Symplectic Bregman Divergences [PDF]
EntropyWe 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 ...
Frank Nielsen
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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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Block-Active ADMM to Minimize NMF with Bregman Divergences [PDF]
Sensors, 2023 Over the last ten years, there has been a significant interest in employing nonnegative matrix factorization (NMF) to reduce dimensionality to enable a more efficient clustering analysis in machine learning.
Xinyao Li, Akhilesh Tyagi
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Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences [PDF]
Entropy, 2022 By calculating the Kullback–Leibler divergence between two probability measures belonging to different exponential families dominated by the same measure, we obtain a formula that generalizes the ordinary Fenchel–Young divergence.
Frank Nielsen
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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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On Voronoi Diagrams on the Information-Geometric Cauchy Manifolds [PDF]
Entropy, 2020 We study the Voronoi diagrams of a finite set of Cauchy distributions and their dual complexes from the viewpoint of information geometry by considering the Fisher-Rao distance, the Kullback-Leibler divergence, the chi square divergence, and a flat ...
Frank Nielsen
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Divergences Induced by the Cumulant and Partition Functions of Exponential Families and Their Deformations Induced by Comparative Convexity [PDF]
EntropyExponential families are statistical models which are the workhorses in statistics, information theory, and machine learning, among others. An exponential family can either be normalized subtractively by its cumulant or free energy function, or ...
Frank Nielsen
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On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid [PDF]
Entropy, 2020 The Jensen−Shannon divergence is a renown bounded symmetrization of the Kullback−Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the scalar
Frank Nielsen
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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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Adaptive Mixture Methods Based on Bregman Divergences [PDF]
Digital Signal Processing, 2012 We investigate adaptive mixture methods that linearly combine outputs of $m$ constituent filters running in parallel to model a desired signal. We use "Bregman divergences" and obtain certain multiplicative updates to train the linear combination weights
Arenas-Garcia +21 more
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