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A recently introduced canonical divergence $mathcal{D}$ for a dual structure $(mathrm{g}, abla, abla^*)$ is discussed in connection to other divergence functions. Finally, open problems concerning symmetry properties are outlined.
In Riemannian geometry geodesics are integral curves of the Riemannian distance gradient. We extend this classical result to the framework of Information Geometry. In particular, we prove that the rays of level-sets defined by a pseudo-distance are g
We show that a Frobenius sturcture is equivalent to a dually flat sturcture in information geometry. We define a multiplication structure on the tangent spaces of statistical manifolds, which we call the statistical product. We also define a scalar q
We prove the correspondence between the information geometry of a signal filter and a Kahler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kahler manifold. The square of the complex cepst
In this paper, we introduce directed networks called `divergence network in order to perform graphical calculation of divergence functions. By using the divergence networks, we can easily understand the geometric meaning of calculation results and gr
Information divergences are commonly used to measure the dissimilarity of two elements on a statistical manifold. Differentiable manifolds endowed with different divergences may possess different geometric properties, which can result in totally diff