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Information Geometry for Random Walk
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作者 吴利萍 孙华飞 曹丽梅 《Journal of Beijing Institute of Technology》 EI CAS 2009年第3期356-360,共5页
The random walk(RW)is investigated from the viewpoint of information geometry and shown to be an exponential family distribution.It has a dual coordinate system and a dual geometric structure.Then submanifolds of RW... The random walk(RW)is investigated from the viewpoint of information geometry and shown to be an exponential family distribution.It has a dual coordinate system and a dual geometric structure.Then submanifolds of RW manifold is studied,and the e-flat hierarchical structure and the orthogonal foliations of RW manifold are obtained.Finally,using the Kullback-Leibler divergence,the projections are given from the RW manifold to its submanifolds. 展开更多
关键词 information geometry random walk hierarchical structure DIVERGENCE
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Information Geometry and Low Density Parity Check Codes
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作者 韩栋 孙华飞 阎达远 《Journal of Beijing Institute of Technology》 EI CAS 2009年第3期361-364,共4页
The application of information geometry in the low density parity check(LDPC)codes based on the work of Ikeda and Amari is considered.The method is to turn the decoding process into the change of the parameter.When ... The application of information geometry in the low density parity check(LDPC)codes based on the work of Ikeda and Amari is considered.The method is to turn the decoding process into the change of the parameter.When the LDPC decoding procedure converges,both the convergent probability distribution and the true probability distribution belong to the same submanifold,but this does not mean they are equimarginal,that points out the origin of the decoding error. 展开更多
关键词 information geometry LDPC codes euqimarginal
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Information Geometry of Positive Definite Matrices
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作者 张士诚 孙华飞 李春辉 《Journal of Beijing Institute of Technology》 EI CAS 2009年第4期484-487,共4页
A new Riemannian metric for positive definite matrices is defined and its geometric structures are investigated by means of dual connections introduced to statistical analysis by S. Amari. A few interesting results ar... A new Riemannian metric for positive definite matrices is defined and its geometric structures are investigated by means of dual connections introduced to statistical analysis by S. Amari. A few interesting results are obtained and some of those obtained by other authors are extended in our research. 展开更多
关键词 Riemannian manifold dual connection information geometry
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Information Geometry of GARCH Model
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作者 曹丽梅 孙华飞 王晓洁 《Journal of Beijing Institute of Technology》 EI CAS 2009年第2期243-246,共4页
A statistical manifold of non-exponential type coming from a model for economics describing stock return process is constructed, with its geometric structure investigated and both Gaussian curvatures and mean curvatur... A statistical manifold of non-exponential type coming from a model for economics describing stock return process is constructed, with its geometric structure investigated and both Gaussian curvatures and mean curvatures of its curved exponential submanifolds deducted. A few graphs describing relevant scalar curvature, mean curvature and Gaussian curvature are also introduced. 展开更多
关键词 information geometry GARCH model statistical manifold
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Riemann-Finsler Geometry with Applications to Information Geometry 被引量:28
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作者 Zhongmin SHEN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2006年第1期73-94,共22页
Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce Riemann-Finsler geometry, by which we establish Informat... Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce Riemann-Finsler geometry, by which we establish Information Geometry on a much broader base, so that the potential applications of Information Geometry will be beyond statistics. 展开更多
关键词 Riemann-Finsler geometry information geometry
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Information geometry in optimization,machine learning and statistical inference 被引量:1
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作者 Shun-ichi AMARI 《Frontiers of Electrical and Electronic Engineering in China》 CSCD 2010年第3期241-260,共20页
The present article gives an introduction to information geometry and surveys its applications in the area of machine learning,optimization and statistical inference.Information geometry is explained intuitively by us... The present article gives an introduction to information geometry and surveys its applications in the area of machine learning,optimization and statistical inference.Information geometry is explained intuitively by using divergence functions introduced in a manifold of probability distributions and other general manifolds.They give a Riemannian structure together with a pair of dual flatness criteria.Many manifolds are dually flat.When a manifold is dually flat,a generalized Pythagorean theorem and related projection theorem are introduced.They provide useful means for various approximation and optimization problems.We apply them to alternative minimization problems,Ying-Yang machines and belief propagation algorithm in machine learning. 展开更多
