Download or read book Nonlinear Principal Component Analysis and Its Applications written by Yuichi Mori and published by Springer. This book was released on 2016-12-09 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed measurement levels data, sparse MCA, joint dimension reduction and clustering methods for categorical data, and acceleration of ALS computation. The variable selection methods in PCA that originally were developed for numerical data can be applied to any types of measurement levels by using nonlinear PCA. Sparseness and joint dimension reduction and clustering for nonlinear data, the results of recent studies, are extensions obtained by the same matrix operations in nonlinear PCA. Finally, an acceleration algorithm is proposed to reduce the problem of computational cost in the ALS iteration in nonlinear multivariate methods. This book thus presents the usefulness of nonlinear PCA which can be applied to different measurement levels data in diverse fields. As well, it covers the latest topics including the extension of the traditional statistical method, newly proposed nonlinear methods, and computational efficiency in the methods.

Download or read book Principal Manifolds for Data Visualization and Dimension Reduction written by Alexander N. Gorban and published by Springer Science & Business Media. This book was released on 2007-09-11 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described. Presentation of algorithms is supplemented by case studies. The volume ends with a tutorial PCA deciphers genome.

Download or read book Advances in Principal Component Analysis written by Ganesh R. Naik and published by Springer. This book was released on 2017-12-11 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports on the latest advances in concepts and further developments of principal component analysis (PCA), addressing a number of open problems related to dimensional reduction techniques and their extensions in detail. Bringing together research results previously scattered throughout many scientific journals papers worldwide, the book presents them in a methodologically unified form. Offering vital insights into the subject matter in self-contained chapters that balance the theory and concrete applications, and especially focusing on open problems, it is essential reading for all researchers and practitioners with an interest in PCA.

Download or read book Principal Component Analysis written by I.T. Jolliffe and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principal component analysis is probably the oldest and best known of the It was first introduced by Pearson (1901), techniques ofmultivariate analysis. and developed independently by Hotelling (1933). Like many multivariate methods, it was not widely used until the advent of electronic computers, but it is now weIl entrenched in virtually every statistical computer package. The central idea of principal component analysis is to reduce the dimen sionality of a data set in which there are a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This reduction is achieved by transforming to a new set of variables, the principal components, which are uncorrelated, and which are ordered so that the first few retain most of the variation present in all of the original variables. Computation of the principal components reduces to the solution of an eigenvalue-eigenvector problem for a positive-semidefinite symmetrie matrix. Thus, the definition and computation of principal components are straightforward but, as will be seen, this apparently simple technique has a wide variety of different applications, as weIl as a number of different deri vations. Any feelings that principal component analysis is a narrow subject should soon be dispelled by the present book; indeed some quite broad topics which are related to principal component analysis receive no more than a brief mention in the final two chapters.

Download or read book Variable Selection in Nonlinear Principal Component Analysis written by Hiroko Katayama and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principal components analysis (PCA) is a popular dimension reduction method and is applied to analyze quantitative data. For PCA to qualitative data, nonlinear PCA can be applied, where the data are quantified by using optimal scaling that nonlinearly transforms qualitative data into quantitative data. Then nonlinear PCA reveals nonlinear relationships among variables with different measurement levels. Using this quantification, we can consider variable selection in the context of PCA for qualitative data. In PCA for quantitative data, modified PCA (M.PCA) of Tanaka and Mori derives principal components which are computed as a linear combination of a subset of variables but can reproduce all the variables very well. This means that M.PCA can select a reasonable subset of variables with different measurement levels if it is extended so as to deal with qualitative data by using the idea of nonlinear PCA. A nonlinear M.PCA is therefore proposed for variable selection in nonlinear PCA. The method, in this chapter, is based on the idea in ,ÄúNonlinear Principal Component Analysis and its Applications,Äù by Mori et al. (Springer). The performance of the method is evaluated in a numerical example.

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 Principal Component Analysis and Its Extensions with Applications on Nonlinear Feature Extraction and Self similar Network Traffic Analysis written by Sek Kin Neng and published by . This book was released on 2000 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Principal Component Neural Networks written by K. I. Diamantaras and published by Wiley-Interscience. This book was released on 1996-03-08 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematically explores the relationship between principal component analysis (PCA) and neural networks. Provides a synergistic examination of the mathematical, algorithmic, application and architectural aspects of principal component neural networks. Using a unified formulation, the authors present neural models performing PCA from the Hebbian learning rule and those which use least squares learning rules such as back-propagation. Examines the principles of biological perceptual systems to explain how the brain works. Every chapter contains a selected list of applications examples from diverse areas.

Download or read book Numerical Methods for Unconstrained Optimization and Nonlinear Equations written by J. E. Dennis, Jr. and published by SIAM. This book was released on 1996-12-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.

