Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities
Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities
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DOI：
10.3390/e12061532
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发表时间：
2010-06-01
期刊：
影响因子：
2.7
通讯作者：
Amari, Shun-ichi
中科院分区：
文献类型：
--
作者：
Cichocki, Andrzej;Amari, Shun-ichi
在本文中，我们推广和概述了广泛的家庭的α，β和γ发散，并讨论其基本性质。在文献中，通常只考虑一个单一的非对称（α，β或γ）发散。我们在本文中，存在家庭的分歧具有相同的一致性。此外，我们建立这些分歧之间的联系和对应关系，通过应用适当的非线性变换。例如，我们可以直接从α-散度生成β-散度，反之亦然.此外，我们还证明了一类新的广义Gamma-发散不仅可以由Beta-发散族生成，而且可以由Alpha-发散族生成。本文弥合这些分歧，并显示他们的联系Tsallis和Renyi熵。大多数这些分歧有一个自然的信息理论的解释。
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 Renyi entropies. Most of these divergences have a natural information theoretic interpretation.