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Author : Arthur Yu Lu
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.:/5 (836 download)
Download or read book Sparse Principal Component Analysis for Functional Data written by Arthur Yu Lu and published by . This book was released on 2002 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Denis Bosq
Publisher : Springer Science & Business Media
ISBN 13 : 1461211549
Total Pages : 295 pages
Book Rating : 4.4/5 (612 download)
Download or read book Linear Processes in Function Spaces written by Denis Bosq and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.
Author : Justin Petrovich
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (15 download)
Download or read book Functional Principal Component Analysis and Sparse Functional Regression written by Justin Petrovich and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this dissertation is on functional data which are sparsely and irregularlyobserved. Such data require special consideration, as classical functional datamethods and theory were developed for densely-observed data. As is the casein much of functional data analysis, the functional principal components (FPCs)play a key role in current sparse functional data methods via the Karhunen-Loveexpansion. Thus, after a review of relevant background material in chapter 1, thisthesis is divided roughly into two parts, the first focusing specifically on theoreticalproperties of FPCs, and the second on regression for sparsely observed functionaldata.Chapter 2 discusses functional principal component analysis and, in particular,provides a theoretical framework to relax the commonly-made assumption of distincteigenvalues. This is done by shifting analysis from individual FPCs to the projectionof FPCs. In addition, it is shown that one can still obtain asymptotic normality ofthe FPC projections.In chapter 3, focus shifts to scalar-on-function regression. Bridging ideasfrom the missing data literature with the more traditional sparse functional datamethods, we propose a multiple imputation approach to imputing the sparselyobserved(functional) covariate in a scalar-on-function regression model. Theproposed methodology is applied to both linear and logistic scalar-on-functionregression. Extensive simulations are performed to validate the proposed approach,and consistency of the resulting estimated coefficient function is established. Finally,we apply our new approach to a study on childhood macrocephaly, and show thatthe development of pathological conditions are linked both to an average level ofhead circumference, as well as the velocity of head circumference growth.
Author : James Ramsay
Publisher : Springer Science & Business Media
ISBN 13 : 0387981853
Total Pages : 213 pages
Book Rating : 4.3/5 (879 download)
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
Author : Gareth James
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (782 download)
Download or read book Principal Component Models for Sparse Functional Data written by Gareth James and published by . This book was released on 1999 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Piotr Kokoszka
Publisher : CRC Press
ISBN 13 : 1498746691
Total Pages : 371 pages
Book Rating : 4.4/5 (987 download)
Download or read book Introduction to Functional Data Analysis written by Piotr Kokoszka and published by CRC Press. This book was released on 2017-09-27 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.
Author : J.O. Ramsay
Publisher : Springer
ISBN 13 : 0387224653
Total Pages : 194 pages
Book Rating : 4.3/5 (872 download)
Download or read book Applied Functional Data Analysis written by J.O. Ramsay and published by Springer. This book was released on 2007-11-23 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the ideas of functional data analysis by a number of case studies. The case studies are accessible to research workers in a wide range of disciplines. Every reader should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. There is an associated web site with MATLABr and S?PLUSr implementations of the methods discussed.
Author : René Vidal
Publisher : Springer
ISBN 13 : 0387878114
Total Pages : 590 pages
Book Rating : 4.3/5 (878 download)
Download or read book Generalized Principal Component Analysis written by René Vidal and published by Springer. This book was released on 2016-04-11 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Frédéric Ferraty
Publisher : Springer Science & Business Media
ISBN 13 : 3790827363
Total Pages : 322 pages
Book Rating : 4.7/5 (98 download)
Download or read book Recent Advances in Functional Data Analysis and Related Topics written by Frédéric Ferraty and published by Springer Science & Business Media. This book was released on 2011-06-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: New technologies allow us to handle increasingly large datasets, while monitoring devices are becoming ever more sophisticated. This high-tech progress produces statistical units sampled over finer and finer grids. As the measurement points become closer, the data can be considered as observations varying over a continuum. This intrinsic continuous data (called functional data) can be found in various fields of science, including biomechanics, chemometrics, econometrics, environmetrics, geophysics, medicine, etc. The failure of standard multivariate statistics to analyze such functional data has led the statistical community to develop appropriate statistical methodologies, called Functional Data Analysis (FDA). Today, FDA is certainly one of the most motivating and popular statistical topics due to its impact on crucial societal issues (health, environment, etc). This is why the FDA statistical community is rapidly growing, as are the statistical developments . Therefore, it is necessary to organize regular meetings in order to provide a state-of-art review of the recent advances in this fascinating area. This book collects selected and extended papers presented at the second International Workshop of Functional and Operatorial Statistics (Santander, Spain, 16-18 June, 2011), in which many outstanding experts on FDA will present the most relevant advances in this pioneering statistical area. Undoubtedly, these proceedings will be an essential resource for academic researchers, master students, engineers, and practitioners not only in statistics but also in numerous related fields of application.