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.

Download or read book Quasi objective Nonlinear Principal Component Analysis and Applications to the Atmosphere written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: NonLinear Principal Component Analysis (NLPCA) using three-hidden-layer feed-forward neural networks can produce solutions that over-fit the data and are non-unique. These problems have been dealt with by subjective methods during the network training. This study shows that these problems are intrinsic due to the three-hidden-layer architecture. A simplified two-hidden-layer feed-forward neural network that has no encoding layer and no bottleneck and output biases is proposed. This new, compact NLPCA model alleviates these problems without employing the subjective methods and is called quasi-objective. The compact NLPCA is applied to the zonal winds observed at seven pressure levels between 10 and 70 hPa in the equatorial stratosphere to represent the Quasi-Biennial Oscillation (QBO) and investigate its variability and structure. The two nonlinear principal components of the dataset offer a clear picture of the QBO. In particular, their structure shows that the QBO phase consists of a predominant 28.4-month cycle that is modulated by an 11-year cycle and a longer-period cycle. The significant difference in variability of the winds between cold and warm seasons and the tendency for a seasonal synchronization of the QBO phases are well captured. The one-dimensional NLPCA approximation of the dataset provides a better representation of the QBO than the classical principal component analysis and a better description of the asymmetry of the QBO between westerly and easterly shear zones and between their transitions. The compact NLPCA is then applied to the Arctic Oscillation (AO) index and aforementioned zonal winds to investigate the relationship of the AO with the QBO. The NLPCA of the AO index and zonal-winds dataset shows clearly that, of covariation of the two oscillations, the phase defined by the two nonlinear principal components progresses with a predominant 28.4-month periodicity, plus the 11-year and longer-period modulations. Large positive values of the AO i.

Download or read book Hyperspectral Image Analysis written by Saurabh Prasad and published by Springer Nature. This book was released on 2020-04-27 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the state of the art in algorithmic approaches addressing the practical challenges that arise with hyperspectral image analysis tasks, with a focus on emerging trends in machine learning and image processing/understanding. It presents advances in deep learning, multiple instance learning, sparse representation based learning, low-dimensional manifold models, anomalous change detection, target recognition, sensor fusion and super-resolution for robust multispectral and hyperspectral image understanding. It presents research from leading international experts who have made foundational contributions in these areas. The book covers a diverse array of applications of multispectral/hyperspectral imagery in the context of these algorithms, including remote sensing, face recognition and biomedicine. This book would be particularly beneficial to graduate students and researchers who are taking advanced courses in (or are working in) the areas of image analysis, machine learning and remote sensing with multi-channel optical imagery. Researchers and professionals in academia and industry working in areas such as electrical engineering, civil and environmental engineering, geosciences and biomedical image processing, who work with multi-channel optical data will find this book useful.

Download or read book Principal Component Analysis written by Parinya Sanguansat and published by BoD – Books on Demand. This book was released on 2012-03-07 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at raising awareness of researchers, scientists and engineers on the benefits of Principal Component Analysis (PCA) in data analysis. In this book, the reader will find the applications of PCA in fields such as energy, multi-sensor data fusion, materials science, gas chromatographic analysis, ecology, video and image processing, agriculture, color coating, climate and automatic target recognition.

Download or read book Artificial Neural Networks Icann 97 written by Wulfram Gerstner and published by Springer Science & Business Media. This book was released on 1997-09-29 with total page 1300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content Description #Includes bibliographical references and index.

Download or read book Three mode Principal Component Analysis written by Pieter M. Kroonenberg and published by . This book was released on 1983 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Model Based Machine Learning written by John Winn and published by CRC Press. This book was released on 2023-11-30 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today, machine learning is being applied to a growing variety of problems in a bewildering variety of domains. A fundamental challenge when using machine learning is connecting the abstract mathematics of a machine learning technique to a concrete, real world problem. This book tackles this challenge through model-based machine learning which focuses on understanding the assumptions encoded in a machine learning system and their corresponding impact on the behaviour of the system. The key ideas of model-based machine learning are introduced through a series of case studies involving real-world applications. Case studies play a central role because it is only in the context of applications that it makes sense to discuss modelling assumptions. Each chapter introduces one case study and works through step-by-step to solve it using a model-based approach. The aim is not just to explain machine learning methods, but also showcase how to create, debug, and evolve them to solve a problem. Features: Explores the assumptions being made by machine learning systems and the effect these assumptions have when the system is applied to concrete problems. Explains machine learning concepts as they arise in real-world case studies. Shows how to diagnose, understand and address problems with machine learning systems. Full source code available, allowing models and results to be reproduced and explored. Includes optional deep-dive sections with more mathematical details on inference algorithms for the interested reader.

Download or read book Nonlinear Principal Component Analysis written by Ralf Der and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: