{"product_id":"nonparametric-inference-on-manifolds-with-applications-to-shape-spaces-paperback-9781107484313","title":"Nonparametric Inference on Manifolds; With Applications to Shape Spaces (Paperback \/ softback) 9781107484313","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eNonparametric Inference on Manifolds\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eWith Applications to Shape Spaces\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eA systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAbhishek Bhattacharya (Author), Rabi Bhattacharya (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107484313, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 9 April 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e252 pages, 20 b\/w illus.\u003cbr\u003e23 x 15.2 x 1.3 cm, 0.37 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'… 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\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. Examples\u003cbr\u003e 3. Location and spread on metric spaces\u003cbr\u003e 4. Extrinsic analysis on manifolds\u003cbr\u003e 5. Intrinsic analysis on manifolds\u003cbr\u003e 6. Landmark-based shape spaces\u003cbr\u003e 7. Kendall's similarity shape spaces ?km\u003cbr\u003e 8. The planar shape space ?k2\u003cbr\u003e 9. Reflection similarity shape spaces R?km\u003cbr\u003e 10. Stiefel manifolds\u003cbr\u003e 11. Affine shape spaces A?km\u003cbr\u003e 12. Real projective spaces and projective shape spaces\u003cbr\u003e 13. Nonparametric Bayes inference\u003cbr\u003e 14. Regression, classification and testing\u003cbr\u003e i. Differentiable manifolds\u003cbr\u003e ii. Riemannian manifolds\u003cbr\u003e iii. Dirichlet processes\u003cbr\u003e iv. Parametric models on Sd and ?k2\u003cbr\u003e References\u003cbr\u003e Subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265749799192,"sku":"9781107484313","price":31.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107484313i_df5dde61-9874-4df9-9b79-4870d244216f.jpg?v=1696754691","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/nonparametric-inference-on-manifolds-with-applications-to-shape-spaces-paperback-9781107484313","provider":"Freshly Printed Books","version":"1.0","type":"link"}