一类新的熵信息测度，形式群论与信息几何
A new class of entropic information measures, formal group theory and information geometry
摘要：
在这项工作中，我们研究广义熵和信息几何的群论框架。我们探讨的条件，确保存在的一些自然属性，并在同一时间的一个组理论结构的一大类熵。此外，还提出了一种使用先前已知的具有一些所需群论性质的熵来定义新熵的方法。在这项工作的第二部分中，信息几何对应的前面的建设进行了检查，并提出了一般类的分歧和研究。最后，从已知的构造新的分歧的方法进行了讨论，特别是，一些结果制定与调查中的分歧类的黎曼结构。
英文摘要：
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for a large class of entropies. In addition, a method for defining new entropies, using previously known ones with some desired group-theoretical properties is proposed. In the second part of this work, the information geometrical counterpart of the previous construction is examined and a general class of divergences are proposed and studied. Finally, a method of constructing new divergences from known ones is discussed; in particular, some results concerning the Riemannian structure associated with the class of divergences under investigation are formulated.
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