关键词 information geometry machine learning OPTIMIZATION statistical inference DIVERGENCE graphical model Ying-Yang machine
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Information geometry in neural spike sequences
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作者 Kazushi IKEDA Daisuke KOMAZAWA Hiroyuki FUNAYA 《Frontiers of Electrical and Electronic Engineering in China》 CSCD 2011年第1期146-150,共5页
An information geometrical method is developed for characterizing or classifying neurons in cortical areas whose spike rates fluctuate in time.The interspike intervals(ISIs)of a spike sequence of a neuron is modeled a... An information geometrical method is developed for characterizing or classifying neurons in cortical areas whose spike rates fluctuate in time.The interspike intervals(ISIs)of a spike sequence of a neuron is modeled as a gamma process with a time-variant spike rate,a fixed shape parameter and a fixed absolute refractory period.We formulate the problem of estimating the fixed parameters as semiparametric estimation and apply an information geometrical method to derive the optimal estimators from a statistical viewpoint. 展开更多
关键词 information geometry neural spikes semiparametric estimation interspike intervals(ISIs)
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Information Geometric Structures for the Thermodynamic Manifold
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作者 张士诚 孙华飞 李春辉 《Journal of Beijing Institute of Technology》 EI CAS 2010年第4期491-494,共4页
In view of information geometry,the state space S of thermodynamic parameters is investigated.First a Riemannian metric for S is defined and then the α-geometric structures of S is given.Some of results obtained by o... In view of information geometry,the state space S of thermodynamic parameters is investigated.First a Riemannian metric for S is defined and then the α-geometric structures of S is given.Some of results obtained by other authors are extended. 展开更多
关键词 thermodynamic manifold information geometry geometric structure
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Encoding Energy-Density as Geometry 被引量:3
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作者 Edwin Eugene Klingman 《Journal of Modern Physics》 2021年第9期1190-1209,共20页
Physicists possess an intuitive awareness of Euclidian space and time and Galilean transformation, and are then challenged with Minkowski space-time and Einstein’s curved space-time. Relativistic experiments support ... Physicists possess an intuitive awareness of Euclidian space and time and Galilean transformation, and are then challenged with Minkowski space-time and Einstein’s curved space-time. Relativistic experiments support the “time-dilation” interpretation and others support “curved space-time” interpretation. In this, and related work, we investigate the key issues in terms of the intuitive space-time frame. In particular, we provide alternative approaches to explain “time dilation” and to explain the energy density for gravity systems. We approach the latter problem from an information perspective. 展开更多
关键词 Curved Space-Time Gravitational Energy Stress-Energy Tensor Encoding information in geometry Time Dilation Equivalence Principle Minkowski Relation Schwarzschild Metric Linearized General Relativity COSMOLOGY
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Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm 被引量:1
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作者 Muhammad Shoaib Arif Mairaj Bibi Adnan Jhangir 《Computers, Materials & Continua》 SCIE EI 2018年第2期181-195,共15页
This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance between􀀀AHX􀀀XA an... This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance between􀀀AHX􀀀XA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the solution.Finally,several numerical experiments give you an idea about the effectiveness of the proposed algorithms.We also show the comparison between these two algorithms EHA and NGA.Obtained results are provided and analyzed graphically.We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature. 展开更多
关键词 information geometry algebraic lyapunov equation positive-definite hermitianmatrix manifold natural gradient algorithm extended hamiltonian algorithm
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Geometrical Structures of Certain Class of Statistical Manifolds
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作者 张真宁 孙华飞 仲锋惟 《Journal of Beijing Institute of Technology》 EI CAS 2008年第3期368-371,共4页
The geometrical structures of the certain class of statistical manifolds are investigated. The geometwhich includes the original geometrical metrics of S.Amari.
