Clustering with Bregman Divergences

Summary

This paper proposes and analyzes parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences, and shows that there is a bijection between regular exponential families and a largeclass of BRegman diverGences, that is called regular Breg man divergence.

Keywords

Cluster analysis, Library science, Mahalanobis distance, Computer science, Artificial intelligence

References

Pattern ClassificationShigeo Abe — 2012
Scaling Clustering Algorithms to Large DatabasesPatricia Bradley, Usama M. Fayyad, Cory Reina — 1998
Information Theory: 1948-1998 - Guest EditorialSergio Verdú — 1998
Duality and Auxiliary Functions for Bregman DistancesS. Della Pietra, V. Della Pietra, John Lafferty — 2001
Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of DistributionsKaty S. Azoury, Manfred K. Warmuth — 1999
The representation of functions as a Laplace-Stieltjes integralsAllen Devinatz — 1955
Impact of Similarity Measures on Web-page ClusteringAlexander L. Strehl, Joydeep Ghosh, Raymond J. Mooney — 2000
Kolmogorov Complexity and Information Theory. With an Interpretation in Terms of Questions and AnswersPeter Grünwald, Paul Vitányi — 2003
Methods of information geometryШун-ичи Амари, Hiroshi Nagaoka — 2000
Harmonic Analysis on Semigroups: Theory of Positive Definite and Related FunctionsChristian Berg, Jens Peter Christensen, Paul Ressel — 1984
Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theoryPeter Grünwald, A. P. Dawid — 2004
Rate distortion theory : a mathematical basis for data compressionToby Berger — 1971
Vector quantization and signal compressionA. Gersho, Robert M. Gray — 1991
Generalized projections for non-negative functionsImre Csiszár — 1995
Spectral distance measures between Gaussian processesD. Kazakos, P. Papantoni‐Kazakos — 1980
Feature Weighting in k-Means ClusteringDharmendra S. Modha, W. Scott Spangler — 2003
Algorithms for Clustering DataWarren S. Sarle, Anil K. Jain, Richard C. Dubes — 1988
Mixture densities, maximum likelihood, and the EM algorithmRichard A. Redner, Homer F. Walker — 1984
ON ENTROPY RATES OF DYNAMICAL SYSTEMS AND GAUSSIAN PROCESSESMilan Paluš — 1997
A modern approach to probability theoryBert Fristedt, Lawrence Gray — 1996

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An Introduction to Functional DerivativesA. Frigyik, Santosh Kumar Srivastava, Maya R. Gupta — 2008
Transductive De-Noising and Dimensionality Reduction using Total Bregman RegressionSreangsu Acharyya — 2006
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Learning in modular systemsJ. Andrew Bagnell, David M. Bradley — 2010
Hardness and Non-Approximability of Bregman Clustering ProblemsMarcel R. Ackermann, Johannes Blömer, Christoph Scholz — 2011
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