Nonparametric inference on manifolds : with applications to shape spaces [E-Book] / Abhishek Bhattacharya, Rabi Bhattacharya.
Bhattacharya, Abhishek, (author)
Bhattacharya, R. N., (author)
Cambridge : Cambridge University Press, 2012
1 online resource (xiii, 237 pages)
Institute of Mathematical Statistics monographs ; 2
Full Text
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490 |a Institute of Mathematical Statistics monographs ;  |v 2 
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505 0 |a Introduction -- Examples -- Location and spread on metric spaces -- Extrinsic analysis on manifolds -- Intrinsic analysis on manifolds -- Landmark-based shape spaces -- Kendall's similarity shape spaces [characters omitted] -- The planar shape space [characters omitted] -- Reflection similarity shape spaces R[characters omitted] -- Stiefel manifolds V[characters omitted] -- Affine shape spaces A[characters omitted] -- Real projective spaces and projective shape spaces -- Nonparametric Bayes inference on manifolds -- Nonparametric Bayes regression, classification and hypothesis testing on manifolds -- Appendixes: A. Differentiable manifolds -- B. Riemannian manifolds -- C. Dirichlet processes -- D. Parametric models on S[character omitted] and [characters omitted]. 
520 |a 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. 
650 0 |a Nonparametric statistics. 
650 0 |a Manifolds (Mathematics) 
700 1 |a Bhattacharya, R. N.,  |e author 
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