Bilinear And Trilinear Regression Models With Structured Covariance Matrices
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Bilinear And Trilinear Regression Models With Structured Covariance Matrices
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Author : Joseph Nzabanita
language : en
Publisher: Linköping University Electronic Press
Release Date : 2015-05-21
Bilinear And Trilinear Regression Models With Structured Covariance Matrices written by Joseph Nzabanita and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-21 with Matrices categories.
This thesis focuses on the problem of estimating parameters in bilinear and trilinear regression models in which random errors are normally distributed. In these models the covariance matrix has a Kronecker product structure and some factor matrices may be linearly structured. The interest of considering various structures for the covariance matrices in different statistical models is partly driven by the idea that altering the covariance structure of a parametric model alters the variances of the model’s estimated mean parameters. Firstly, the extended growth curve model with a linearly structured covariance matrix is considered. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into appropriate orthogonal subspaces and how to derive explicit estimators of the covariance matrix from the sum of squared residuals obtained by projecting observations on those subspaces. Also an explicit estimator of the mean is derived and some properties of the proposed estimators are studied. Secondly, we study a bilinear regression model with matrix normally distributed random errors. For those models, the dispersion matrix follows a Kronecker product structure and it can be used, for example, to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations, a flip-flop relation, are established. At last, the models based on normally distributed random third order tensors are studied. These models are useful in analyzing 3-dimensional data arrays. In some studies the analysis is done using the tensor normal model, where the focus is on the estimation of the variance-covariance matrix which has a Kronecker structure. Little attention is paid to the structure of the mean, however, there is a potential to improve the analysis by assuming a structured mean. We formally introduce a 2-fold growth curve model by assuming a trilinear structure for the mean in the tensor normal model and propose an estimation algorithm for parameters. Also some extensions are discussed.
Bilinear Regression Analysis
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Author : Dietrich Von Rosen
language : en
Publisher:
Release Date : 2018
Bilinear Regression Analysis written by Dietrich Von Rosen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Algebra categories.
This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions. In order to analyze the bilinear regression models in an interpretable way, concepts from linear models are extended and applied to tensor spaces. Further, the book considers decompositions of tensor products into natural subspaces, and addresses maximum likelihood estimation, residual analysis, influential observation analysis and testing hypotheses, where properties of estimators such as moments, asymptotic distributions or approximations of distributions are also studied. Throughout the text, examples and several analyzed data sets illustrate the different approaches, and fresh insights into classical multivariate analysis are provided. This monograph is of interest to researchers and Ph. D. students in mathematical statistics, signal processing and other fields where statistical multivariate analysis is utilized. It can also be used as a text for second graduate-level courses on multivariate analysis.
Comprehensive Chemometrics
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Author :
language : en
Publisher: Elsevier
Release Date : 2009-03-09
Comprehensive Chemometrics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-09 with Science categories.
Designed to serve as the first point of reference on the subject, Comprehensive Chemometrics presents an integrated summary of the present state of chemical and biochemical data analysis and manipulation. The work covers all major areas ranging from statistics to data acquisition, analysis, and applications. This major reference work provides broad-ranging, validated summaries of the major topics in chemometrics—with chapter introductions and advanced reviews for each area. The level of material is appropriate for graduate students as well as active researchers seeking a ready reference on obtaining and analyzing scientific data. Features the contributions of leading experts from 21 countries, under the guidance of the Editors-in-Chief and a team of specialist Section Editors: L. Buydens; D. Coomans; P. Van Espen; A. De Juan; J.H. Kalivas; B.K. Lavine; R. Leardi; R. Phan-Tan-Luu; L.A. Sarabia; and J. Trygg Examines the merits and limitations of each technique through practical examples and extensive visuals: 368 tables and more than 1,300 illustrations (750 in full color) Integrates coverage of chemical and biological methods, allowing readers to consider and test a range of techniques Consists of 2,200 pages and more than 90 review articles, making it the most comprehensive work of its kind Offers print and online purchase options, the latter of which delivers flexibility, accessibility, and usability through the search tools and other productivity-enhancing features of ScienceDirect
Physics Briefs
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Author :
language : en
Publisher:
Release Date : 1987
Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Physics categories.
The Handbook Of Organic Compounds Three Volume Set
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Author : Jerry Workman, Jr.
language : en
Publisher: Elsevier
Release Date : 2000-10-18
The Handbook Of Organic Compounds Three Volume Set written by Jerry Workman, Jr. and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-18 with Science categories.
