Skip to content
Cart

Your Cart

×

You have 0 items in your cart.

Register Sign in Wishlist

Nonparametric Inference on Manifolds
With Applications to Shape Spaces

£29.99

Part of Institute of Mathematical Statistics Monographs

  • Date Published: April 2015
  • availability: Available
  • format: Paperback
  • isbn: 9781107484313

£ 29.99
Paperback

Add to cart Add to wishlist

Other available formats:
Hardback, eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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 Fréchet 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.

    • Expository appendices on differentiable manifolds, Riemannian geometry, parametric models and nonparametric Bayes theory
    • Nonparametric Bayes theory is adapted and extended to manifolds for purposes of density estimation, regression, and classification
    • Suitable for special topics courses at the graduate level
    Read more

    Reviews & endorsements

    '… this is an excellent text that will benefit many students in computer science, mathematics, and physics … A significant plus of the book is the library of MATLAB codes and datasets available for download from the authors' site.' Alexander Tzanov, Computing Reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: April 2015
    • format: Paperback
    • isbn: 9781107484313
    • length: 252 pages
    • dimensions: 230 x 152 x 13 mm
    • weight: 0.37kg
    • contains: 20 b/w illus.
    • availability: Available
  • Table of Contents

    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 Σkm
    8. The planar shape space Σk2
    9. Reflection similarity shape spaces RΣkm
    10. Stiefel manifolds
    11. Affine shape spaces AΣkm
    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 Σk2
    References
    Subject index.

  • Authors

    Abhishek Bhattacharya, Indian Statistical Institute, Kolkata
    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.

    Rabi Bhattacharya, University of Arizona
    Rabi Bhattacharya is Professor in the Department of Mathematics at the University of Arizona, Tucson.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×