Abstract. Subgroup discovery is the task of finding subgroups of a population which exhibit both distributional unusualness and high generality. Due to the non monotonicity of the corresponding evaluation functions, standard pruning techniques cannot be used for subgroup discovery, requiring the use of optimistic estimate techniques instead. So far, however, optimistic estimate pruning has only been considered for the extremely simple case of a binary target attribute and up to now no attempt was made to move beyond suboptimal heuristic optimistic estimates. In this paper, we show that optimistic estimate pruning can be developed into a sound and highly effective pruning approach for subgroup discovery. Based on a precise definition of optimality we show that previous estimates have been tight only in special cases. Thereafter, we present tight optimistic estimates for the most popular binary and multi-class quality functions, and present a family of increasingly efficient approximations to these optimal functions. As we show in empirical experiments, the use of our newly proposed optimistic estimates can lead to a speed up of an order of magnitude compared to previous approaches.

We describe a Metropolis-Hastings algorithm for sampling formal concepts, i.e., closed (item-) sets, according to any desired strictly positive distribution. Important applications are (a) estimating the number of all formal concepts as well as (b) discovering any number of interesting, non-redundant, and representative local patterns. Setting (a) can be used for estimating the runtime of algorithms examining all formal concepts. An application of setting (b) is the construction of data mining systems that do not require any user-specified threshold like minimum frequency or confidence.

Abstract. Subgroup discovery is a Knowledge Discovery task that aims at finding subgroups of a population with high generality and distributional unusualness. While several subgroup discovery algorithms have been presented in the past, they focus on databases with nominal attributes or make use of discretization to get rid of the numerical attributes. In this paper, we illustrate why the replacement of numerical attributes by nominal attributes can result in suboptimal results. Thereafter, we present a new subgroup discovery algorithm that prunes large parts of the search space by exploiting bounds between related numerical subgroup descriptions. The same algorithm can also be applied to ordinal attributes. In an experimental section, we show that the use of our new pruning scheme results in a huge performance gain when more that just a few split-points are considered for the numerical attributes.

Subgroup discovery is a Knowledge Discovery task that aims at finding subgroups of a population with high generality and distribu-tional unusualness. While several subgroup discovery algorithms have been presented in the past, they focus on databases with nominal attributes or make use of discretization to get rid of the numerical attributes. In this paper, we illustrate why the replacement of numerical attributes by nominal attributes can result in suboptimal results. Thereafter , we present a new subgroup discovery algorithm that prunes large parts of the search space by exploiting bounds between related numerical subgroup descriptions. The same algorithm can also be applied to ordinal attributes. In an experimental section, we show that the use of our new pruning scheme results in a huge performance gain when more that just a few split-points are considered for the numerical attributes. This is an extended abstract of an article published in the Data Mining and Knowledge Discovery journal [1].

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