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.
Описание: In multivariate data analysis, regression techniques predict one set of variables from another while principal component analysis (PCA) finds a subspace of minimal dimensionality that captures the largest variability in the data. How can regression analysis and PCA be combined in a beneficial way? Why and when is it a good idea to combine them? What kind of benefits are we getting from them? Addressing these questions, Constrained Principal Component Analysis and Related Techniques shows how constrained PCA (CPCA) offers a unified framework for these approaches. The book begins with four concrete examples of CPCA that provide readers with a basic understanding of the technique and its applications. It gives a detailed account of two key mathematical ideas in CPCA: projection and singular value decomposition. The author then describes the basic data requirements, models, and analytical tools for CPCA and their immediate extensions. He also introduces techniques that are special cases of or closely related to CPCA and discusses several topics relevant to practical uses of CPCA. The book concludes with a technique that imposes different constraints on different dimensions (DCDD), along with its analytical extensions. MATLAB® programs for CPCA and DCDD as well as data to create the book’s examples are available on the author’s website.
Автор: Roberts Название: Independent Component Analysis ISBN: 0521792983 ISBN-13(EAN): 9780521792981 Издательство: Cambridge Academ Рейтинг: Цена: 18620 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Series of edited papers on Independent Component Analysis, containing theory and applications.
Автор: Hwang Название: Generalized Structured Component ISBN: 146659294X ISBN-13(EAN): 9781466592940 Издательство: Taylor&Francis Рейтинг: Цена: 15426 р. Наличие на складе: Поставка под заказ.
Описание: Winner of the 2015 Sugiyama Meiko Award (Publication Award) of the Behaviormetric Society of Japan Developed by the authors, generalized structured component analysis is an alternative to two longstanding approaches to structural equation modeling: covariance structure analysis and partial least squares path modeling. Generalized structured component analysis allows researchers to evaluate the adequacy of a model as a whole, compare a model to alternative specifications, and conduct complex analyses in a straightforward manner. Generalized Structured Component Analysis: A Component-Based Approach to Structural Equation Modeling provides a detailed account of this novel statistical methodology and its various extensions. The authors present the theoretical underpinnings of generalized structured component analysis and demonstrate how it can be applied to various empirical examples. The book enables quantitative methodologists, applied researchers, and practitioners to grasp the basic concepts behind this new approach and apply it to their own research. The book emphasizes conceptual discussions throughout while relegating more technical intricacies to the chapter appendices. Most chapters compare generalized structured component analysis to partial least squares path modeling to show how the two component-based approaches differ when addressing an identical issue. The authors also offer a free, online software program (GeSCA) and an Excel-based software program (XLSTAT) for implementing the basic features of generalized structured component analysis.
Автор: J. Edward Jackson Название: A User`s Guide to Principal Components ISBN: 0471471348 ISBN-13(EAN): 9780471471349 Издательство: Wiley Рейтинг: Цена: 24321 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Dealing with the "how to do it" as well as the `"why it works," this book is designed for practitioners of principal component analysis. It explores topics such as: extension to p variables, scaling input data, inferential procedures, operations with group data, and vector interpretation.
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