A Study of Nonlinear Principal Component Analysis Using Neural Networks PDF Download
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Author: Ryō Saegusa
Publisher:
ISBN:
Category :
Languages : en
Pages : 58
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Book Description
Author: Ryō Saegusa
Publisher:
ISBN:
Category :
Languages : en
Pages : 58
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Book Description
Author: Alexander N. Gorban
Publisher: Springer Science & Business Media
ISBN: 3540737502
Category : Technology & Engineering
Languages : en
Pages : 361
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Book Description
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: Yuichi Mori
Publisher: Springer
ISBN: 9811001596
Category : Mathematics
Languages : en
Pages : 87
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Book Description
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: K. I. Diamantaras
Publisher: Wiley-Interscience
ISBN:
Category : Computers
Languages : en
Pages : 282
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Book Description
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: Agus Sudjianto
Publisher:
ISBN:
Category :
Languages : en
Pages : 318
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Book Description
Author: Rui Wu
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"F(x) = sin(x) + x", the Lorenz Attractor, and sunspot data. The results from the experiments have been analyzed and compared. Generally speaking, NLPCA can explain more variance than a neural network PCA (NN PCA) in lower dimensions. However, as a result of increasing the dimension, the NLPCA approximation will eventually loss its advantage. Finally, we introduce a new combination of NN PCA and NLPCA, and analyze and compare its performance.
Author: Brigitta Voss
Publisher:
ISBN: 9783832218034
Category :
Languages : en
Pages : 161
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Book Description
Author: A. R. Perrino
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Aapo Hyvärinen
Publisher: John Wiley & Sons
ISBN: 0471464198
Category : Science
Languages : en
Pages : 505
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Book Description
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: Wulfram Gerstner
Publisher: Springer Science & Business Media
ISBN: 9783540636311
Category : Computers
Languages : en
Pages : 1300
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Book Description
Content Description #Includes bibliographical references and index.
