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Cost-Sensitive Sequences of Bregman Divergences
IEEE Transactions on Neural Networks and Learning Systems, 2012The minimization of the empirical risk based on an arbitrary Bregman divergence is known to provide posterior class probability estimates in classification problems, but the accuracy of the estimate for a given value of the true posterior depends on the specific choice of the divergence.
Raúl Santos-Rodríguez +1 more
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Clustering with Bregman Divergences
Proceedings of the 2004 SIAM International Conference on Data Mining, 2004A wide variety of distortion functions, such as squared Euclidean distance, Mahalanobis distance, Itakura-Saito distance and relative entropy, have been used for clustering. In this paper, we propose and analyze parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences.
Arindam Banerjee 0001 +3 more
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2008 IEEE International Symposium on Information Theory, 2008
To characterize the differences between two positive functions or two distributions, a class of distortion functions has recently been defined termed the functional Bregman divergences. The class generalizes the standard Bregman divergence defined for vectors, and includes total squared difference and relative entropy.
Bela A. Frigyik +2 more
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To characterize the differences between two positive functions or two distributions, a class of distortion functions has recently been defined termed the functional Bregman divergences. The class generalizes the standard Bregman divergence defined for vectors, and includes total squared difference and relative entropy.
Bela A. Frigyik +2 more
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Bregman Divergences and Surrogates for Learning
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009Bartlett et al. (2006) recently proved that a ground condition for surrogates, classification calibration, ties up their consistent minimization to that of the classification risk, and left as an important problem the algorithmic questions about their minimization.
Richard Nock, Frank Nielsen
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Quasiconvex Jensen Divergences and Quasiconvex Bregman Divergences
2021We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are asymmetric distances, and study some of their properties. We then define the strictly quasiconvex Bregman divergences as the limit case of scaled and skewed quasiconvex Jensen divergences, and report a simple closed-form formula which shows that ...
Frank Nielsen, Gaëtan Hadjeres
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Extending Sammon mapping with Bregman divergences
Information Sciences, 2012The Sammon mapping has been one of the most successful nonlinear metric multidimensional scaling methods since its advent in 1969, but effort has been focused on algorithm improvement rather than on the form of the stress function. This paper further investigates using left Bregman divergences to extend the Sammon mapping and by analogy develops right ...
Colin Fyfe, Malcolm Crowe
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Bregman divergences in the -partitioning problem
Computational Statistics and Data Analysis, 2006A method of fixed cardinality partition is examined. This methodology can be applied on many problems, such as the confidentiality protection, in which the protection of confidential information has to be ensured, while preserving the information content of the data.
Dimitris Fouskakis
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Preconditioner Design via Bregman Divergences [PDF]
SIAM Journal on Matrix Analysis and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreas A Böck, Martin S Andersen
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Cost-Sensitive Learning Based on Bregman Divergences [PDF]
Lecture Notes in Computer Science, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Raúl Santos-Rodríguez +2 more
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Bregman Divergences and Multi-dimensional Scaling
2009We discuss Bregman divergences and the very close relationship between a class of these divergences and the regular family of exponential distributions before applying them to various topology preserving dimension reducing algorithms. We apply these to multidimensional scaling (MDS) and show the effect of different Bregman divergences. In particular we
Pei Ling Lai, Colin Fyfe
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