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Equivalence of Informations Characterizes Bregman Divergences [PDF]
EntropyBregman divergences form a class of distance-like comparison functions which plays fundamental roles in optimization, statistics, and information theory.
Philip S. Chodrow
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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 +4 more
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The Bregman chord divergence [PDF]
, 2018 Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor.
A Banerjee +25 more
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Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence [PDF]
Entropy, 2018 This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices ...
Xiaoqiang Hua +3 more
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Upper and lower bounds for the Bregman divergence [PDF]
Journal of Inequalities and Applications, 2019 In this paper we study upper and lower bounds on the Bregman divergence ΔFξ(y,x):=F(y)−F(x)−〈ξ,y−x〉 $\Delta_{\mathcal {F}}^{\xi }(y,x):=\mathcal {F}(y)-\mathcal {F}(x)- \langle \xi , y-x \rangle$ for some convex functional F $\mathcal {F}$ on a normed ...
Benjamin Sprung
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Wireless Sensor Network Localization via Matrix Completion Based on Bregman Divergence [PDF]
Sensors, 2018 One of the main challenges faced by wireless sensor network (WSN) localization is the positioning accuracy of the WSN node. The existing algorithms are arduous to use for dealing with the pulse noise that is universal and ineluctable in practical ...
Chunsheng Liu, Hong Shan, Bin Wang
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Tight Bounds Between the Jensen–Shannon Divergence and the Minmax Divergence [PDF]
EntropyMotivated by questions arising at the intersection of information theory and geometry, we compare two dissimilarity measures between finite categorical distributions.
Arseniy Akopyan +3 more
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Symplectic Bregman Divergences. [PDF]
Entropy (Basel)We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel–Young inequality which relies on the notion of symplectic subdifferentials.
Nielsen F.
europepmc +5 more sources
Topological Data Analysis with Bregman Divergences [PDF]
, 2016 Given a finite set in a metric space, the topological analysis generalizes hierarchical clustering using a 1-parameter family of homology groups to quantify connectivity in all dimensions.
Edelsbrunner, Herbert, Wagner, Hubert
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Multivariate Time Series Change-Point Detection with a Novel Pearson-like Scaled Bregman Divergence [PDF]
StatsChange-point detection is a challenging problem that has a number of applications across various real-world domains. The primary objective of CPD is to identify specific time points where the underlying system undergoes transitions between different ...
Tong Si +5 more
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