Author : Joo Yoon Han
Publisher :
ISBN 13 :
Total Pages : 61 pages
Book Rating : 4.:/5 (949 download)
Download or read book Parameter Selection of Sparse Functional Principal Component Analysis with FMRI Data written by Joo Yoon Han and published by . This book was released on 2016 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of high throughput biotechnologies, it is increasingly common for the number of features measured on each subject to vastly exceed the number of subjects in modern biomedical studies. In this manuscript we focus on these high dimensional issues for brain imaging data. Principal component analysis (PCA) is commonly used to reduce dimension of the data and to examine the major patterns. However, with such high dimensional data, PCA is inconsistent (Johnstone & Lu 2009). Moreover, when the underlying patterns are smooth and sparse, PCA will not be able to properly detect patterns. Sparse and smooth PCA may be of interest for high dimensional data, where the principal components are linear combinations of a subset of the features (with coefficient values that are spatially smooth). Specifically for fMRI data, where data are collected across time and regions of brain, smooth principal components can show major patterns in time. Also finding specific brain regions that are associated with the major patterns may be of interest. Allen (2013) introduced an optimization problem for this scenario, sparse and functional principal component analysis (SFPCA), which encourages both row and/or column factors are sparse and smooth. We apply SFPCA to brain imaging data Xn×p with n regions and p time points, where the row factors are sparse and the column factors are smooth. SFPCA problem involves three regularization parameters: sparsity parameter, smoothing parameter and number of components. The main goal of this thesis is to develop an automated method to select those regularization parameters involved in the SFPCA problem. The method is based on cross-validation; however, cross-validation with an unsupervised problem is not trivial. We leverage the time structure of brain imaging data in estimating held-out time-points in the test set. We also define the cross-validated proportion of variance explained for our problem and use it to select appropriate number of components (and regularization parameters for those components). We search for the regularization parameters sequentially, component- by-component. We compare performance of SFPCA (with our selected tuning parameters) to classical PCA with different signal to noise ratios (SNR). For sparse and smooth data, SFPCA sub- stantially outperforms PCA (classical PCA gives estimates that are not sparse, and much too non-smooth). As expected, when signal to noise ratio increases, SFPCA performance improves. In addition, as SNR increases, cross-validated proportion of variance explained more accurately estimates the true proportion of variance explained. From simulation studies, we find that we need enough signal to estimate factors using SFPCA properly. Moreover, we need reasonable candidate values of the regularization parameters.
Author : Lajos Horváth
Publisher : Springer Science & Business Media
ISBN 13 : 1461436559
Total Pages : 426 pages
Book Rating : 4.4/5 (614 download)
Download or read book Inference for Functional Data with Applications written by Lajos Horváth and published by Springer Science & Business Media. This book was released on 2012-05-08 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recently developed statistical methods and theory required for the application of the tools of functional data analysis to problems arising in geosciences, finance, economics and biology. It is concerned with inference based on second order statistics, especially those related to the functional principal component analysis. While it covers inference for independent and identically distributed functional data, its distinguishing feature is an in depth coverage of dependent functional data structures, including functional time series and spatially indexed functions. Specific inferential problems studied include two sample inference, change point analysis, tests for dependence in data and model residuals and functional prediction. All procedures are described algorithmically, illustrated on simulated and real data sets, and supported by a complete asymptotic theory. The book can be read at two levels. Readers interested primarily in methodology will find detailed descriptions of the methods and examples of their application. Researchers interested also in mathematical foundations will find carefully developed theory. The organization of the chapters makes it easy for the reader to choose an appropriate focus. The book introduces the requisite, and frequently used, Hilbert space formalism in a systematic manner. This will be useful to graduate or advanced undergraduate students seeking a self-contained introduction to the subject. Advanced researchers will find novel asymptotic arguments.
