Data Mining and Knowledge Discovery

, Volume 33, Issue 5, pp 1298–1322 | Cite as

Mining skypatterns in fuzzy tensors

  • Nicolas Nadisic
  • Aurélien Coussat
  • Loïc CerfEmail author
Part of the following topical collections:
  1. Journal Track of ECML PKDD 2019


Many data mining tasks rely on pattern mining. To identify the patterns of interest in a dataset, an analyst may define several measures that score, in different ways, the relevance of a pattern. Until recently, most algorithms have only handled constraints in an efficient way, i.e., every measure had to be associated with a user-defined threshold, which can be tricky to determine. Skypatterns were introduced to allow analysts to simply define the measures of interest, and to get as a result a set of globally optimal and semantically relevant patterns. Skypatterns are Pareto-optimal patterns: no other pattern scores better on one of the chosen measures and scores at least as well on every remaining measure. This article tackles the search of the skypatterns in a more general context than the 0/1 (aka Boolean) matrix: the fuzzy tensor. The proposed solution supports a large class of measures. After explaining why and how their common mathematical property enables a safe pruning of the search space, an algorithm is presented. It builds upon multidupehack, a generalist pattern mining framework, which is now able to efficiently list skypatterns in addition to enforcing constraints on them. Experiments on two real-world fuzzy tensors illustrate the versatility of the proposal. Other experiments show it is typically more than one order of magnitude faster than the state-of-the-art algorithms, which can only mine 0/1 matrices.


Pattern mining Skypattern Fuzzy tensor Search space pruning 



We would like to thank Willy Ugarte, Bruno Crémilleux, Chedy Raïssi and Benjamin Négrevergne for providing the source codes of their algorithms and for their valuable comments.


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Copyright information

© The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Operational ResearchUniversity of MonsMonsBelgium
  2. 2.Université de Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR, 5220, U1206LyonFrance
  3. 3.Department of Computer ScienceUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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