Geometry of Information Integration
Information Theory
2017-09-08 v1 math.IT
Abstract
Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and information transmission between the parts is removed. Multiple measures have been proposed as a measure of integrated information. Here, we analyze four of the previously proposed measures and elucidate their relations from a viewpoint of information geometry. Two of them use dually flat manifolds and the other two use curved manifolds to define a split model. We show that there are hierarchical structures among the measures. We provide explicit expressions of these measures.
Keywords
Cite
@article{arxiv.1709.02050,
title = {Geometry of Information Integration},
author = {Shun-ichi Amari and Naotsugu Tsuchiya and Masafumi Oizumi},
journal= {arXiv preprint arXiv:1709.02050},
year = {2017}
}