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Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature [PDF]
Mathematics, 2018 We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.
Adela Mihai, Ion Mihai
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Degenerate Hessian structures on radiant manifolds [PDF]
International Journal of Geometric Methods in Modern Physics, 2017 We present a rigorous mathematical treatment of Ruppeiner geometry, by considering degenerate Hessian metrics defined on radiant manifolds. A manifold $M$ is said to be radiant if it is endowed with a symmetric, flat connection $\bar\nabla$ and a global ...
García-Ariza, M. Á.
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Complex Hessian Equations on Some Compact Kähler Manifolds [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 On a compact connected 2m-dimensional Kähler manifold with Kähler form ω, given a smooth function f:M→ℝ and an integer ...
Asma Jbilou
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Generalized Legendre Transforms Have Roots in Information Geometry [PDF]
EntropyArtstein-Avidan and Milman [Annals of mathematics (2009), (169):661–674] characterized invertible reverse-ordering transforms in the space of lower, semi-continuous, extended, real-valued convex functions as affine deformations of the ordinary Legendre ...
Frank Nielsen
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A Study on Dimensionality Reduction and Parameters for Hyperspectral Imagery Based on Manifold Learning [PDF]
SensorsWith the rapid advancement of remote-sensing technology, the spectral information obtained from hyperspectral remote-sensing imagery has become increasingly rich, facilitating detailed spectral analysis of Earth’s surface objects.
Wenhui Song +5 more
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Mathematics, 2022 The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in ...
Aliya Naaz Siddiqui +2 more
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Selfsimilar Hessian manifolds [PDF]
Journal of Geometry and Physics, 2022 A selfsimiar manifold is a Riemannian manifold $\left(M,g\right)$ endowed with a homothetic vector field $ $. We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian manifold or a Eucledean space.
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Hessian-regularized co-training for social activity recognition. [PDF]
PLoS ONE, 2014 Co-training is a major multi-view learning paradigm that alternately trains two classifiers on two distinct views and maximizes the mutual agreement on the two-view unlabeled data.
Weifeng Liu +4 more
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Curvature of Hessian manifolds [PDF]
Differential Geometry and its Applications, 2014 18 ...
S. Amari, J. Armstrong
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Hessian Regularization Based Factorization Algorithm Combining Multi-view and Non-negative Matrix [PDF]
Jisuanji gongcheng, 2017 Non-negative matrix does not consider the manifold of data when represents multi-view data,which results in the ineffective express of the data internal expression.In this paper,Hessian regularized Non-negative Matrix Factorization(NMF) is proposed.By ...
WANG Chaofeng,SHI Jun,WU Jinjie,ZHU Jie
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