Download or read book Bilinear and Trilinear Regression Models with Structured Covariance Matrices written by Joseph Nzabanita and published by Linköping University Electronic Press. This book was released on 2015-05-21 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Comprehensive Chemometrics written by and published by Elsevier. This book was released on 2009-03-09 with total page 2880 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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.

Download or read book Physics Briefs written by and published by . This book was released on 1987 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multiple View Geometry in Computer Vision written by Richard Hartley and published by Cambridge University Press. This book was released on 2004-03-25 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Download or read book Accurate Visual Metrology from Single and Multiple Uncalibrated Images written by Antonio Criminisi and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Nonnegative Matrix and Tensor Factorizations written by Andrzej Cichocki and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMF’s various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD). NMF/NTF and their extensions are increasingly used as tools in signal and image processing, and data analysis, having garnered interest due to their capability to provide new insights and relevant information about the complex latent relationships in experimental data sets. It is suggested that NMF can provide meaningful components with physical interpretations; for example, in bioinformatics, NMF and its extensions have been successfully applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining. As such, the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models. Key features: Acts as a single source reference guide to NMF, collating information that is widely dispersed in current literature, including the authors’ own recently developed techniques in the subject area. Uses generalized cost functions such as Bregman, Alpha and Beta divergences, to present practical implementations of several types of robust algorithms, in particular Multiplicative, Alternating Least Squares, Projected Gradient and Quasi Newton algorithms. Provides a comparative analysis of the different methods in order to identify approximation error and complexity. Includes pseudo codes and optimized MATLAB source codes for almost all algorithms presented in the book. The increasing interest in nonnegative matrix and tensor factorizations, as well as decompositions and sparse representation of data, will ensure that this book is essential reading for engineers, scientists, researchers, industry practitioners and graduate students across signal and image processing; neuroscience; data mining and data analysis; computer science; bioinformatics; speech processing; biomedical engineering; and multimedia.

Download or read book The Handbook of Organic Compounds Three Volume Set written by Jerry Workman Jr. and published by Elsevier. This book was released on 2000-10-18 with total page 1536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 handbookproject 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

Download or read book Spectral Learning on Matrices and Tensors written by MAJID JANZAMIN;RONG GE;JEAN KOSSAIFI;ANIMA ANANDKU. and published by . This book was released on 2019 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a theoretical and practical introduction to designing and deploying spectral learning on both matrices and tensors. It is of interest for all students, researchers and practitioners working on modern day machine learning problems.

Download or read book Discrete Data Analysis with R written by Michael Friendly and published by CRC Press. This book was released on 2015-12-16 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Applied Treatment of Modern Graphical Methods for Analyzing Categorical DataDiscrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data presents an applied treatment of modern methods for the analysis of categorical data, both discrete response data and frequency data. It explains how to use graphical meth

Download or read book Signal Processing Advances in Wireless and Mobile Communications Trends in single user and multi user systems written by Georgios B. Giannakis and published by . This book was released on 2001 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Numerical Recipes in C written by William H. Press and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now the acclaimed Second Edition of Numerical Recipes is available in the C++ object-oriented programming language. Including and updating the full mathematical and explanatory contents of Numerical Recipes in C, this new version incorporates completely new C++ versions of the more than 300 Numerical Recipes routines that are widely recognized as the most accessible and practical basis for scientific computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. Highlights include linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations and inverse theory. The authors approach to C++ preserves the efficient execution that C users expect, while simultaneously employing a clear, object-oriented interface to the routines. Tricks and tips for scientific computing in C++ are liberally included. The routines, in ANSI/ISO C++ source code, can thus be used with almost any existing C++ vector/matrix class library, according to user preference. A simple class library for stand-alone use is also included in the book. Both scientific programmers new to C++, and experienced C++ programmers who need access to the Numerical Recipes routines, can benefit from this important new version of an invaluable, classic text.

Download or read book Interpolatory Methods for Model Reduction written by A. C. Antoulas and published by SIAM. This book was released on 2020-01-13 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

Download or read book Representation Learning for Natural Language Processing written by Zhiyuan Liu and published by Springer Nature. This book was released on 2020-07-03 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advanced Multivariate Statistics with Matrices written by Tõnu Kollo and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course ”Matrices in Statistics” at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course ”Multivariate Asymptotic Statistics” in spring 2002. An advanced course ”Multivariate Linear Models” may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.

Download or read book Uncertain Projective Geometry written by Stephan Heuel and published by Springer Science & Business Media. This book was released on 2004-04-29 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic projective geometry, with its multilinear relations and its embedding into Grassmann-Cayley algebra, has become the basic representation of multiple view geometry, resulting in deep insights into the algebraic structure of geometric relations, as well as in efficient and versatile algorithms for computer vision and image analysis. This book provides a coherent integration of algebraic projective geometry and spatial reasoning under uncertainty with applications in computer vision. Beyond systematically introducing the theoretical foundations from geometry and statistics and clear rules for performing geometric reasoning under uncertainty, the author provides a collection of detailed algorithms. The book addresses researchers and advanced students interested in algebraic projective geometry for image analysis, in statistical representation of objects and transformations, or in generic tools for testing and estimating within the context of geometric multiple-view analysis.

Download or read book Data Reconciliation and Gross Error Detection written by Shankar Narasimhan and published by Elsevier. This book was released on 1999-11-29 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and comprehensive treatment of the variety of methods available for applying data reconciliation techniques. Data filtering, data compression and the impact of measurement selection on data reconciliation are also exhaustively explained.Data errors can cause big problems in any process plant or refinery. Process measurements can be correupted by power supply flucutations, network transmission and signla conversion noise, analog input filtering, changes in ambient conditions, instrument malfunctioning, miscalibration, and the wear and corrosion of sensors, among other factors. Here's a book that helps you detect, analyze, solve, and avoid the data acquisition problems that can rob plants of peak performance. This indispensable volume provides crucial insights into data reconciliation and gorss error detection techniques that are essential fro optimal process control and information systems. This book is an invaluable tool for engineers and managers faced with the selection and implementation of data reconciliation software, or for those developing such software. For industrial personnel and students, Data Reconciliation and Gross Error Detection is the ultimate reference.