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Classification by separating hypersurfaces: An entropic approach

Author

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  • Arratia, Argimiro
  • Daou, Mahmoud El
  • Gzyl, Henryk

Abstract

This work introduces a variation on the theme of the classical linear classification problem, extending it to the separation of data by non-linear polynomial hypersurfaces, which allows for more complex decision boundaries. The classification problem, central to machine learning since the perceptron model, is transformed into an ill-posed, linear inverse problem with convex constraints.

Suggested Citation

  • Arratia, Argimiro & Daou, Mahmoud El & Gzyl, Henryk, 2026. "Classification by separating hypersurfaces: An entropic approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 685(C).
    • Handle: RePEc:eee:phsmap:v:685:y:2026:i:c:s0378437126000166
    DOI: 10.1016/j.physa.2026.131280
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    References listed on IDEAS

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    1. Rau, Albrecht & Nadal, Jean-Pierre, 1992. "A model for a multi-class classification machine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 428-432.
    2. Gzyl, Henryk & ter Horst, Enrique & Molina, German, 2015. "Application of the method of maximum entropy in the mean to classification problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 101-108.
    3. Neirotti, Juan P. & Saad, David, 2006. "Efficient Bayesian inference for learning in the Ising linear perceptron and signal detection in CDMA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 203-210.
    4. Kinzel, Wolfgang, 1993. "Statistical mechanics of generalization: new results for perceptrons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 613-618.
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