This book on Principal Component Analysis (PCA) extensively explores the core analyses and case studies within this field, incorporating the latest advancements. Each chapter delves into various disciplines like engineering, administration, economics, and technology, showcasing diverse applications and the utility of PCA. The book emphasizes the integration of PCA with other algorithms and methodologies, highlighting the enhancements achieved through combined approaches. Moreover, the book elucidates updated versions or iterations of PCA, detailing their descriptions and practical applications.
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.
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.
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.
This book proposes applications of tensor decomposition to unsupervised feature extraction and feature selection. The author posits that although supervised methods including deep learning have become popular, unsupervised methods have their own advantages. He argues that this is the case because unsupervised methods are easy to learn since tensor decomposition is a conventional linear methodology. This book starts from very basic linear algebra and reaches the cutting edge methodologies applied to difficult situations when there are many features (variables) while only small number of samples are available. The author includes advanced descriptions about tensor decomposition including Tucker decomposition using high order singular value decomposition as well as higher order orthogonal iteration, and train tenor decomposition. The author concludes by showing unsupervised methods and their application to a wide range of topics. Allows readers to analyze data sets with small samples and many features; Provides a fast algorithm, based upon linear algebra, to analyze big data; Includes several applications to multi-view data analyses, with a focus on bioinformatics.
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.
This book brings together international scientists who focus on present-day and fossil cephalopods, ranging broadly from Paleozoic ammonoids to today's octopods. It covers systematics and evolution; hard- and soft part morphology; and ecology, biogeography, and taphonomy. The book also includes new evidence for the existence of an ink sac in fossil ammonoids and features the first record of an in-depth study of octopus ecology in Alaska.
Experimental Medicine: New Insights for the Healthcare Professional / 2012 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Experimental Medicine. The editors have built Experimental Medicine: New Insights for the Healthcare Professional / 2012 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Experimental Medicine in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Experimental Medicine: New Insights for the Healthcare Professional / 2012 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Osteonecrosis: New Insights for the Healthcare Professional: 2013 Edition is a ScholarlyBrief™ that delivers timely, authoritative, comprehensive, and specialized information about Genetics in a concise format. The editors have built Osteonecrosis: New Insights for the Healthcare Professional: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Genetics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Osteonecrosis: New Insights for the Healthcare Professional: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Multiple Sclerosis: New Insights for the Healthcare Professional: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Diagnosis and Screening. The editors have built Multiple Sclerosis: New Insights for the Healthcare Professional: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Diagnosis and Screening in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Multiple Sclerosis: New Insights for the Healthcare Professional: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
