Matrix information geometry

Front Matter....Pages i-xii
Front Matter....Pages 1-1
Supremum/Infimum and Nonlinear Averaging of Positive Definite Symmetric Matrices....Pages 3-33
The Riemannian Mean of Positive Matrices....Pages 35-51
The Geometry of Low-Rank Kalman Filters....Pages 53-68
KV Cohomology in Information Geometry....Pages 69-92
Derivatives of Multilinear Functions of Matrices....Pages 93-109
Jensen Divergence-Based Means of SPD Matrices....Pages 111-122
Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups....Pages 123-166
Front Matter....Pages 167-167
Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation....Pages 169-197
Information Geometry of Covariance Matrix: Cartan-Siegel Homogeneous Bounded Domains, Mostow/Berger Fibration and Fréchet Median....Pages 199-255
On the Use of Matrix Information Geometry for Polarimetric SAR Image Classification....Pages 257-276
Doppler Information Geometry for Wake Turbulence Monitoring....Pages 277-290
Front Matter....Pages 291-291
Review of the Application of Matrix Information Theory in Video Surveillance....Pages 293-321
Comparative Evaluation of Symmetric SVD Algorithms for Real-Time Face and Eye Tracking....Pages 323-340
Real-Time Detection of Overlapping Sound Events with Non-Negative Matrix Factorization....Pages 341-371
Mining Matrix Data with Bregman Matrix Divergences for Portfolio Selection....Pages 373-402
Learning Mixtures by Simplifying Kernel Density Estimators....Pages 403-426
Particle Filtering on Riemannian Manifolds. Application to Covariance Matrices Tracking....Pages 427-449
Back Matter....Pages 451-454