The Mathematical Structure of Information Bottleneck Methods

Entropy

Tomáš Gedeon¹  Albert E. Parker² 

[1] Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA;Center for Biofilm Engineering, Montana State University, Bozeman, MT 59717, USA; E-Mail:

关键词: information distortion;    spontaneous symmetry breaking;    bifurcations;    phase transition;   

DOI  :  10.3390/e14030456

来源: mdpi

【 摘 要 】

Information Bottleneck-based methods use mutual information as a distortion function in order to extract relevant details about the structure of a complex system by compression. One of the approaches used to generate optimal compressed representations is by annealing a parameter. In this manuscript we present a common framework for the study of annealing in information distortion problems. We identify features that should be common to any annealing optimization problem. The main mathematical tools that we use come from the analysis of dynamical systems in the presence of symmetry (equivariant bifurcation theory). Through the compression problem, we make connections to the world of combinatorial optimization and pattern recognition. The two approaches use very different vocabularies and consider different problems to be “interesting". We provide an initial link, through the Normalized Cut Problem, where the two disciplines can exchange tools and ideas.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.