Information Geometry: An Introduction to New Models for Signal Processing

[1]  Shun-ichi Amari,et al.  Blind source separation-semiparametric statistical approach , 1997, IEEE Trans. Signal Process..

[2]  Visa Koivunen,et al.  Efficient Riemannian algorithms for optimization under unitary matrix constraint , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[3]  Mark D. Plumbley.  Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras , 2005, Neurocomputing.

[4]  Nicolas Le Bihan,et al.  Introduction to the issue on differential geometry in signal processing , 2013, IEEE J. Sel. Top. Signal Process..

[5]  Giovanni Pistone,et al.  Combinatorial Optimization with Information Geometry: The Newton Method , 2014, Entropy.

[6]  Jonathan H. Manton,et al.  On the role of differential geometry in signal processing , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[7]  Charles Casimiro Cavalcante,et al.  The Δ2-Condition and ϕ-Families of Probability Distributions , 2013, GSI.

[8]  Mark D. Plumbley.  Geometry and Manifolds for Independent Component Analysis , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[9]  Visa Koivunen,et al.  Steepest Descent Algorithms for Optimization Under Unitary Matrix Constraint , 2008, IEEE Transactions on Signal Processing.

[10]  Shun-ichi Amari,et al.  Information geometry on hierarchy of probability distributions , 2001, IEEE Trans. Inf. Theory.

[11]  Dual connections in nonparametric classical information geometry , 2001, math-ph/0104031.

[12]  Steven Thomas Smith,et al.  Geometric Optimization Methods for Adaptive Filtering , 2013, ArXiv.

[13]  Giovanni Pistone,et al.  An Infinite-Dimensional Geometric Structure on the Space of all the Probability Measures Equivalent to a Given One , 1995 .

[14]  S.T. Smith,et al.  Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds , 2005, IEEE Transactions on Signal Processing.

[15]  Rui F. Vigelis,et al.  On φ-Families of Probability Distributions , 2013 .

[16]  B. Efron.  Defining the Curvature of a Statistical Problem (with Applications to Second Order Efficiency) , 1975 .

[17]  Giovanni Pistone,et al.  Nonparametric Information Geometry , 2013, GSI.

[18]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[19]  Frank Nielsen.  Geometric Theory of Information , 2014 .

[20]  Bamdev Mishra,et al.  Manopt, a matlab toolbox for optimization on manifolds , 2013, J. Mach. Learn. Res..

[21]  C. Tsallis.  What are the Numbers that Experiments Provide , 1994 .

[22]  Visa Koivunen,et al.  Conjugate gradient algorithm for optimization under unitary matrix constraint , 2009, Signal Process..

[23]  Athanassios Manikas,et al.  Manifold studies of nonlinear antenna array geometries , 2001, IEEE Trans. Signal Process..

[24]  Giovanni Pistone,et al.  Exponential statistical manifold , 2007 .

[25]  Jonathan H. Manton,et al.  Optimization algorithms exploiting unitary constraints , 2002, IEEE Trans. Signal Process..

[26]  Frank Nielsen,et al.  Matrix Information Geometry , 2012 .

[27]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.