Dimension Reduction For Functional Data

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Dimension Reduction for Functional Data

Author : Jun Song
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (1 download)

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Book Synopsis Dimension Reduction for Functional Data by : Jun Song

Download or read book Dimension Reduction for Functional Data written by Jun Song and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In regression problems, sufficient dimension reduction (SDR) allows us to reduce the dimension of predictor variables without losing any regression information which is considered to be a part of supervised machine learning. In particular, new theories and methodologies are in increasing demand to adapt to complex types of data with a drastically increased dimension such as functional data of infinite dimension. In this work, we established theories and methods of dimension reduction for functional data in three ways: (1) nonlinear supervised dimension reduction, (2) linear supervised dimension reduction, (3) nonlinear unsupervised dimension reduction. The fundamental idea of the theories is the construction of a feature space over a function space where real data live. We construct a feature space by using reproducing kernel Hilbert space (RKHS) in a nested way, called nested RKHS. Which allows us to treat functional data and capture nonlinear characteristics of data at the same time. In addition, nested RKHS can be used to develop weak conditional moments for developing general theories and methods for linear dimension reduction. We employ additive structure over the functional data so that the methods work for multivariate functional data. We develop two methods of nonlinear SDR for functional data, three methods of linear SDR for functional data, and a general framework of nonlinear functional PCA. Then asymptotic results, dimension determination, and its consistency have been studied for parts of methods. Simulation studies and real data application results show that the methods can reduce the dimension of functional data, and can be used for functional classification with high effectiveness.

Sufficient Dimension Reduction

Author : Bing Li
Publisher : CRC Press
ISBN 13 : 1351645730
Total Pages : 362 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Sufficient Dimension Reduction by : Bing Li

Download or read book Sufficient Dimension Reduction written by Bing Li and published by CRC Press. This book was released on 2018-04-27 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field. Features Provides comprehensive coverage of this emerging research field. Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion. Reflects most recent advances such as nonlinear sufficient dimension reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data. Includes a set of computer codes written in R that are easily implemented by the readers. Uses real data sets available online to illustrate the usage and power of the described methods. Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones. The author Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.

Functional and Shape Data Analysis

Author : Anuj Srivastava
Publisher : Springer
ISBN 13 : 1493940201
Total Pages : 454 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Functional and Shape Data Analysis by : Anuj Srivastava

Download or read book Functional and Shape Data Analysis written by Anuj Srivastava and published by Springer. This book was released on 2016-10-03 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Functional Data Analysis with R

Author : Ciprian M. Crainiceanu
Publisher : CRC Press
ISBN 13 : 1003856306
Total Pages : 338 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Functional Data Analysis with R by : Ciprian M. Crainiceanu

Download or read book Functional Data Analysis with R written by Ciprian M. Crainiceanu and published by CRC Press. This book was released on 2024-03-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emerging technologies generate data sets of increased size and complexity that require new or updated statistical inferential methods and scalable, reproducible software. These data sets often involve measurements of a continuous underlying process, and benefit from a functional data perspective. Functional Data Analysis with R presents many ideas for handling functional data including dimension reduction techniques, smoothing, functional regression, structured decompositions of curves, and clustering. The idea is for the reader to be able to immediately reproduce the results in the book, implement these methods, and potentially design new methods and software that may be inspired by these approaches. Features: Functional regression models receive a modern treatment that allows extensions to many practical scenarios and development of state-of-the-art software. The connection between functional regression, penalized smoothing, and mixed effects models is used as the cornerstone for inference. Multilevel, longitudinal, and structured functional data are discussed with emphasis on emerging functional data structures. Methods for clustering functional data before and after smoothing are discussed. Multiple new functional data sets with dense and sparse sampling designs from various application areas are presented, including the NHANES linked accelerometry and mortality data, COVID-19 mortality data, CD4 counts data, and the CONTENT child growth study. Step-by-step software implementations are included, along with a supplementary website (www.FunctionalDataAnalysis.com) featuring software, data, and tutorials. More than 100 plots for visualization of functional data are presented. Functional Data Analysis with R is primarily aimed at undergraduate, master's, and PhD students, as well as data scientists and researchers working on functional data analysis. The book can be read at different levels and combines state-of-the-art software, methods, and inference. It can be used for self-learning, teaching, and research, and will particularly appeal to anyone who is interested in practical methods for hands-on, problem-forward functional data analysis. The reader should have some basic coding experience, but expertise in R is not required.

