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Matrix Information Geometry

  • Book
  • © 2013

Overview

Editors:
  1. Frank Nielsen

    1. Shinagawa-Ku, Japan

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    You can also search for this editor in PubMed   Google Scholar

  2. Rajendra Bhatia

    1. Delhi, India

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    You can also search for this editor in PubMed   Google Scholar

  • Presents advances in matrix and tensor data processing in the domain of signal, image and information processing
  • Written by experts in the areas of theoretical mathematics or engineering sciences
  • Discusses potential applications in sensor and cognitive systems engineering
  • Includes supplementary material: sn.pub/extras

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xii
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  2. State-of-the-Art Surveys and Original Matrix Theory Work

    1. Front Matter

      Pages 1-1
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  3. State-of-the-art surveys & original matrix theory work:

    1. Supremum/Infimum and Nonlinear Averaging of Positive Definite Symmetric Matrices

      • Jesús Angulo
      Pages 3-33

    2. The Riemannian Mean of Positive Matrices

      • Rajendra Bhatia
      Pages 35-51

    3. The Geometry of Low-Rank Kalman Filters

      • Silvère Bonnabel, Rodolphe Sepulchre
      Pages 53-68

    4. KV Cohomology in Information Geometry

      • Michel Nguiffo Boyom, Paul Mirabeau Byande
      Pages 69-92

    5. Derivatives of Multilinear Functions of Matrices

      • Priyanka Grover
      Pages 93-109

    6. Jensen Divergence-Based Means of SPD Matrices

      • Frank Nielsen, Meizhu Liu, Baba C. Vemuri
      Pages 111-122

    7. Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups

      • Xavier Pennec, Vincent Arsigny
      Pages 123-166

  4. Advanced Matrix Theory for Radar Processing

    1. Front Matter

      Pages 167-167
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  5. Advanced matrix theory for radar processing:

    1. Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation

      • Marc Arnaudon, Frédéric Barbaresco, Le Yang
      Pages 169-197

    2. Information Geometry of Covariance Matrix: Cartan-Siegel Homogeneous Bounded Domains, Mostow/Berger Fibration and Fréchet Median

      • Frédéric Barbaresco
      Pages 199-255

    3. On the Use of Matrix Information Geometry for Polarimetric SAR Image Classification

      • Pierre Formont, Jean-Philippe Ovarlez, Frédéric Pascal
      Pages 257-276

    4. Doppler Information Geometry for Wake Turbulence Monitoring

      • Zhongxun Liu, Frédéric Barbaresco
      Pages 277-290

  6. Matrix-Based Signal Processing Applications

    1. Front Matter

      Pages 291-291
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  7. Matrix-based signal processing applications:

    1. Review of the Application of Matrix Information Theory in Video Surveillance

      • M K Bhuyan, Malathi T
      Pages 293-321

    2. Comparative Evaluation of Symmetric SVD Algorithms for Real-Time Face and Eye Tracking

      • Tapan Pradhan, Aurobinda Routray, Bibek Kabi
      Pages 323-340

    3. Real-Time Detection of Overlapping Sound Events with Non-Negative Matrix Factorization

      • Arnaud Dessein, Arshia Cont, Guillaume Lemaitre
      Pages 341-371

    4. Mining Matrix Data with Bregman Matrix Divergences for Portfolio Selection

      • Richard Nock, Brice Magdalou, Eric Briys, Frank Nielsen
      Pages 373-402

    5. Learning Mixtures by Simplifying Kernel Density Estimators

      • Olivier Schwander, Frank Nielsen
      Pages 403-426
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Keywords

About this book

This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems engineering.
The topics and application include Information Geometry, Differential Geometry of structured Matrix, Positive Definite Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and  Applications in Cognitive systems, in particular Data Mining.

Editors and Affiliations

  • Shinagawa-Ku, Japan

    Frank Nielsen

  • Delhi, India

    Rajendra Bhatia

About the editors

Frank Nielsen is Senior Researcher at Sony Computer Science Laboratories Inc, Tokyo, Japan.
He is conducting research on information sciences for data analytics based on the framework of computational information geometry  with applications in visual computing.
He has authored more than hundred research papers and two books including "Visual Computing: Geometry, Graphics, and Vision".

Rajendra Bhatia is Professor of Mathematics at the Indian Statistical Institute in New Delhi, India.
He is the author of five books including "Matrix Analysis" and "Positive Definite Matrices"..

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