https://elib.bsu.by:443/handle/123456789/267407 NPCS Vol.23, no.2 (2020), pp. 102-253 Mon, 20 Apr 2026 01:20:01 GMT 2026-04-20T01:20:01Z https://elib.bsu.by:443/handle/123456789/267549 Заглавие документа: Using the Alpha Geodesic Distance in Shapes K-Means Clustering Авторы: Oikonomou, F. D.; Sanctis, A. De Аннотация: This paper is based mainly on the relevant work [1]. In that paper the authors studied the problem of clustering of different shapes using Information Geometry tools including, among others, the Fisher Information and the resulting distance. Here we are using the same methods but for the geodesics of the alpha connection for three different values of the alpha parameter. Wed, 01 Jan 2020 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/267549 2020-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/267547 Заглавие документа: Information Geometry Tools for Shape Analysis Авторы: Sanctis, A. De; Gattone, S. A. Аннотация: In this work, the use of Information Geometry tools in Shape Analysis is investigated. Landmarks of complex shapes are represented as probability distributions in a statistical manifold where geodesics with respect to different Riemannian metrics could be defined. Geodesics are considered both for studying the shape evolution in time and for deriving shape distances to be used in shape clustering. Wed, 01 Jan 2020 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/267547 2020-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/267546 Заглавие документа: Information Geometry of the Probability Simplex: A Short Course Авторы: Pistone, G. Аннотация: This set of notes is intended for a short course aiming to provide an (almost) self-contained and (almost) elementary introduction to the topic of Information Geometry (IG) of the probability simplex. Such a course can be considered an introduction to the original monograph by Amari and Nagaoka [1], and to the recent monographs by Amari [2] and by Ay, Jost, L˄e, and Schwachh¨ofer [3]. The focus is on a non-parametric approach, that is, I consider the geometry of the full probability simplex and compare the IG formalism with what is classically done in Statistical Physics. Wed, 01 Jan 2020 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/267546 2020-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/267545 Заглавие документа: From Complexity to Information Geometry and Beyond Авторы: Ghikas, D. P. K. Аннотация: Complex Systems are ubiquitous in nature and man-made systems. In natural sciences, in social and economic models and in mathematical constructions are studied and analyzed, are applied in practical problems but without a clear and universal definition of ”complexity”, let alone classification and quantification. Following the "three-level scheme" of physical theories, observations/experiments, phenomenology, microscopic interactions, we need, starting from the experience of observation to establish appropriate phenomenological parameters and concepts, and in conjunction with a possible knowledge of the nature of microscopic structures to deepen our understanding of a particular system which we ”understand as complex”. Information Geometry seems to be a useful phenomenological framework, which using generalized entropies, provides some classification and quantification tools. But we need the next level, microscopic structure and interactions of the parts of complex systems. A useful direction is the conceptual niche of hyper-networks and super graphs, where a strong involvement of algebra offers concrete techniques. We believe that appropriate algebraic structures may systematize our approach to microscopic structures of complex systems, and help associate the information geometric phenomenology with concrete properties. In this paper after a short discussion of the problem of ”definition of complexity”, we introduce our information geometric quantities derived from generalized entropies. Then we present our results of application of information geometry for classification of complex systems. Finally we present our ideas for an abstract algebraic approach which may offer a framework for the microscopic study of complex systems. Wed, 01 Jan 2020 00:00:00 GMT https://elib.bsu.by:443/handle/123456789/267545 2020-01-01T00:00:00Z