Author : Ciprian M. Crainiceanu
Publisher : CRC Press
ISBN 13 : 1003856306
Total Pages : 338 pages
Book Rating : 4.0/5 (38 download)
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.
Author : Wenfei Zhang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (867 download)
Download or read book Regression Based Principal Component Analysis for Sparse Functional Data with Applications to Screening Pubertal Growth Paths written by Wenfei Zhang and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: When it is applied to the same group of Finnish teens, it shows enhanced screening performance in identifying possible abnormal growth paths. Simulation studies are also conducted to validate the proposed covariate adjusted method.
Author : Noel Cressie
Publisher : John Wiley & Sons
ISBN 13 : 1119243068
Total Pages : 596 pages
Book Rating : 4.1/5 (192 download)
Download or read book Statistics for Spatio-Temporal Data written by Noel Cressie and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of the 2013 DeGroot Prize. A state-of-the-art presentation of spatio-temporal processes, bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods Noel Cressie and Christopher K. Wikle, are also winners of the 2011 PROSE Award in the Mathematics category, for the book “Statistics for Spatio-Temporal Data” (2011), published by John Wiley and Sons. (The PROSE awards, for Professional and Scholarly Excellence, are given by the Association of American Publishers, the national trade association of the US book publishing industry.) Statistics for Spatio-Temporal Data has now been reprinted with small corrections to the text and the bibliography. The overall content and pagination of the new printing remains the same; the difference comes in the form of corrections to typographical errors, editing of incomplete and missing references, and some updated spatio-temporal interpretations. From understanding environmental processes and climate trends to developing new technologies for mapping public-health data and the spread of invasive-species, there is a high demand for statistical analyses of data that take spatial, temporal, and spatio-temporal information into account. Statistics for Spatio-Temporal Data presents a systematic approach to key quantitative techniques that incorporate the latest advances in statistical computing as well as hierarchical, particularly Bayesian, statistical modeling, with an emphasis on dynamical spatio-temporal models. Cressie and Wikle supply a unique presentation that incorporates ideas from the areas of time series and spatial statistics as well as stochastic processes. Beginning with separate treatments of temporal data and spatial data, the book combines these concepts to discuss spatio-temporal statistical methods for understanding complex processes. Topics of coverage include: Exploratory methods for spatio-temporal data, including visualization, spectral analysis, empirical orthogonal function analysis, and LISAs Spatio-temporal covariance functions, spatio-temporal kriging, and time series of spatial processes Development of hierarchical dynamical spatio-temporal models (DSTMs), with discussion of linear and nonlinear DSTMs and computational algorithms for their implementation Quantifying and exploring spatio-temporal variability in scientific applications, including case studies based on real-world environmental data Throughout the book, interesting applications demonstrate the relevance of the presented concepts. Vivid, full-color graphics emphasize the visual nature of the topic, and a related FTP site contains supplementary material. Statistics for Spatio-Temporal Data is an excellent book for a graduate-level course on spatio-temporal statistics. It is also a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.
Author : Jane-Ling Wang
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
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.
Author : Aapo Hyvärinen
Publisher : John Wiley & Sons
ISBN 13 : 0471464198
Total Pages : 505 pages
Book Rating : 4.4/5 (714 download)
Download or read book Independent Component Analysis written by Aapo Hyvärinen and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more. Independent Component Analysis is divided into four sections that cover: * General mathematical concepts utilized in the book * The basic ICA model and its solution * Various extensions of the basic ICA model * Real-world applications for ICA models Authors Hyvarinen, Karhunen, and Oja are well known for their contributions to the development of ICA and here cover all the relevant theory, new algorithms, and applications in various fields. Researchers, students, and practitioners from a variety of disciplines will find this accessible volume both helpful and informative.
Author : Jianqing Fan
Publisher : CRC Press
ISBN 13 : 0429527616
Total Pages : 942 pages
Book Rating : 4.4/5 (295 download)
Download or read book Statistical Foundations of Data Science written by Jianqing Fan and published by CRC Press. This book was released on 2020-09-21 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
