Results 31 to 40 of about 57,386 (264)
Point Cloud Denoising Algorithm via Geometric Metrics on the Statistical Manifold
Applied Sciences, 2023 A denoising algorithm was proposed for point cloud with high-density noise. The algorithm utilized geometric metrics on the statistical manifold and applied the idea of clustering K-means based on local statistical characteristics between noise and valid
Xiaomin Duan, Li Feng, Xinyu Zhao
doaj +1 more source
Foundations of Structural Statistics: Statistical Manifolds
CoRR, 2020 Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices, which in the category of statistical models are induced by statistical divergences.
openaire +2 more sources
Conformal Control Tools for Statistical Manifolds and for γ-Manifolds
Mathematics, 2022 The theory of statistical manifolds w.r.t. a conformal structure is reviewed in a creative manner and developed. By analogy, the γ-manifolds are introduced. New conformal invariant tools are defined. A necessary condition for the f-conformal equivalence of γ-manifolds is found, extending that for the α-conformal equivalence for statistical manifolds ...
Iulia-Elena Hirica +3 more
openaire +2 more sources
Entropy, 2015 In this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending ...
Alina-Daniela Vîlcu +1 more
doaj +1 more source
Mathematics, 2022 In this study, some identities involving the Riemannian curvature invariants are presented on lightlike hypersurfaces of a statistical manifold in the Lorentzian settings. Several inequalities characterizing lightlike hypersurfaces are obtained.
Oğuzhan Bahadır +3 more
doaj +1 more source
Latent Network Construction for Univariate Time Series Based on Variational Auto-Encode
Entropy, 2021 Time series analysis has been an important branch of information processing, and the conversion of time series into complex networks provides a new means to understand and analyze time series.
Jiancheng Sun +4 more
doaj +1 more source
Characterizations of Transversal Lightlike Submanifolds in Indefinite Golden Statistical Geometry
MathematicsWe investigate transversal and radical transversal lightlike submanifolds (TLSs) of indefinite golden statistical manifolds (IGSMs). Using the dual affine connections associated with statistical structures, we obtain decomposition formulas and derive ...
Md Aquib
doaj +1 more source
F-Geometry and Amari’s α-Geometry on a Statistical Manifold
Entropy, 2014 In this paper, we introduce a geometry called F-geometry on a statistical manifold S using an embedding F of S into the space RX of random variables. Amari’s α-geometry is a special case of F-geometry.
Harsha K. V. +1 more
doaj +1 more source
Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds
Mathematics, 2019 Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products R ×
Aliya Naaz Siddiqui +2 more
doaj +1 more source
Hypersurfaces in statistical manifolds
Differential Geometry and its Applications, 2009 A statistical structure on a manifold \(M\) consists of a Riemannian metric \(g\) and a torsion-free affine connection \(\nabla\) that satisfies \( (\nabla_Xg)(Y,Z) = (\nabla_Yg)(X,Z)\) for all vector fields \(X\), \(Y\), and \(Z\) on \(M\). The statistical manifold \((M, \nabla, g)\) has constant curvature \(k\) if \[ R^\nabla(X,Y)Z = k(g(Y,Z)X-g(X,Z ...
openaire +3 more sources