GENERALIZED PRINCIPAL COMPONENT ANALYSIS INTERDISCIPLINARY APPLIED MATHEMATICS

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Generalized Principal Component Analysis

Author : René Vidal
ISBN : 9780387878119
Genre : Science
File Size : 35.34 MB
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This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.
Category: Science

A User S Guide To Principal Components

Author : J. Edward Jackson
ISBN : 9780471725329
Genre : Mathematics
File Size : 87.62 MB
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WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. From the Reviews of A User’s Guide to Principal Components "The book is aptly and correctly named–A User’s Guide. It is the kind of book that a user at any level, novice or skilled practitioner, would want to have at hand for autotutorial, for refresher, or as a general-purpose guide through the maze of modern PCA." –Technometrics "I recommend A User’s Guide to Principal Components to anyone who is running multivariate analyses, or who contemplates performing such analyses. Those who write their own software will find the book helpful in designing better programs. Those who use off-the-shelf software will find it invaluable in interpreting the results." –Mathematical Geology
Category: Mathematics

Principal Component Analysis

Author : I.T. Jolliffe
ISBN : 9781475719048
Genre : Mathematics
File Size : 31.98 MB
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Principal component analysis is probably the oldest and best known of the It was first introduced by Pearson (1901), techniques ofmultivariate analysis. and developed independently by Hotelling (1933). Like many multivariate methods, it was not widely used until the advent of electronic computers, but it is now weIl entrenched in virtually every statistical computer package. The central idea of principal component analysis is to reduce the dimen sionality of a data set in which there are a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This reduction is achieved by transforming to a new set of variables, the principal components, which are uncorrelated, and which are ordered so that the first few retain most of the variation present in all of the original variables. Computation of the principal components reduces to the solution of an eigenvalue-eigenvector problem for a positive-semidefinite symmetrie matrix. Thus, the definition and computation of principal components are straightforward but, as will be seen, this apparently simple technique has a wide variety of different applications, as weIl as a number of different deri vations. Any feelings that principal component analysis is a narrow subject should soon be dispelled by the present book; indeed some quite broad topics which are related to principal component analysis receive no more than a brief mention in the final two chapters.
Category: Mathematics

Manifold Learning Theory And Applications

Author : Yunqian Ma
ISBN : 9781466558878
Genre : Business & Economics
File Size : 83.8 MB
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Trained to extract actionable information from large volumes of high-dimensional data, engineers and scientists often have trouble isolating meaningful low-dimensional structures hidden in their high-dimensional observations. Manifold learning, a groundbreaking technique designed to tackle these issues of dimensionality reduction, finds widespread application in machine learning, neural networks, pattern recognition, image processing, and computer vision. Filling a void in the literature, Manifold Learning Theory and Applications incorporates state-of-the-art techniques in manifold learning with a solid theoretical and practical treatment of the subject. Comprehensive in its coverage, this pioneering work explores this novel modality from algorithm creation to successful implementation—offering examples of applications in medical, biometrics, multimedia, and computer vision. Emphasizing implementation, it highlights the various permutations of manifold learning in industry including manifold optimization, large scale manifold learning, semidefinite programming for embedding, manifold models for signal acquisition, compression and processing, and multi scale manifold. Beginning with an introduction to manifold learning theories and applications, the book includes discussions on the relevance to nonlinear dimensionality reduction, clustering, graph-based subspace learning, spectral learning and embedding, extensions, and multi-manifold modeling. It synergizes cross-domain knowledge for interdisciplinary instructions, offers a rich set of specialized topics contributed by expert professionals and researchers from a variety of fields. Finally, the book discusses specific algorithms and methodologies using case studies to apply manifold learning for real-world problems.
Category: Business & Economics

Principal Component Analysis Handbook

Author : Rebecca Cross
ISBN : 1632404168
Genre : Mathematics
File Size : 65.75 MB
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This book on Principal component analysis (PCA) is a significant contribution to the field of data analysis. PCA involves a statistical procedure which orthogonally transforms a set of possibly correlated observations into set of values of linearly uncorrelated variables called principal components. The aim of this book is to enhance knowledge of scientists, engineers and researchers regarding the advantages of this technique in data analysis and includes information on the uses of PCA in distinct fields like multi-sensor data fusion, ecology, energy, agriculture, climate, image and video processing, gas chromatographic examination, color coating, materials science and automatic target identification.
Category: Mathematics

Interdisciplinary Topics In Applied Mathematics Modeling And Computational Science

Author : Monica Cojocaru
ISBN : 9783319123073
Genre : Computers
File Size : 42.33 MB
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The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26—30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics and its areas of applications.
Category: Computers

Fundamentals Of Two Fluid Dynamics

Author : Daniel D. Joseph
ISBN : 9781461570615
Genre : Mathematics
File Size : 50.49 MB
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Two-fluid dynamics is a challenging subject rich in physics and prac tical applications. Many of the most interesting problems are tied to the loss of stability which is realized in preferential positioning and shaping of the interface, so that interfacial stability is a major player in this drama. Typically, solutions of equations governing the dynamics of two fluids are not uniquely determined by the boundary data and different configurations of flow are compatible with the same data. This is one reason why stability studies are important; we need to know which of the possible solutions are stable to predict what might be observed. When we started our studies in the early 1980's, it was not at all evident that stability theory could actu ally work in the hostile environment of pervasive nonuniqueness. We were pleasantly surprised, even astounded, by the extent to which it does work. There are many simple solutions, called basic flows, which are never stable, but we may always compute growth rates and determine the wavelength and frequency of the unstable mode which grows the fastest. This proce dure appears to work well even in deeply nonlinear regimes where linear theory is not strictly valid, just as Lord Rayleigh showed long ago in his calculation of the size of drops resulting from capillary-induced pinch-off of an inviscid jet.
Category: Mathematics

Molecular Modeling And Simulation

Author : Tamar Schlick
ISBN : 9780387224640
Genre : Science
File Size : 58.65 MB
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Very broad overview of the field intended for an interdisciplinary audience; Lively discussion of current challenges written in a colloquial style; Author is a rising star in this discipline; Suitably accessible for beginners and suitably rigorous for experts; Features extensive four-color illustrations; Appendices featuring homework assignments and reading lists complement the material in the main text
Category: Science

Mathematics Of Multidimensional Seismic Imaging Migration And Inversion

Author : N. Bleistein
ISBN : 9781461300014
Genre : Mathematics
File Size : 77.10 MB
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For more than 80 years, the oil and gas industry has used seismic methods to construct images and determine physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. This book presents the different seismic data processing methods, also known as seismic "migration," in a unified mathematical way. The book serves as a bridge between the applied math and geophysics communities by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophisticated geophysicist.
Category: Mathematics

Branching Processes In Biology

Author : Marek Kimmel
ISBN : 9781493915590
Genre : Mathematics
File Size : 31.73 MB
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This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition. This second expanded edition adds new material published during the last decade, with nearly 200 new references. More material has been added on infinitely-dimensional multitype processes, including the infinitely-dimensional linear-fractional case. Hypergeometric function treatment of the special case of the Griffiths-Pakes infinite allele branching process has also been added. There are additional applications of recent molecular processes and connections with systems biology are explored, and a new chapter on genealogies of branching processes and their applications. Reviews of First Edition: "This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology." (Siam Review, Vol. 45 (2), 2003) “This book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences.” (Short Book Reviews of the ISI, Vol. 23 (2), 2003)
Category: Mathematics