Results 151 to 160 of about 7,890 (182)

Functional Bregman divergence

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.
Maya R Gupta
exaly   +2 more sources

Clustering with Bregman Divergences

Proceedings of the 2004 SIAM International Conference on Data Mining, 2004
A 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, Srujana Merugu, Inderjit S. Dhillon, Joydeep Ghosh   +3 more
openaire   +2 more sources

Bregman Divergences and Surrogates for Learning

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009
Bartlett 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
openaire   +2 more sources

Quasiconvex Jensen Divergences and Quasiconvex Bregman Divergences

2021
We 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
openaire   +1 more source

Cost-Sensitive Sequences of Bregman Divergences

IEEE Transactions on Neural Networks and Learning Systems, 2012
The 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, Jesús Cid-Sueiro   +1 more
openaire   +3 more sources

Extending Sammon mapping with Bregman divergences

Information Sciences, 2012
The 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 ...
Jigang Sun, Colin Fyfe, Malcolm K. Crowe
openaire   +1 more source

Bregman divergences in the -partitioning problem

Computational Statistics & Data Analysis, 2006
A 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.
George Kokolakis, Ph. Nanopoulos, Dimitris Fouskakis   +2 more
openaire   +1 more source

Bregman Divergences and Multi-dimensional Scaling

2009
We 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
openaire   +1 more source

Bregman Divergences from Comparative Convexity

2017
Comparative convexity is a generalization of ordinary convexity based on abstract means instead of arithmetic means. We define and study the Bregman divergences with respect to comparative convexity. As an example, we consider the convexity induced by quasi-arithmetic means, report explicit formulas, and show that those Bregman divergences are ...
Frank Nielsen, Richard Nock
openaire   +1 more source

Information Geometry of U-Boost and Bregman Divergence

Neural Computation, 2004
We aim at an extension of AdaBoost to U-Boost, in the paradigm to build a stronger classification machine from a set of weak learning machines. A geometric understanding of the Bregman divergence defined by a generic convex function U leads to the U-Boost method in the framework of information geometry extended to the space of the finite measures over
Noboru Murata, Takashi Takenouchi, Takafumi Kanamori, Shinto Eguchi   +3 more
openaire   +3 more sources