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 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 Variable Selection in Principal Component Analysis written by Moses Mefika Sithole and published by . This book was released on 1992 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: The remainder of the thesis focuses on variable selection in PCA using measures of MVA. Various existing selection methods are described, and comparative studies on these methods available in the literature are reviewed. New methods for selecting variables, based of measures of MVA are then proposed and compared among themselves as well as with the M(subscript)2-procrustes criterion. This comparison is based on Monte Carlo simulation, and the behaviour of the selection methods is assessed in terms of the performance of the selected variables. In summary, the Monte Carlo results suggest that the proposed bootstrap technique for choosing k generally performs better than the cross-validatory technique of Eastment and Krzanowski (1982). Similarly, the Monte Carlo comparison of the variable selection methods shows that the proposed methods are comparable with or better than Krzanowski's (1987) M(subscript)2-procrustes criterion. These conclusions are mainly based on data simulated by means of Monte Carlo experiments. However, these techniques for choosing k and the various variable selection techniques are also evaluated on some real data sets. Some comments on alternative approaches and suggestions for possible extensions conclude the thesis.

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 and Interpretation in Principal Component Analysis written by Noriah Al-Kandari and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many research fields such as medicine, psychology, management and zoology, large numbers of variables are sometimes measured on each individual. As a result, the researcher will end up with a huge data set consisting of large number of variables, say p. Using this collected data set in any statistical analyses may cause several troubles. Thus, many cases demand a prior selection of the best subset of variables of size q, with q « p, to represent the entire data set in any data analysis. Evidently, the best subset of size q for some specified objective can always be determined by investigating systematically all possible subsets of size q, but such a procedure may be computationally difficult especially for large p. Also, in many applications, when a Principal Component Analysis (PCA) is done on a large number of variables, the resultant Principal Components (PCs) may not be easy to interpret. To aid interpretation, it is useful to reduce the number of variables as much as possible whilst capturing most of the variation of the complete data set, X. Thus, this thesis is aimed to reduce the studied number of variables in a given data set by selecting the best q out of p measured variables to highlight the main features of a structured data set as well as aiding the simultaneous interpretation of the first k (covariance or correlation) PCs. This desired aim can be achieved by generating several artificial data sets having different types of structures such as nearly independent variables, highly dependent variables and clustered variables. Then, for each structure, several Variable Selection Criteria (VSC) are applied in order to retain some subsets of size q. The efficiencies of these subsets retained are measured in order to determine the best criteria for retaining subsets of size q. Finally, the general results obtained from the entire artificial data analyses are evaluated on some real data sets having interesting covariance and correlation structures.

Download or read book Advances in Principal Component Analysis written by Fausto Pedro García Márquez and published by BoD – Books on Demand. This book was released on 2022-08-25 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Principal Component Analysis written by Parinya Sanguansat and published by BoD – Books on Demand. This book was released on 2012-03-02 with total page 304 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 image processing, biometric, face recognition and speech processing. It also includes the core concepts and the state-of-the-art methods in data analysis and feature extraction.

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 Neural Computing An Introduction written by R Beale and published by CRC Press. This book was released on 1990-01-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural computing is one of the most interesting and rapidly growing areas of research, attracting researchers from a wide variety of scientific disciplines. Starting from the basics, Neural Computing covers all the major approaches, putting each in perspective in terms of their capabilities, advantages, and disadvantages. The book also highlights the applications of each approach and explores the relationships among models developed and between the brain and its function. A comprehensive and comprehensible introduction to the subject, this book is ideal for undergraduates in computer science, physicists, communications engineers, workers involved in artificial intelligence, biologists, psychologists, and physiologists.

Download or read book Nonlinear System Identification written by Stephen A. Billings and published by John Wiley & Sons. This book was released on 2013-09-23 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.

Download or read book Introduction to Multivariate Analysis written by Sadanori Konishi and published by CRC Press. This book was released on 2014-06-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Select the Optimal Model for Interpreting Multivariate Data Introduction to Multivariate Analysis: Linear and Nonlinear Modeling shows how multivariate analysis is widely used for extracting useful information and patterns from multivariate data and for understanding the structure of random phenomena. Along with the basic concepts of various procedures in traditional multivariate analysis, the book covers nonlinear techniques for clarifying phenomena behind observed multivariate data. It primarily focuses on regression modeling, classification and discrimination, dimension reduction, and clustering. The text thoroughly explains the concepts and derivations of the AIC, BIC, and related criteria and includes a wide range of practical examples of model selection and evaluation criteria. To estimate and evaluate models with a large number of predictor variables, the author presents regularization methods, including the L1 norm regularization that gives simultaneous model estimation and variable selection. For advanced undergraduate and graduate students in statistical science, this text provides a systematic description of both traditional and newer techniques in multivariate analysis and machine learning. It also introduces linear and nonlinear statistical modeling for researchers and practitioners in industrial and systems engineering, information science, life science, and other areas.

