Nonlinear Principal Component Analysis And Its Applications

Author : Yuichi Mori,Masahiro Kuroda,Naomichi Makino
Publisher : Springer
Page : 80 pages
File Size : 47,6 Mb
Release : 2016-12-09
Category : Mathematics
ISBN : 9789811001598

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Nonlinear Principal Component Analysis and Its Applications by Yuichi Mori,Masahiro Kuroda,Naomichi Makino Pdf

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.

Author : Alexander N. Gorban,Balázs Kégl,Donald C. Wunsch,Andrei Zinovyev
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 54,8 Mb
Release : 2007-09-11
Category : Technology & Engineering
ISBN : 9783540737506

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Principal Manifolds for Data Visualization and Dimension Reduction by Alexander N. Gorban,Balázs Kégl,Donald C. Wunsch,Andrei Zinovyev Pdf

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.

Author : I.T. Jolliffe
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 47,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719048

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Principal Component Analysis by I.T. Jolliffe Pdf

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.

Author : Ganesh R. Naik
Publisher : Springer
Page : 252 pages
File Size : 41,8 Mb
Release : 2017-12-11
Category : Technology & Engineering
ISBN : 9789811067044

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Advances in Principal Component Analysis by Ganesh R. Naik Pdf

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.

Author : René Vidal,Yi Ma,Shankar Sastry
Publisher : Springer
Page : 566 pages
File Size : 54,7 Mb
Release : 2016-04-11
Category : Science
ISBN : 9780387878119

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Generalized Principal Component Analysis by René Vidal,Yi Ma,Shankar Sastry Pdf

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 : Fausto Pedro García Márquez
Publisher : BoD – Books on Demand
Page : 254 pages
File Size : 48,9 Mb
Release : 2022-08-25
Category : Computers
ISBN : 9781803557656

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Advances in Principal Component Analysis by Fausto Pedro García Márquez Pdf

This book describes and discusses the use of principal component analysis (PCA) for different types of problems in a variety of disciplines, including engineering, technology, economics, and more. It presents real-world case studies showing how PCA can be applied with other algorithms and methods to solve both large and small and static and dynamic problems. It also examines improvements made to PCA over the years.

Author : Parinya Sanguansat
Publisher : BoD – Books on Demand
Page : 234 pages
File Size : 54,8 Mb
Release : 2012-03-07
Category : Computers
ISBN : 9789535101826

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Principal Component Analysis by Parinya Sanguansat Pdf

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.

Author : K. I. Diamantaras,S. Y. Kung
Publisher : Wiley-Interscience
Page : 282 pages
File Size : 55,9 Mb
Release : 1996-03-08
Category : Computers
ISBN : UOM:39015037330696

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Principal Component Neural Networks by K. I. Diamantaras,S. Y. Kung Pdf

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.

Author : Petra Perner
Publisher : Springer
Page : 356 pages
File Size : 44,5 Mb
Release : 2007-08-18
Category : Computers
ISBN : 9783540734352

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Advances in Data Mining - Theoretical Aspects and Applications by Petra Perner Pdf

The papers in this volume represent the proceedings of the 7th Industrial Conference on Data Mining. They are organized into topical sections on aspects of classification and prediction, clustering, web mining, data mining in medicine, applications of data mining, time series and frequent pattern mining, and association rule mining. Readers gain new insights into theories underlying data mining and discover state-of-the-technology applications.

Author : De-Shuang Huang,Donald C. Wunsch,Daniel S. Levine,Kang-Hyun Jo
Publisher : Springer Science & Business Media
Page : 1299 pages
File Size : 55,7 Mb
Release : 2008-08-28
Category : Computers
ISBN : 9783540874409

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Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues by De-Shuang Huang,Donald C. Wunsch,Daniel S. Levine,Kang-Hyun Jo Pdf

The International Conference on Intelligent Computing (ICIC) was formed to p- vide an annual forum dedicated to the emerging and challenging topics in artificial intelligence, machine learning, bioinformatics, and computational biology, etc. It aims to bring together researchers and practitioners from both academia and ind- try to share ideas, problems and solutions related to the multifaceted aspects of intelligent computing. ICIC 2008, held in Shanghai, China, September 15–18, 2008, constituted the 4th International Conference on Intelligent Computing. It built upon the success of ICIC 2007, ICIC 2006 and ICIC 2005 held in Qingdao, Kunming and Hefei, China, 2007, 2006 and 2005, respectively. This year, the conference concentrated mainly on the theories and methodologies as well as the emerging applications of intelligent computing. Its aim was to unify the picture of contemporary intelligent computing techniques as an integral concept that highlights the trends in advanced computational intelligence and bridges theoretical research with applications. Therefore, the theme for this conference was “Emerging Intelligent Computing Technology and Applications”. Papers focusing on this theme were solicited, addressing theories, methodologies, and applications in science and technology.