Functional and High-Dimensional Statistics and Related Fields

Author : Germán Aneiros
Publisher : Springer Nature
ISBN 13 : 3030477568
Total Pages : 254 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Functional and High-Dimensional Statistics and Related Fields by : Germán Aneiros

Download or read book Functional and High-Dimensional Statistics and Related Fields written by Germán Aneiros and published by Springer Nature. This book was released on 2020-06-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

Functional Data Analysis

Author : Jane-Ling Wang
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Functional Data Analysis by : Jane-Ling Wang

Download or read book Functional Data Analysis written by Jane-Ling Wang and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. These are both examples of functional data, which has become a commonly encountered type of data. Functional data analysis (FDA) encompasses the statistical methodology for such data. Broadly interpreted, FDA deals with the analysis and theory of data that are in the form of functions. This paper provides an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA). FPCA is an important dimension reduction tool, and in sparse data situations it can be used to impute functional data that are sparsely observed. Other dimension reduction approaches are also discussed. In addition, we review another core technique, functional linear regression, as well as clustering and classification of functional data. Beyond linear and single- or multiple- index methods, we touch upon a few nonlinear approaches that are promising for certain applications. They include additive and other nonlinear functional regression models and models that feature time warping, manifold learning, and empirical differential equations. The paper concludes with a brief discussion of future directions.

Functional Statistics and Related Fields

Author : Germán Aneiros
Publisher : Springer
ISBN 13 : 3319558463
Total Pages : 297 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Functional Statistics and Related Fields by : Germán Aneiros

Download or read book Functional Statistics and Related Fields written by Germán Aneiros and published by Springer. This book was released on 2017-04-25 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects latest methodological and applied contributions on functional, high-dimensional and other complex data, related statistical models and tools as well as on operator-based statistics. It contains selected and refereed contributions presented at the Fourth International Workshop on Functional and Operatorial Statistics (IWFOS 2017) held in A Coruña, Spain, from 15 to 17 June 2017. The series of IWFOS workshops was initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008. Since then, many of the major advances in functional statistics and related fields have been periodically presented and discussed at the IWFOS workshops.

Dimension Reduction and Automatic Smoothing in High Dimensional and Functional Data Analysis

Author : Heather Suzanne Battey
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Dimension Reduction and Automatic Smoothing in High Dimensional and Functional Data Analysis by : Heather Suzanne Battey

Download or read book Dimension Reduction and Automatic Smoothing in High Dimensional and Functional Data Analysis written by Heather Suzanne Battey and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Machine Learning Techniques for Multimedia

Author : Matthieu Cord
Publisher : Springer Science & Business Media
ISBN 13 : 3540751718
Total Pages : 297 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Machine Learning Techniques for Multimedia by : Matthieu Cord

Download or read book Machine Learning Techniques for Multimedia written by Matthieu Cord and published by Springer Science & Business Media. This book was released on 2008-02-07 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Processing multimedia content has emerged as a key area for the application of machine learning techniques, where the objectives are to provide insight into the domain from which the data is drawn, and to organize that data and improve the performance of the processes manipulating it. Arising from the EU MUSCLE network, this multidisciplinary book provides a comprehensive coverage of the most important machine learning techniques used and their application in this domain.

New Methods and Models in Functional Data Analysis

Author : Peijun Sang
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.:/5 (112 download)

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Book Synopsis New Methods and Models in Functional Data Analysis by : Peijun Sang

Download or read book New Methods and Models in Functional Data Analysis written by Peijun Sang and published by . This book was released on 2018 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional data analysis (FDA) plays an important role in analyzing function-valued data such as growth curves, medical images and electromagnetic spectrum profiles, etc. Since dimension reduction can be achieved for infinite-dimensional functional data via functional principal component analysis (FPCA), this technique has attracted substantial attention. We develop an easy-to-implement algorithm to perform FPCA and find that this algorithm compares favorably with traditional methods in numerous applications. Knowing how ran- dom functions interact is critical to studying mechanisms like gene regulations and event- related brain activation. A new approach is proposed to calibrate dynamical correlations of random functions and we apply this approach to quantify functional connectivity from medical images. Scalar-on-function regression, which is widely used to characterize the re- lationship between a functional covariate and a scalar response, is an important ingredient of FDA. We propose several new scalar-on-function regression models and investigate their properties from both theoretical and practical perspectives.

