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Monoparametric family of metrics derived from classical Jensen–Shannon divergence

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  • Osán, Tristán M.
  • Bussandri, Diego G.
  • Lamberti, Pedro W.

Abstract

Jensen–Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic properties of a distance, it also satisfies the triangle inequality. In this work we extend this last result to prove that in fact it is possible to derive a monoparametric family of metrics from the classical Jensen–Shannon divergence. Motivated by our results, an application into the field of symbolic sequences segmentation is explored. Additionally, we analyze the possibility to extend this result into the quantum realm.

Suggested Citation

  • Osán, Tristán M. & Bussandri, Diego G. & Lamberti, Pedro W., 2018. "Monoparametric family of metrics derived from classical Jensen–Shannon divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 336-344.
    • Handle: RePEc:eee:phsmap:v:495:y:2018:i:c:p:336-344
    DOI: 10.1016/j.physa.2017.12.073
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    References listed on IDEAS

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    1. Lamberti, Pedro W. & Majtey, Ana P., 2003. "Non-logarithmic Jensen–Shannon divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 81-90.
    2. Ferdinand Österreicher & Igor Vajda, 2003. "A new class of metric divergences on probability spaces and its applicability in statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 639-653, September.
    3. Majtey, Ana P. & Lamberti, Pedro W. & Plastino, A., 2004. "A monoparametric family of metrics for statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 547-553.
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    1. Osán, T.M. & Bussandri, D.G. & Lamberti, P.W., 2022. "Quantum metrics based upon classical Jensen–Shannon divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).

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