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Spline Interpolation on the Manifold of Probability Measures

In: Regression and Fitting on Manifold-valued Data

Author

Listed:
  • Ines Adouani

    (University of Sousse, Higher Institute of Applied Sciences and Technology of Sousse (ISSAT))

  • Chafik Samir

    (University of Clermont Auvergne (UCA))

Abstract

In this chapter, we present an efficient and accurate algorithm for constructing a $$C^{2}$$ C 2 Bézier spline that interpolates a given ordered set of data points on the space of probability measuresSpace of probability measures $$\mathcal {P}_{+}$$ P + $$\mathcal {P}_{+}$$ P + , equipped with the Fisher–Rao metric. The distinctive aspect of the proposed method lies in its exploration of the inherent Riemannian structure within the space of probability measures, making the solution computationally feasible.

Suggested Citation

  • Ines Adouani & Chafik Samir, 2024. "Spline Interpolation on the Manifold of Probability Measures," Springer Books, in: Regression and Fitting on Manifold-valued Data, chapter 0, pages 85-113, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61712-6_6
    DOI: 10.1007/978-3-031-61712-6_6
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