关键词 information geometry geometrical structure probability density function
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Computational implementation of a GIS developed tool for prediction of dynamic ground movement and deformation due to underground extraction sequence 被引量:3
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作者 Yue Cai Yujing Jiang +1 位作者 Baoguo Liu Ibrahim Djamaluddin 《International Journal of Coal Science & Technology》 EI 2016年第4期379-398,共20页
In the last century, there has been a significant development in the evaluation of methods to predict ground movement due to underground extraction. Some remarkable developments in three-dimensional computational meth... In the last century, there has been a significant development in the evaluation of methods to predict ground movement due to underground extraction. Some remarkable developments in three-dimensional computational methods have been supported in civil engineering, subsidence engineering and mining engineering practice. However, ground movement problem due to mining extraction sequence is effectively four dimensional (4D). A rational prediction is getting more and more important for long-term underground mining planning. Hence, computer-based analytical methods that realistically simulate spatially distributed time-dependent ground movement process are needed for the reliable long-term underground mining planning to minimize the surface environmental damages. In this research, a new computational system is developed to simulate four-dimensional (4D) ground movement by combining a stochastic medium theory, Knothe time-delay model and geographic information system (GIS) technology. All the calculations are implemented by a computational program, in which the components of GIS are used to fulfill the spatial-temporal analysis model. In this paper a tight coupling strategy based on component object model of GIS technology is used to overcome the problems of complex three-dimensional extraction model and spatial data integration. Moreover, the implementation of computational of the interfaces of the developed tool is described. The GIS based developed tool is validated by two study cases. The developed computational tool and models are achieved within the GIS system so the effective and efficient calculation methodology can be obtained, so the simulation problems of 4D ground movement due to underground mining extraction sequence can be solved by implementation of the developed tool in GIS. 展开更多
关键词 Computational model Geographical information system - Component object model - Complex mining geometry Ground deformation Surface subsidence
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A Re-Interpretation of Quasi-Local Mass 被引量:1
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作者 Edwin Eugene Klingman 《Journal of Modern Physics》 2022年第4期347-367,共21页
Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ... Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ago by Penrose, and many papers have since extended the concept. Currently there is no satisfactory physical understanding of the nature of quasi-local mass. In this paper I review the key issues, the current status, and propose an alternative interpretation of the problem of local mass and energy density for gravity systems from an information perspective. 展开更多
关键词 Quasi-Local Mass Curved Space-Time Gravitational Energy Stress-Energy Tensor Encoding information in geometry Schwarzschild Metric
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The α-Geometric Structures on Manifold of Positive Definite Hermite Matrices 被引量:2
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作者 Xiao Min DUAN Hua Fei SUN Lin Yu PENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第12期2137-2145,共9页
Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry.A Riemannian metric is defined and dual α-connections are introduced.Then the fact th... Geometric structures of a manifold of positive definite Hermite matrices are considered from the viewpoint of information geometry.A Riemannian metric is defined and dual α-connections are introduced.Then the fact that the manifold is ±l-flat is shown.Moreover,the divergence of two points on the manifold is given through dual potential functions.Furthermore,the optimal approximation of a point onto the submanifold is gotten.Finally,some simulations are given to illustrate our results. 展开更多
关键词 Positive definite Hermite matrices information geometry optimal approximation
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Articulated Estimator Random Field and Geometrical Approach Applied in System Identification
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作者 CORBIER Christophe 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2018年第5期1164-1185,共22页
A new point of view of robust statistics based on a geometrical approach is tackled in this paper. Estimation procedures are carried out from a new robust cost function based on a chaining of elementary convex norms. ... A new point of view of robust statistics based on a geometrical approach is tackled in this paper. Estimation procedures are carried out from a new robust cost function based on a chaining of elementary convex norms. This chain is randomly articulated in order to treat more efficiently natural outliers in data-set. Estimated parameters are considered as random fields and each of them, named articulated estimator random field (AERF) is a manifold or stratum of a stratified space with Riemannian geometry properties, From a high level excursion set, a probability distribution model Mata is presented and a system model validation geometric criterion (SYMOVAGEC) for system model structures Msys based on Rieeian scalar curvatures is proposed. Numerical results are drawn in a context of system identification. 展开更多
关键词 Articulated robust estimation estimators random field information geometry stratifiedspace system identification.
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