Download or read book Data Science Classification and Related Methods written by Chikio Hayashi and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers covering a wide range of topics, including theoretical and methodological advances relating to data gathering, classification and clustering, exploratory and multivariate data analysis, and knowledge seeking and discovery. The result is a broad view of the state of the art, making this an essential work not only for data analysts, mathematicians, and statisticians, but also for researchers involved in data processing at all stages from data gathering to decision making.

Download or read book Proceeding of International Conference on Computational Science and Applications written by Subhash Bhalla and published by Springer Nature. This book was released on 2020-01-04 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of high-quality papers presented at the International Conference on Computational Science and Applications (ICCSA 2019), held at Maharashtra Institute of Technology World Peace University, Pune, India, from 7 to 9 August 2019. It covers the latest innovations and developments in information and communication technology, discussing topics such as soft computing and intelligent systems, web of sensor networks, drone operating systems, web of sensor networks, wearable smart sensors, automated guided vehicles and many more.

Download or read book Feature Engineering and Selection written by Max Kuhn and published by CRC Press. This book was released on 2019-07-25 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results.

Download or read book Raman Spectroscopy In Human Health And Biomedicine written by Hidetoshi Sato and published by World Scientific. This book was released on 2023-09-21 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the inelastic scattering of light was predicted nearly 100 years ago, Raman spectroscopy has become a mainstay of characterization techniques, with applications in a vast array of fields from chemistry to materials science and nanotechnology, from forensics to geology and art. More recently, it has found usage in the life sciences, and this book hereby outlines the state-of-the-art advances in applications of Raman spectroscopy to human health and biomedicine. It covers a wide range of human health science including medicine (especially cancer), physiology, biological molecules, pharmaceutical science, cells, viruses, microorganisms, and food science. Another highlight is that it describes recent progress on various Raman techniques such as surface-enhanced Raman scattering, tip-enhanced Raman scattering, non-linear Raman spectroscopy, Raman microscopy, and Raman imaging. Novel spectral analysis methods such as chemometrics are also prominently discussed.

Download or read book Using Traditional Design Methods to Enhance AI Driven Decision Making written by Nguyen, Tien V. T. and published by IGI Global. This book was released on 2024-01-10 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the rapidly evolving landscape of industrial activities, artificial intelligence (AI) has emerged as a powerful force driving transformative change. Among its many applications, AI has proven to be instrumental in reducing processing costs associated with optimization challenges. The intersection of AI with optimization and multi-criteria decision making (MCDM) techniques has led to practical solutions in diverse fields such as manufacturing, transportation, finance, economics, and artificial intelligence. Using Traditional Design Methods to Enhance AI-Driven Decision Making delves into a wide array of topics related to optimization, decision-making, and their applications. Drawing on foundational contributions, system developments, and innovative techniques, the book explores the synergy between traditional design methods and AI-driven decision-making approaches. The book is ideal for higher education faculty and administrators, students of higher education, librarians, researchers, graduate students, and academicians. Contributors are invited to explore a wide range of topics, including the role of AI-driven decision-making in leadership, trends in AI-driven decision-making in Industry 5.0, applications in various industries such as manufacturing, transportation, healthcare, and banking services, as well as AI-driven optimization in mechanical engineering and materials.

Download or read book XIII Mediterranean Conference on Medical and Biological Engineering and Computing 2013 written by Laura M. Roa Romero and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 1978 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theme of MEDICON 2013 is "Research and Development of Technology for Sustainable Healthcare". This decade is being characterized by the appearance and use of emergent technologies under development. This situation has produced a tremendous impact on Medicine and Biology from which it is expected an unparalleled evolution in these disciplines towards novel concept and practices. The consequence will be a significant improvement in health care and well-fare, i.e. the shift from a reactive medicine to a preventive medicine. This shift implies that the citizen will play an important role in the healthcare delivery process, what requires a comprehensive and personalized assistance. In this context, society will meet emerging media, incorporated to all objects, capable of providing a seamless, adaptive, anticipatory, unobtrusive and pervasive assistance. The challenge will be to remove current barriers related to the lack of knowledge required to produce new opportunities for all the society, while new paradigms are created for this inclusive society to be socially and economically sustainable, and respectful with the environment. In this way, these proceedings focus on the convergence of biomedical engineering topics ranging from formalized theory through experimental science and technological development to practical clinical applications.