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arXiv · 2210.06926

Delta-Closure Structure for Studying Data Distribution

Aleksey Buzmakov·Tatiana Makhalova·Sergei O. Kuznetsov·Amedeo Napoli
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Abstract

In this paper, we revisit pattern mining and study the distribution underlying a binary dataset thanks to the closure structure which is based on passkeys, i.e., minimum generators in equivalence classes robust to noise. We introduce $Δ$-closedness, a generalization of the closure operator, where $Δ$ measures how a closed set differs from its upper neighbors in the partial order induced by closure. A $Δ$-class of equivalence includes minimum and maximum elements and allows us to characterize the distribution underlying the data. Moreover, the set of $Δ$-classes of equivalence can be partitioned into the so-called $Δ$-closure structure. In particular, a $Δ$-class of equivalence with a high level demonstrates correlations among many attributes, which are supported by more observations when $Δ$ is large. In the experiments, we study the $Δ$-closure structure of several real-world datasets and show that this structure is very stable for large $Δ$ and does not substantially depend on the data sampling used for the analysis.

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Aleksey Buzmakov, Tatiana Makhalova, Sergei O. Kuznetsov, Amedeo Napoli. 2022-10-13. Delta-Closure Structure for Studying Data Distribution. https://arxiv.org/abs/2210.06926

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