Gradual Discovery with Closure Structure of a Concept Lattice

S. Kuznetsov; Napoli A.; T. Makhalova

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Gradual Discovery with Closure Structure of a Concept Lattice

P. 145–157.

Kuznetsov S., Napoli A., Makhalova T.

An approximate discovery of closed itemsets is usually based on either setting a frequency threshold or computing a sequence of projections. Both approaches, being incremental, do not provide any estimate of the size of the next output and do not ensure that “more interesting patterns” will be generated first. We propose to generate closed itemsets incrementally, w.r.t. the size of the smallest (cardinality-minimal or minimum) generators and show that this approach (i) exhibits anytime property, and (ii) first generates itemsets of better quality and then those of lower quality.

Language: English

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Keywords: pattern mining closed itemsets Anytime algorithms

Publication based on the results of:

Intelligent Data Analysis in Interactive Systems for Transdisciplinary Applications (2020)

In book

The 15th International Conference on Concept Lattices and Their Applications CLA2020

Issue 2668. , CEUR-WS, 2020.

2022 IEEE International Conference on Data Mining (ICDM)

Sergei O. Kuznetsov, Buzmakov A., Makhalova T. et al., IEEE, 2022.

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 △-closedness, a generalization of the closure operator, where △ measures how a closed set differs from its upper neighbors ...

Added: February 25, 2026

On Shapley value interpretability in concept-based learning with formal concept analysis

Ignatov D. I., Kwuida L., Annals of Mathematics and Artificial Intelligence 2022 Vol. 90 No. 11 P. 1197–1222

We propose the usage of two power indices from cooperative game theory and public choice theory for ranking attributes of closed sets, namely intents of formal concepts (or closed itemsets). The introduced indices are related to extensional concept stability and are also based on counting of generators, especially of those that contain a selected attribute. ...

Added: January 31, 2023

Introducing the closure structure and the GDPM algorithm for mining and understanding a tabular dataset

Makhalova T., Buzmakov A., Napoli A. et al., [б.и.], 2022.

Pattern mining is one of the most studied fields in data mining. Being mostly motivated by practitioners, pattern mining algorithms are often based on heuristics and are lacking suitable formalization. In this paper, we are revisiting pattern mining, and especially itemset mining, which allows one to analyze binary datasets in searching for interesting and meaningful itemsets and ...

Added: June 27, 2022

Shapley and Banzhaf Vectors of a Formal Concept

Ignatov D. I., Kwuida L., , in: Proceedings of the Fifthteenth International Conference on Concept Lattices and Their ApplicationsVol. 2668.: CEUR-WS.org, 2020. P. 259–271.

We propose the usage of two power indices from cooperative game theory and public choice theory for ranking attributes of closed sets, namely intents of formal concepts (or closed itemsets). The introduced indices are related to extensional concept stability and based on counting generators, especially those that contain a selected attribute. The introduction of such ...

Added: October 30, 2020

Numerical Pattern Mining Through Compression

Makhalova T., Kuznetsov S., Napoli A., , in: 2019 Data Compression Conference Proceedings.: IEEE, 2019. P. 112–121.

Pattern Mining (PM) has a prominent place in Data Science and finds its application in a wide range of domains. To avoid the exponential explosion of patterns different methods have been proposed. They are based on assumptions on interestingness and usually return very different pattern sets. In this paper, we propose to use a compression-based ...

Added: July 2, 2019