Feature Engineering and Selection

Author : Max Kuhn
Publisher : CRC Press
ISBN 13 : 1351609467
Total Pages : 266 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Feature Engineering and Selection by : Max Kuhn

Download or read book Feature Engineering and Selection written by Max Kuhn and published by CRC Press. This book was released on 2019-07-25 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results.

Methods for Sparse Functional Data

Author : Edwin Kam Fai Lei
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Methods for Sparse Functional Data by : Edwin Kam Fai Lei

Download or read book Methods for Sparse Functional Data written by Edwin Kam Fai Lei and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Functional Data Analysis with R and MATLAB

Author : James Ramsay
Publisher : Springer Science & Business Media
ISBN 13 : 0387981853
Total Pages : 213 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Functional Data Analysis with R and MATLAB by : James Ramsay

Download or read book Functional Data Analysis with R and MATLAB written by James Ramsay and published by Springer Science & Business Media. This book was released on 2009-06-29 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an application-oriented overview of functional analysis, with extended and accessible presentations of key concepts such as spline basis functions, data smoothing, curve registration, functional linear models and dynamic systems Functional data analysis is put to work in a wide a range of applications, so that new problems are likely to find close analogues in this book The code in R and Matlab in the book has been designed to permit easy modification to adapt to new data structures and research problems

Description Length and Dimensionality Reduction in Functional Data Analysis

Author : Donald Stephen Poskitt
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (838 download)

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Book Synopsis Description Length and Dimensionality Reduction in Functional Data Analysis by : Donald Stephen Poskitt

Download or read book Description Length and Dimensionality Reduction in Functional Data Analysis written by Donald Stephen Poskitt and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Wavelets in Functional Data Analysis

Author : Pedro A. Morettin
Publisher : Springer
ISBN 13 : 3319596233
Total Pages : 112 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Wavelets in Functional Data Analysis by : Pedro A. Morettin

Download or read book Wavelets in Functional Data Analysis written by Pedro A. Morettin and published by Springer. This book was released on 2017-11-07 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet-based procedures are key in many areas of statistics, applied mathematics, engineering, and science. This book presents wavelets in functional data analysis, offering a glimpse of problems in which they can be applied, including tumor analysis, functional magnetic resonance and meteorological data. Starting with the Haar wavelet, the authors explore myriad families of wavelets and how they can be used. High-dimensional data visualization (using Andrews' plots), wavelet shrinkage (a simple, yet powerful, procedure for nonparametric models) and a selection of estimation and testing techniques (including a discussion on Stein’s Paradox) make this a highly valuable resource for graduate students and experienced researchers alike.

Analysis of Variance for Functional Data

Author : Jin-Ting Zhang
Publisher : CRC Press
ISBN 13 : 1439862745
Total Pages : 406 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Analysis of Variance for Functional Data by : Jin-Ting Zhang

Download or read book Analysis of Variance for Functional Data written by Jin-Ting Zhang and published by CRC Press. This book was released on 2013-06-18 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite research interest in functional data analysis in the last three decades, few books are available on the subject. Filling this gap, Analysis of Variance for Functional Data presents up-to-date hypothesis testing methods for functional data analysis. The book covers the reconstruction of functional observations, functional ANOVA, functional l

Nonparametric Functional Data Analysis

Author : Frédéric Ferraty
Publisher : Springer Science & Business Media
ISBN 13 : 0387366202
Total Pages : 260 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Nonparametric Functional Data Analysis by : Frédéric Ferraty

Download or read book Nonparametric Functional Data Analysis written by Frédéric Ferraty and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.