Book 2013

Matrix Information Geometry


ISBN: 978-3-642-30231-2 (Print) 978-3-642-30232-9 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xii

  2. State-of-the-art surveys & original matrix theory work:

    1. Front Matter

      Pages 1-1

    2. Chapter

      Pages 3-33

      Supremum/Infimum and Nonlinear Averaging of Positive Definite Symmetric Matrices

    3. Chapter

      Pages 35-51

      The Riemannian Mean of Positive Matrices

    4. Chapter

      Pages 53-68

      The Geometry of Low-Rank Kalman Filters

    5. Chapter

      Pages 69-92

      KV Cohomology in Information Geometry

    6. Chapter

      Pages 93-109

      Derivatives of Multilinear Functions of Matrices

    7. Chapter

      Pages 111-122

      Jensen Divergence-Based Means of SPD Matrices

    8. Chapter

      Pages 123-166

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

  3. Advanced matrix theory for radar processing:

    1. Front Matter

      Pages 167-167

    2. Chapter

      Pages 169-197

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

    3. Chapter

      Pages 199-255

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

    4. Chapter

      Pages 257-276

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

    5. Chapter

      Pages 277-290

      Doppler Information Geometry for Wake Turbulence Monitoring

  4. Matrix-based signal processing applications:

    1. Front Matter

      Pages 291-291

    2. Chapter

      Pages 293-321

      Review of the Application of Matrix Information Theory in Video Surveillance

    3. Chapter

      Pages 323-340

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

    4. Chapter

      Pages 341-371

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

    5. Chapter

      Pages 373-402

      Mining Matrix Data with Bregman Matrix Divergences for Portfolio Selection

    6. Chapter

      Pages 403-426

      Learning Mixtures by Simplifying Kernel Density Estimators

    7. Chapter

      Pages 427-449

      Particle Filtering on Riemannian Manifolds. Application to Covariance Matrices Tracking

  5. Back Matter

    Pages 451-454