Abhishek Bhattacharya

Nonparametric Inference on Manifolds (eBook, PDF)

With Applications to Shape Spaces

• Format: PDF

Produktbeschreibung

This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Frechet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicians, computer scientists, and morphometricians with mathematical training.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 5. April 2012
• Englisch
• ISBN-13: 9781139335287
• Artikelnr.: 38278273

Autorenporträt

Abhishek Bhattacharya is currently working as an assistant professor at the Indian Statistical Institute. After gaining BStat and MStat degrees from the Institute in 2002 and 2004 respectively, and a PhD from the University of Arizona in 2008, he was a postdoctoral researcher at Duke University until the end of 2010, before joining ISI in 2011. Before writing this book, he published several articles in areas as diverse as nonparametric frequentist and Bayesian statistics on non-Euclidean manifolds. All those articles can be accessed from his website.

Inhaltsangabe

1. Introduction; 2. Examples; 3. Location and spread on metric spaces; 4. Extrinsic analysis on manifolds; 5. Intrinsic analysis on manifolds; 6. Landmark-based shape spaces; 7. Kendall's similarity shape spaces
km; 8. The planar shape space
k2; 9. Reflection similarity shape spaces R
km; 10. Stiefel manifolds; 11. Affine shape spaces A
km; 12. Real projective spaces and projective shape spaces; 13. Nonparametric Bayes inference; 14. Regression, classification and testing; i. Differentiable manifolds; ii. Riemannian manifolds; iii. Dirichlet processes; iv. Parametric models on Sd and
k2; References; Subject index.