The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities
Open accessAbstract
In this paper, we extend and overview wide families of Alpha-, Beta- and Gamma-divergences and discuss their fundamental properties. In literature usually only one single asymmetric (Alpha, Beta or Gamma) divergence is considered. We show in this paper that there exist families of such divergences with the same consistent properties. Moreover, we establish links and correspondences among these divergences by applying suitable nonlinear transformations. For example, we can generate the Beta-divergences directly from Alpha-divergences and vice versa. Furthermore, we show that a new wide class of Gamma-divergences can be generated not only from the family of Beta-divergences but also from a family of Alpha-divergences. The paper bridges these divergences and shows also their links to Tsallis and Rényi entropies. Most of these divergences have a natural information theoretic interpretation.
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Cites
Possible generalization of Boltzmann-Gibbs statistics
Tsallis, C. (1988) · Journal of Statistical Physics · doi:10.1007/bf01016429 · Cited by 9,589
Differential-Geometrical Methods in Statistics
Amari, S.-I. (1985) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-5056-2 · Cited by 1,673
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Millidge, B., Seth, A., & Buckley, C. L. (2021) · arXiv · doi:10.48550/arxiv.2107.12979 · Cited by 106
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Schleif, F.-M., & Tino, P. (2017) · Pattern Recognition · doi:10.1016/j.patcog.2017.06.003 · Cited by 26
Frank, S. A. (2012) · Journal of Evolutionary Biology · doi:10.1111/jeb.12010 · Cited by 21
Metadata
- Authors
- Cichocki, A., & Amari, S.-I.
- Venue
- Entropy
- Publisher
- MDPI AG
- Published
- 2010-06-14
- Volume
- 12
- Issue
- 6
- Pages
- 1532-1568
- ISSN
- 1099-4300 (ISSN-L)
- OpenAlex
- W2150070703
- Cited by
- 459
- References
- 2
- FWCI
- 13.63
- Type
- journal article
- Language
- en
- Open access
- gold
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