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Dichotomic lattices and local discretization for Galois lattices

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Abstract

The present paper deals with supervised classification methods based on Galois lattices and decision trees. Such ordered structures require attributes discretization and it is known that, for decision trees, local discretization improves the classification performance compared with global discretization. While most literature on discretization for Galois lattices relies on global discretization, the presented work introduces a new local discretization algorithm for Galois lattices which hinges on a property of some specific lattices that we introduce as dichotomic lattices. Their properties, co-atomicity and \(\vee \)-complementarity are proved along with their links with decision trees. Finally, some quantitative and qualitative evaluations of the local discretization are proposed.

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Notes

  1. Galois lattices defined from a closed/finite data set.

  2. The convergence property relies on the complete definition of objects, i.e. if knowledge on objects increases the concepts just become more precise and are not modified.

  3. Considering that the number of concepts in a lattice can be exponential in the number of objects and attributes, note that concepts can be generated on demand during the navigation process, see Visani et al. (2011).

  4. Noisy data contain useless and cumbersome information, as an example the image artefact representation in signatures extracted from images forms a noise.

  5. Since we perform supervised classification, we focus on supervised discretization, for more details on other discretization methods the reader may refer to (Dougherty et al. 1995; Fayyad and Irani 1993; Muhlenbach and Rakotomalala 2002).

  6. Binary table reduction deletes the attributes satisfied by all objects, and the objects satisfying all attributes.

  7. An inseparable problem occurs when objects belonging to different classes have the same description.

  8. For comparison with other decision trees refer to Visani et al. (2011), where experiments have shown that Galois lattice obtains better recognition rates than decision trees in a context of noisy data.

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Authors and Affiliations

  1. Laboratory L3i, University of La Rochelle, La Rochelle, France

    Nathalie Girard, Karell Bertet & Muriel Visani

  2. LI EA 6300, Université François-Rabelais de Tours, Tours, France

    Nathalie Girard

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  1. Nathalie Girard
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  2. Karell Bertet
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  3. Muriel Visani
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Correspondence to Nathalie Girard.

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Girard, N., Bertet, K. & Visani, M. Dichotomic lattices and local discretization for Galois lattices. Adv Data Anal Classif 11, 49–77 (2017). https://doi.org/10.1007/s11634-015-0225-7

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