Near Extensions and Alignment of Data in R^n: Whitney extensions of near isometries, shortest paths, equidistribution, clustering and non-rigid alignment of data in Euclidean space

Near Extensions and Alignment of Data in Rn

Comprehensive resource illustrating the mathematical richness of Whitney Extension Problems, enabling readers to develop new insights, tools, and mathematical techniques

Near Extensions and Alignment of Data in Rn demonstrates a range of hitherto unknown connections between current research problems in engineering, mathematics, and data science, exploring the mathematical richness of near Whitney Extension Problems, and presenting a new nexus of applied, pure and computational harmonic analysis, approximation theory, data science, and real algebraic geometry. For example, the book uncovers connections between near Whitney Extension Problems and the problem of alignment of data in Euclidean space, an area of considerable interest in computer vision.

Written by a highly qualified author, Near Extensions and Alignment of Data in Rn includes information on:

• Areas of mathematics and statistics, such as harmonic analysis, functional analysis, and approximation theory, that have driven significant advances in the field
• Development of algorithms to enable the processing and analysis of huge amounts of data and data sets
• Why and how the mathematical underpinning of many current data science tools needs to be better developed to be useful
• New insights, potential tools, and mathematical techniques to solve problems in Whitney extensions, signal processing, shortest paths, clustering, computer vision, optimal transport, manifold learning, minimal energy, and equidistribution

Providing comprehensive coverage of several subjects, Near Extensions and Alignment of Data in Rn is an essential resource for mathematicians, applied mathematicians, and engineers working on problems related to data science, signal processing, computer vision, manifold learning, and optimal transport.

Steven B. Damelin is a mathematical scientist having earned his BSc (Hon), Masters and PhD at the University of the Witwatersrand. His PhD advisor, Doron Lubinsky is Full Professor at Georgia Tech. His research interests include Approximation theory, Manifold Learning, Neural Science, Computer Vision, Data Science and Signal Processing having published over 77 research papers and 2 books. He has held several academic positions including Visiting Scholar at University of Michigan, IMA new Directions Professor, University of Minnesota, Full Professor at Georgia Southern University and Editor, Mathematical Reviews, American Mathematical Society. He resides in Ann Arbor, Michigan, USA.