Results 81 to 90 of about 3,323 (160)
On the Centroids of Symmetrized Bregman Divergences
CoRR, 2007 In this paper, we generalize the notions of centroids and barycenters to the broad class of information-theoretic distortion measures called Bregman divergences. Bregman divergences are versatile, and unify quadratic geometric distances with various statistical entropic measures.
Frank Nielsen, Richard Nock
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Total Jensen divergences: Definition, Properties and k-Means++ Clustering
, 2013 We present a novel class of divergences induced by a smooth convex function called total Jensen divergences. Those total Jensen divergences are invariant by construction to rotations, a feature yielding regularization of ordinary Jensen divergences by a ...
Nielsen, Frank, Nock, Richard
core
Proper scoring rules and Bregman divergence
Bernoulli, 2018 We revisit the mathematical foundations of proper scoring rules (PSRs) and Bregman divergences and present their characteristic properties in a unified theoretical framework. In many situations it is preferable not to generate a PSR directly from its convex entropy on the unit simplex but instead by the sublinear extension of the entropy to the ...
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Boundary Value ProblemsFixed point theory is a rapidly developing area of mathematics that provides a unifying perspective across topology, optimization, and analysis. Classical theorems such as Brower’s, Banach’s contraction principle, Schauder’s topological theorems, and ...
Salah H. Alshabhi
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Approximation Algorithms for Bregman Co-clustering and Tensor Clustering
, 2008 In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor clustering [8,34 ...
Banerjee, Arindam +2 more
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Bregman Divergences and Triangle Inequality [PDF]
Proceedings of the 2013 SIAM International Conference on Data Mining, 2013 Sreangsu Acharyya +2 more
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Geometric Structures Induced by Deformations of the Legendre Transform. [PDF]
Entropy (Basel), 2023 Morales PA, Korbel J, Rosas FE.
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The Bregman Variational Dual-Tree Framework
, 2013 Graph-based methods provide a powerful tool set for many non-parametric frameworks in Machine Learning. In general, the memory and computational complexity of these methods is quadratic in the number of examples in the data which makes them quickly ...
Amizadeh, Saeed +2 more
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Revisiting Chernoff Information with Likelihood Ratio Exponential Families. [PDF]
Entropy (Basel), 2022 Nielsen F.
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A generalized Bayes framework for probabilistic clustering. [PDF]
Biometrika, 2023 Rigon T, Herring AH, Dunson DB.
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