The Handbook of Organic Compounds: NIR, IR, Raman, and UV-Vis Spectra Featuring Polymers and Surfactants represents a compendium of practical spectroscopic methodology, comprehensive reviews, and basic information for organic materials, surfactants, and polymer spectra covering the Ultraviolet, Visible, Near Infrared, Infrared, Raman and Dielectric measurement techniques. This set represents a complementary organic compound handbook to the Nyquist inorganic handbook, published in 1996. This set comprises the first comprehensive multi-volume handbook to provide basic coverage for UV-Vis, 4th overtone NIR, 3rd overtone NIR, NIR, Infrared, Raman spectra, and Dielectric data for common organic compounds, polymers, surfactants, contaminants, and inorganic materials commonly encountered in the laboratory. The text includes a description and reviews of interpretive and chemometric techniques used for spectral data analysis. The spectra included within the atlas are useful for identification purposes as well as pedagogical for the instruction of the various interpretive and data processing methods discussed. This work is designed to be of help to students and vibrational spectroscopists in their efforts of daily spectral interpretation and data processing of organic spectra, polymers, and surfactants. All spectra are presented in wavenumber and transmittance, with the addition of ultraviolet, visible, 4th overtone NIR, 3rd overtone NIR, and NIR spectra also represented in nanometers and absorbance space. In addition, some Horizontal infrared ATR spectra are presented in wavenumber and absorbance space. All spectra are shown with essential peaks labeled in their respective units. The material in this handbook was contributed to by several individuals, and comments were received from a variety of prominent workers in the field of molecular spectroscopy. This type of handbook project is a daunting task. This Handbook can provide a valuable reference for the daily activities of students and professionals working in modern molecular spectroscopy laboratories. * Indices for UV-Vis, fourth overtone NIR, third overtone NIR, NIR, IR, raman, and dielectric spectra * Unique detailed correlation charts for each of these spectral regions * Indices of spectra by alphabetical order, chemical class, and chemical formula * Cross referencing of common compounds for all spectral regions * Literature reviews of historical and most useful references in the field * Research oriented for those using molecular spectroscopy on a routine basis for interpretation, qualitative and quantitative analysis * An emphasis on near infrared and infrared spectral regions
Signal Processing Advances In Wireless And Mobile Communications Trends In Single User And Multi User Systems
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Author : Georgios B. Giannakis
language : en
Publisher:
Release Date : 2001
Signal Processing Advances In Wireless And Mobile Communications Trends In Single User And Multi User Systems written by Georgios B. Giannakis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Medical categories.
This is the second in a two-volume set that captures major recent advances in signal processing (SP) tools, as they apply to wireless and mobile communication systems. The set brings together contributions by leaders in the field worldwide, and covers an exceptionally wide range of technologies and methodologies, including noise and interference cancellation, modem design, mobile Internet services, next-generation audio/video broadcasting, cellular telephony, and wireless multimedia networks. Volume II focuses on single- and multi-user communication systems. Volume II presents valuable new signal processing work on blind synchronization with single- and multi-sensor arrays, space-time transmit-receive diversity combining systems, time-varying channel modeling, signal separation with constant modulus constraints and parallel factor analysis tools. Volume II also presents important advances in multiuser systems, notably modern methods for canceling multiuser interference and mitigating multipath effects in CDMA and multicarrier systems at the physical layer, as well as signal processing issues at the network layer.
Generalized Principal Component Analysis
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Author : René Vidal
language : en
Publisher: Springer
Release Date : 2016-04-11
Generalized Principal Component Analysis written by René Vidal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-11 with Science categories.
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.
Representation Learning For Natural Language Processing
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Author : Zhiyuan Liu
language : en
Publisher: Springer Nature
Release Date : 2020-07-03
Representation Learning For Natural Language Processing written by Zhiyuan Liu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-03 with Computers categories.
This open access book provides an overview of the recent advances in representation learning theory, algorithms and applications for natural language processing (NLP). It is divided into three parts. Part I presents the representation learning techniques for multiple language entries, including words, phrases, sentences and documents. Part II then introduces the representation techniques for those objects that are closely related to NLP, including entity-based world knowledge, sememe-based linguistic knowledge, networks, and cross-modal entries. Lastly, Part III provides open resource tools for representation learning techniques, and discusses the remaining challenges and future research directions. The theories and algorithms of representation learning presented can also benefit other related domains such as machine learning, social network analysis, semantic Web, information retrieval, data mining and computational biology. This book is intended for advanced undergraduate and graduate students, post-doctoral fellows, researchers, lecturers, and industrial engineers, as well as anyone interested in representation learning and natural language processing.
Handbook Of Latent Variable And Related Models
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Author :
language : en
Publisher: Elsevier
Release Date : 2011-08-11
Handbook Of Latent Variable And Related Models written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables. - Covers a wide class of important models - Models and statistical methods described provide tools for analyzing a wide spectrum of complicated data - Includes illustrative examples with real data sets from business, education, medicine, public health and sociology. - Demonstrates the use of a wide variety of statistical, computational, and mathematical techniques.
Accurate Visual Metrology From Single And Multiple Uncalibrated Images
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Author : Antonio Criminisi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-10
Accurate Visual Metrology From Single And Multiple Uncalibrated Images written by Antonio Criminisi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-10 with Computers categories.
Accurate Visual Metrology from Single and Multiple Uncalibrated Images presents novel techniques for constructing three-dimensional models from bi-dimensional images using virtual reality tools. Antonio Criminisi develops the mathematical theory of computing world measurements from single images, and builds up a hierarchy of novel, flexible techniques to make measurements and reconstruct three-dimensional scenes from uncalibrated images, paying particular attention to the accuracy of the reconstruction. This book includes examples of interesting viable applications (eg. Forensic Science, History of Art, Virtual Reality, Architectural and indoor measurements), presented in a simple way, accompanied by pictures, diagrams and plenty of worked examples to help the reader understand and implement the algorithms.