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Logical analysis of numerical data

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Abstract

“Logical analysis of data” (LAD) is a methodology developed since the late eighties, aimed at discovering hidden structural information in data sets. LAD was originally developed for analyzing binary data by using the theory of partially defined Boolean functions. An extension of LAD for the analysis of numerical data sets is achieved through the process of “binarization” consisting in the replacement of each numerical variable by binary “indicator” variables, each showing whether the value of the original variable is above or below a certain level. Binarization was successfully applied to the analysis of a variety of real life data sets. This paper develops the theoretical foundations of the binarization process studying the combinatorial optimization problems related to the minimization of the number of binary variables. To provide an algorithmic framework for the practical solution of such problems, we construct compact linear integer programming formulations of them. We develop polynomial time algorithms for some of these minimization problems, and prove NP-hardness of others.

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Authors and Affiliations

  1. RUTCOR, Rutgers University, P.O. Box 5062, 08903, New Brunswick, NJ, USA

    Endre Boros, Peter L. Hammer & Alexander Kogan

  2. Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, 606, Kyoto, Japan

    Toshihide Ibaraki

  3. Department of Accounting and Information Systems, Faculty of Management, Rutgers University, 07102, Newark, NJ, USA

    Alexander Kogan

Authors
  1. Endre Boros
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  2. Peter L. Hammer
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  3. Toshihide Ibaraki
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  4. Alexander Kogan
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Additional information

The authors gratefully acknowledge the partial support by the Office of Naval Research (grants N00014-92-J1375 and N00014-92-J4083).

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Boros, E., Hammer, P.L., Ibaraki, T. et al. Logical analysis of numerical data. Mathematical Programming 79, 163–190 (1997). https://doi.org/10.1007/BF02614316

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  • DOI: https://doi.org/10.1007/BF02614316

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