[HTML][HTML] A simple approximation method for the Fisher–Rao distance between multivariate normal distributions

F Nielsen - Entropy, 2023 - mdpi.com
We present a simple method to approximate the Fisher–Rao distance between multivariate
normal distributions based on discretizing curves joining normal distributions and …

Geomstats: a Python package for Riemannian geometry in machine learning

N Miolane, N Guigui, A Le Brigant, J Mathe… - Journal of Machine …, 2020 - jmlr.org
We introduce Geomstats, an open-source Python package for computations and statistics on
nonlinear manifolds such as hyperbolic spaces, spaces of symmetric positive definite …

Conceptual Framework for Dynamic Optimal Airspace Configuration for Urban Air Mobility

TA Hearn, MT Kotwicz Herniczek… - Journal of Air …, 2023 - arc.aiaa.org
In this work, a framework for optimizing the configuration of service areas in airspace into
disparate partitions is demonstrated in the context of urban air mobility (UAM) operations …

[图书][B] Marginal and functional quantization of stochastic processes

H Luschgy, G Pagès - 2023 - Springer
Vector Quantization is the name given to discretization methods based on nearest
neighbour search. It was developed in the 1950s, mostly in signal processing and …

Multi-objective soft subspace clustering in the composite kernel space

Y Li, Q Zhao, K Luo - Information Sciences, 2021 - Elsevier
Conventional subspace clustering algorithms group the data samples by optimizing the
objective function which aggregates different clustering criteria using the linear combination …

[HTML][HTML] The geometry of the generalized gamma manifold and an application to medical imaging

S Rebbah, F Nicol, S Puechmorel - Mathematics, 2019 - mdpi.com
The Fisher information metric provides a smooth family of probability measures with a
Riemannian manifold structure, which is an object in information geometry. The information …

An efficient algorithm for the Riemannian logarithm on the Stiefel manifold for a family of Riemannian metrics

S Mataigne, R Zimmermann, N Miolane - arXiv preprint arXiv:2403.11730, 2024 - arxiv.org
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a
seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems …

Asymptotic quantization on Riemannian manifolds via covering growth estimates

AD Aydin, M Iacobelli - arXiv preprint arXiv:2402.13164, 2024 - arxiv.org
The quantization problem looks for best approximations of a probability measure on a given
metric space by finitely many points, where the approximation error is measured with respect …

Asymptotics for Optimal Empirical Quantization of Measures

F Quattrocchi - arXiv preprint arXiv:2408.12924, 2024 - arxiv.org
We investigate the minimal error in approximating a general probability measure $\mu $ on
$\mathbb {R}^ d $ by the uniform measure on a finite set with prescribed cardinality $ n …

The geodesic distance on the generalized gamma manifold for texture image retrieval

Z Abbad, ADE Maliani, SOE Alaoui… - Journal of Mathematical …, 2022 - Springer
In this paper, the similarity measurement issue, in the context of texture images comparison,
is tackled from a geometrical point of view by computing the Rao Geodesic distance on the …