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Mathematical and informational tools for classifying blood glucose signals - a pilot study

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  • Amadio, Ariel
  • Rey, Andrea
  • Legnani, Walter
  • Blesa, Manuel García
  • Bonini, Cristian
  • Otero, Dino

Abstract

A survey campaign was carried out on the dynamics of blood glucose measured through interstitial sensors of relative recent diffusion in the market. These sensors generated time series that were labeled according to medical diagnosis in diabetics and non-diabetics, and that constituted the data core of the classification models. Based on the calculation of the distribution of ordinal patterns of the time series, the corresponding points in the entropy-complexity causal plane were located. Moreover, the transition matrices of these ordinal patterns (OPTMs) were calculated in order to find the proximity using the Manhattan distance of every OPTM with respect to the mean of each group, associating the corresponding signal to each class. On the other hand, the Frobenius norm of every OPTM and the norm of its stationary vector were computed given different values for the considered classes. The effect of repeated values in a signal was also analyzed. Notable differences were obtained in the properties of the OPTMs of each class. In another sense, it is shown that diabetes is a disease that reduces the entropy of the temporal evolution of blood glucose in well-defined time periods and presents values of complexity significantly higher than those obtained in subjects without diabetes. The selected alternatives coincide in detecting patients positively diagnosed with Type II Diabetes Mellitus. The calculations on the OPTMs show the correlation among patterns of the signals. At the same time, in the entropy-complexity plane, the considered groups were located in well-defined regions showing the differentiating power of these information measures and indicating variations in the dynamics of the biological system when diabetes is present. With the four mathematical tools selected and the dynamical characterization given by the causal plane, it was possible to define an index that clearly differentiates the classes under study.

Suggested Citation

  • Amadio, Ariel & Rey, Andrea & Legnani, Walter & Blesa, Manuel García & Bonini, Cristian & Otero, Dino, 2023. "Mathematical and informational tools for classifying blood glucose signals - a pilot study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    • Handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s037843712300626x
    DOI: 10.1016/j.physa.2023.129071
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    References listed on IDEAS

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    1. Osvaldo Rosso & Felipe Olivares & Luciano Zunino & Luciana Micco & André Aquino & Angelo Plastino & Hilda Larrondo, 2013. "Characterization of chaotic maps using the permutation Bandt-Pompe probability distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-13, April.
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    3. Martin, M.T. & Plastino, A. & Rosso, O.A., 2006. "Generalized statistical complexity measures: Geometrical and analytical properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 439-462.
    4. Borges, João B. & Ramos, Heitor S. & Mini, Raquel A.F. & Rosso, Osvaldo A. & Frery, Alejandro C. & Loureiro, Antonio A.F., 2019. "Learning and distinguishing time series dynamics via ordinal patterns transition graphs," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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