor of another rule r if and only if it satisfies the following property:…”

Computational Science and Its Applications – ICCSA 2013

“…However, most of these are limited to point or raster data, which have trivial or no topology, and are thus much more straightforward to use and implement. Higher-dimensional point clouds are common in data mining [21], while higher-dimensional rasters are common in medical imaging [22], among other examples. For vector data consisting of closed polytopes (i.e.…”

Extracting semantics in OLAP databases using emerging cubes

“…In this section, we remind the cube lattice concept [4] proposed as a general and soundly founded framework to state and solve several OLAP mining problems, including the Emerging Cube characterization.…”

“…For synthetic data, 3 we use the following notations to describe the relations: D the number of dimensions, C the cardinality of each dimension, T the number of tuples in the relation, M 1 (M 2 , respectively) the threshold corresponding to the C 1 constraint (C 2 , respectively), and S the skewness of data according to the Zipf's law. 4 When S is equal 3 The synthetic data generator is given at http://illimine.cs.uiuc.edu/ 4 Zipf's law models the occurrence of distinct objects in particular sorts of collections. This law predicts that out of a population of N elements, the frequency of elements of rank k is: f ðk; S; NÞ ¼ to 0, the data are uniform.…”