Results 21 to 30 of about 3,323 (160)
Comptes Rendus. Mécanique, 2023 With view on the context of convex thermomechanics, we propose tools based on the concept of Bregman divergence, a notion introduced in the 1960s and used in learning and optimization as well. This study is motivated by the need of “discrepancy measures”
Andrieux, Stéphane
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Hyperlink regression via Bregman divergence [PDF]
Neural Networks, 2020 41 pages, 14 ...
Akifumi Okuno, Hidetoshi Shimodaira
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Beta-Divergence as a Subclass of Bregman Divergence [PDF]
IEEE Signal Processing Letters, 2011 In this paper, we present a complete proof that the β-divergence is a particular case of Bregman divergence. This little-known result makes it possible to straightforwardly apply theorems about Bregman divergences to β-divergences. This is of interest for numerous applications since these divergences are widely used, for instance in non-negative matrix
Romain Hennequin +2 more
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Convergence Rates of Gradient Methods for Convex Optimization in the Space of Measures
Open Journal of Mathematical Optimization, 2023 We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in $O(\log (k)k^{-1 ...
Chizat, Lénaïc
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Bregman Voronoi Diagrams: Properties, Algorithms and Applications [PDF]
, 2007 The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others.
A. Banerjee +33 more
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Algorithms, 2022 The family of α-divergences including the oriented forward and reverse Kullback–Leibler divergences is often used in signal processing, pattern recognition, and machine learning, among others.
Frank Nielsen
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Non-flat clustering whith alpha-divergences [PDF]
, 2011 International audienceThe scope of the well-known $k$-means algorithm has been broadly extended with some recent results: first, the k-means++ initialization method gives some approximation guarantees; second, the Bregman k-means algorithm generalizes ...
Nielsen, Frank, Schwander, Olivier
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Worst-case and smoothed analysis of k-means clustering with Bregman divergences
Journal of Computational Geometry, 2013 The k-means method is the method of choice for clustering large-scale data sets and it performs exceedingly well in practice despite its exponential worst-case running-time.
Bodo Manthey, Heiko Roeglin
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The Burbea-Rao and Bhattacharyya centroids [PDF]
, 2011 We study the centroid with respect to the class of information-theoretic Burbea-Rao divergences that generalize the celebrated Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and differentiable ...
Frank Nielsen +2 more
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Maps on positive definite matrices preserving Bregman and Jensen divergences [PDF]
, 2015 In this paper we determine those bijective maps of the set of all positive definite $n\times n$ complex matrices which preserve a given Bregman divergence corresponding to a differentiable convex function that satisfies certain conditions.
Molnár, Lajos +2 more
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