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GrAFCI+ A fast generator-based algorithm for mining frequent closed itemsets

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Abstract

Mining itemsets for association rule generation is a fundamental data mining task originally stemming from the traditional market basket analysis problem. However, enumerating all frequent itemsets, especially in a dense dataset, or with low support thresholds, remains costly. In this paper, a novel theorem builds the relationship between frequent closed itemsets (FCIs) and frequent generator itemsets (FGIs) and proves that the process of mining FCIs is equivalent to mining FGIs, unified with their full-support and extension items. On the basis of this theorem, a generator-based algorithm for mining FCIs, called GrAFCI+, is proposed and explained in details including its correctness. The comparative effectiveness of the algorithm in terms of scalability is first investigated, along with the compression rate—a measure of the interestingness of a given FIs representation. Extensive experiments are further undertaken on eight datasets and four state-of-the-art algorithms, namely DCI_CLOSED*, DCI_PLUS, FPClose, and NAFCP. The results show that the proposed algorithm is more efficient regarding the execution time in most cases as compared to these algorithms. Because GrAFCI+ main goal is to address the runtime issue, it paid a memory cost, especially when the support is too small. However, this cost is not high since GrAFCI+ is seconded by only one competitor out of four in memory utilization and for large support values. As an overall assessment, GrAFCI+ gives better results than most of its competitors.

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Notes

  1. https://www.philippe-fournier-viger.com/spmf/index.php?link=algorithms.php

  2. https://www.comp.nus.edu.sg/~wongls/projects/pattern-spaces/

  3. https://github.com/rionda/truefis/tree/master/code/grahne

  4. The actual url is http://fimi.uantwerpen.be/data/

  5. Precise calculations can readily be done using formula 9 and data from Table 8. For example, for Accidents dataset, with support \(20\%\), \(CR(FC) = (887 441)/(889 936) = 99.71\%\), which is an extremely poor compression, meaning that we need \(99.7\%\) of FIs to represent \(100\%\) of FIs. For the Connect dataset, and \(30\%\) support, \(CR(FC) = (460 412)/(1 331 880 801) = 0.3\%\), which is an excellent compression rate, meaning that only \(0.3\%\) of FIs are needed in memory to represent \(100\%\) of FIs.

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Acknowledgements

The authors would like to thank the Editor and the Editor-in-Chief and the anonymous reviewers for their constructive comments, pointing to directions of research and additional experimental work that greatly improved the manuscript. The authors would also like to thank Tuong Le and Bay Vo for providing the source code for NAFCP and Sahoo Jayakrushna for the source code for DCI_PLUS.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Abbes Laghrour University of Khenchela, Khenchela, 40000, Algeria

    Makhlouf Ledmi

  2. Department of Computer Science, Chahid Mostefa Ben Boulaid University of Batna 2, Batna, Algeria

    Samir Zidat

  3. Department of Computer Science, Ferhat Abbas University of Setif 1, Setif, Algeria

    Aboubekeur Hamdi-Cherif

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  1. Makhlouf Ledmi
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  2. Samir Zidat
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  3. Aboubekeur Hamdi-Cherif
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Correspondence to Makhlouf Ledmi.

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Ledmi, M., Zidat, S. & Hamdi-Cherif, A. GrAFCI+ A fast generator-based algorithm for mining frequent closed itemsets. Knowl Inf Syst 63, 1873–1908 (2021). https://doi.org/10.1007/s10115-021-01575-3

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