Author : Marie-Noelle Pons,Jan Van Impe
Publisher : Elsevier
Page : 610 pages
File Size : 51,5 Mb
Release : 2005-08-02
Category : Science
ISBN : 008044251X

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Computer Applications in Biotechnology 2004 by Marie-Noelle Pons,Jan Van Impe Pdf

Author : Zengqi Sun,Zhidong Deng
Publisher : Springer Science & Business Media
Page : 841 pages
File Size : 48,8 Mb
Release : 2013-06-24
Category : Technology & Engineering
ISBN : 9783642385247

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Proceedings of 2013 Chinese Intelligent Automation Conference by Zengqi Sun,Zhidong Deng Pdf

Proceedings of the 2013 Chinese Intelligent Automation Conference presents selected research papers from the CIAC’13, held in Yangzhou, China. The topics include e.g. adaptive control, fuzzy control, neural network based control, knowledge based control, hybrid intelligent control, learning control, evolutionary mechanism based control, multi-sensor integration, failure diagnosis, and reconfigurable control. Engineers and researchers from academia, industry, and government can gain an inside view of new solutions combining ideas from multiple disciplines in the field of intelligent automation. Zengqi Sun and Zhidong Deng are professors at the Department of Computer Science, Tsinghua University, China.

Author : Aapo Hyvärinen,Juha Karhunen,Erkki Oja
Publisher : John Wiley & Sons
Page : 505 pages
File Size : 49,8 Mb
Release : 2004-04-05
Category : Science
ISBN : 9780471464198

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Independent Component Analysis by Aapo Hyvärinen,Juha Karhunen,Erkki Oja Pdf

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 : Hong-Yue Zhang
Publisher : Elsevier
Page : 1576 pages
File Size : 52,9 Mb
Release : 2007-03-01
Category : Science
ISBN : 008055539X

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Fault Detection, Supervision and Safety of Technical Processes 2006 by Hong-Yue Zhang Pdf

The safe and reliable operation of technical systems is of great significance for the protection of human life and health, the environment, and of the vested economic value. The correct functioning of those systems has a profound impact also on production cost and product quality. The early detection of faults is critical in avoiding performance degradation and damage to the machinery or human life. Accurate diagnosis then helps to make the right decisions on emergency actions and repairs. Fault detection and diagnosis (FDD) has developed into a major area of research, at the intersection of systems and control engineering, artificial intelligence, applied mathematics and statistics, and such application fields as chemical, electrical, mechanical and aerospace engineering. IFAC has recognized the significance of FDD by launching a triennial symposium series dedicated to the subject. The SAFEPROCESS Symposium is organized every three years since the first symposium held in Baden-Baden in 1991. SAFEPROCESS 2006, the 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes was held in Beijing, PR China. The program included three plenary papers, two semi-plenary papers, two industrial talks by internationally recognized experts and 258 regular papers, which have been selected out of a total of 387 regular and invited papers submitted. * Discusses the developments and future challenges in all aspects of fault diagnosis and fault tolerant control * 8 invited and 36 contributed sessions included with a special session on the demonstration of process monitoring and diagnostic software tools

Author : Nedunchezhian Swaminathan,Alessandro Parente
Publisher : Springer Nature
Page : 353 pages
File Size : 50,7 Mb
Release : 2023-01-01
Category : Technology & Engineering
ISBN : 9783031162480

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Machine Learning and Its Application to Reacting Flows by Nedunchezhian Swaminathan,Alessandro Parente Pdf

This open access book introduces and explains machine learning (ML) algorithms and techniques developed for statistical inferences on a complex process or system and their applications to simulations of chemically reacting turbulent flows. These two fields, ML and turbulent combustion, have large body of work and knowledge on their own, and this book brings them together and explain the complexities and challenges involved in applying ML techniques to simulate and study reacting flows. This is important as to the world’s total primary energy supply (TPES), since more than 90% of this supply is through combustion technologies and the non-negligible effects of combustion on environment. Although alternative technologies based on renewable energies are coming up, their shares for the TPES is are less than 5% currently and one needs a complete paradigm shift to replace combustion sources. Whether this is practical or not is entirely a different question, and an answer to this question depends on the respondent. However, a pragmatic analysis suggests that the combustion share to TPES is likely to be more than 70% even by 2070. Hence, it will be prudent to take advantage of ML techniques to improve combustion sciences and technologies so that efficient and “greener” combustion systems that are friendlier to the environment can be designed. The book covers the current state of the art in these two topics and outlines the challenges involved, merits and drawbacks of using ML for turbulent combustion simulations including avenues which can be explored to overcome the challenges. The required mathematical equations and backgrounds are discussed with ample references for readers to find further detail if they wish. This book is unique since there is not any book with similar coverage of topics, ranging from big data analysis and machine learning algorithm to their applications for combustion science and system design for energy generation.