Computational Information Geometry: For Image and Signal Processing

Description

This book focuses on the application and development of information geometric methods in the analysis, classification and retrieval of images and signals. It provides introductory chapters to help those new to information geometry and applies the theory to several applications. This area has developed rapidly over recent years, propelled by the major theoretical developments in information geometry, efficient data and image acquisition and the desire to process and interpret large databases of digital information. The book addresses both the transfer of methodology to practitioners involved in database analysis and in its efficient computational implementation. Front Matter....Pages i-xii Information Geometry and Its Applications: An Overview....Pages 1-31 Towards the Geometry of Model Sensitivity: An Illustration....Pages 33-62 On the Geometric Interplay Between Goodness-of-Fit and Estimation: Illustrative Examples....Pages 63-77 Spontaneous Learning for Data Distributions via Minimum Divergence....Pages 79-99 Extrinsic Projection of Itô SDEs on Submanifolds with Applications to Non-linear Filtering....Pages 101-120 Fast \((1+\epsilon )\) -Approximation of the Löwner Extremal Matrices of High-Dimensional Symmetric Matrices....Pages 121-132 Dimensionality Reduction for Information Geometric Characterization of Surface Topographies....Pages 133-147 On Clustering Financial Time Series: A Need for Distances Between Dependent Random Variables....Pages 149-174 The Geometry of Orthogonal-Series, Square-Root Density Estimators: Applications in Computer Vision and Model Selection....Pages 175-215 Dimensionality Reduction for Measure Valued Evolution Equations in Statistical Manifolds....Pages 217-265 Batch and Online Mixture Learning: A Review with Extensions....Pages 267-299