Standard divergence in manifold of dual affine connections

Publikationstyp
Conference Paper
Date Issued
2015-10
Sprache
English
Author(s)
Amari, Shun'ichi  
Ay, Nihat 
TORE-URI
http://hdl.handle.net/11420/14097
First published in
Lecture notes in computer science  
Number in series
9389 LNIP
Start Page
320
End Page
325
Citation
Lecture Notes in Computer Science 9389 LNIP: 320-325 (2015)
Contribution to Conference
2nd International Conference on Geometric Science of Information, GSI 2015  
Publisher DOI
10.1007/978-3-319-25040-3_35
Scopus ID
2-s2.0-84950324601
Publisher
Springer
A divergence function defines a Riemannian metric G and dually coupled affine connections (∇,∇∗) with respect to it in a manifold M. When M is dually flat, a canonical divergence is known, which is uniquely determined from G,∇,∇∗. We search for a standard divergence for a general non-flat M. It is introduced by the magnitude of the inverse exponential map, where α = −(1/3) connection plays a fundamental role. The standard divergence is different from the canonical divergence.
DDC Class
004: Informatik
510: Mathematik