Ebook: Matrix Information Geometry
- Tags: Signal Image and Speech Processing, Linear and Multilinear Algebras Matrix Theory, Data Mining and Knowledge Discovery, Mathematical Applications in Computer Science, Remote Sensing/Photogrammetry
- Year: 2013
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Content:
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 Fr?chet 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
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Content:
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 Fr?chet 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
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