Results 11 to 20 of about 248 (141)

Understanding Higher-Order Interactions in Information Space [PDF]

Entropy
Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an
Herbert Edelsbrunner, Katharina Ölsböck, Hubert Wagner   +2 more
doaj   +2 more sources

Mirror Descent and Exponentiated Gradient Algorithms Using Trace-Form Entropies [PDF]

Entropy
This paper introduces a broad class of Mirror Descent (MD) and Generalized Exponentiated Gradient (GEG) algorithms derived from trace-form entropies defined via deformed logarithms. Leveraging these generalized entropies yields MD and GEG algorithms with
Andrzej Cichocki, Toshihisa Tanaka, Frank Nielsen, Sergio Cruces   +3 more
doaj   +2 more sources

Generalized Legendre Transforms Have Roots in Information Geometry [PDF]

Entropy
Artstein-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
doaj   +2 more sources

Information Geometry for Radar Target Detection with Total Jensen–Bregman Divergence [PDF]

Entropy, 2018
This paper proposes a radar target detection algorithm based on information geometry. In particular, the correlation of sample data is modeled as a Hermitian positive-definite (HPD) matrix. Moreover, a class of total Jensen–Bregman divergences, including
Xiaoqiang Hua, Haiyan Fan, Yongqiang Cheng, Hongqiang Wang, Yuliang Qin   +4 more
doaj   +2 more sources

On Minimum Bregman Divergence Inference

Mathematics
The density power divergence (DPD) is a well-studied member of the Bregman divergence family and forms the basis of widely used minimum divergence estimators that balance efficiency and robustness. In this paper, we introduce and study a new sub-class of
Soumik Purkayastha, Ayanendranath Basu
doaj   +3 more sources

Preconditioner Design via Bregman Divergences [PDF]

SIAM Journal on Matrix Analysis and Applications
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martin S Andersen, Andreas Böck
exaly   +2 more sources

On Bregman Distances and Divergences of Probability Measures [PDF]

IEEE Transactions on Information Theory, 2012
12 two-column pages, 2 ...
Igor Vajda
exaly   +3 more sources

Curved Representational Bregman Divergences and Their Applications

Lecture Notes in Computer Science
33 pages, 11 ...
Frank Nielsen, Nielsen Frank
exaly   +3 more sources

The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning

Entropy, 2014
The aim of this paper is to develop a comprehensive study of the geometry involved in combining Bregman divergences with pooling operators over closed convex sets in a discrete probabilistic space. A particular connection we develop leads to an iterative
Martin Adamčík
exaly   +3 more sources

Maximizing the Bregman divergence from a Bregman family [PDF]

Kybernetika, 2020
11 pages, 5 theorems, no ...
Johannes Rauh, Frantisek Matús
openaire   +4 more sources