Download or read book Principal Component Analysis and Its Extensions with Applications on Nonlinear Feature Extraction and Self similar Network Traffic Analysis written by Sek Kin Neng and published by . This book was released on 2000 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Principal Component Analysis Networks and Algorithms written by Xiangyu Kong and published by Springer. This book was released on 2017-01-09 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book not only provides a comprehensive introduction to neural-based PCA methods in control science, but also presents many novel PCA algorithms and their extensions and generalizations, e.g., dual purpose, coupled PCA, GED, neural based SVD algorithms, etc. It also discusses in detail various analysis methods for the convergence, stabilizing, self-stabilizing property of algorithms, and introduces the deterministic discrete-time systems method to analyze the convergence of PCA/MCA algorithms. Readers should be familiar with numerical analysis and the fundamentals of statistics, such as the basics of least squares and stochastic algorithms. Although it focuses on neural networks, the book only presents their learning law, which is simply an iterative algorithm. Therefore, no a priori knowledge of neural networks is required. This book will be of interest and serve as a reference source to researchers and students in applied mathematics, statistics, engineering, and other related fields.
Download or read book Non Linear Feature Extraction by Linear Principal Component Analysis Using Local Kernel written by Kazuhiro Hotta and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose how to solve KPCA with the local summation kernel by linear PCA. In the classification process, KPCA must compute kernel functions with all training samples, and the computational cost and memory required are high. This is the drawback. In this paper, an input feature is divided into some local features, and local feature xli is mapped to high dimensional space by ( xli ). In this formulation, the dimension of new feature vector ( xl1 ) T , . . . , ( xlN ) T.
Download or read book Three mode Principal Component Analysis written by Pieter M. Kroonenberg and published by . This book was released on 1983 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Comparison Study of Principal Component Analysis and Nonlinear Principal Component Analysis written by Rui Wu and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Principal Components Analysis written by George H. Dunteman and published by SAGE Publications, Incorporated. This book was released on 1989-05 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principal components analysis offers researchers a 'feel' for analysing particular sets of multidimensional data. It is particularly useful in coping with multicolinearity in regression analysis, a persistent problem in behavioral and social science data sets.
Download or read book A Study of Nonlinear Principal Component Analysis Using Neural Networks written by Ryō Saegusa and published by . This book was released on 2005 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterative Kernel Principal Component for Large Scale Data Set written by Weiya Shi and published by . This book was released on 2018 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel principal component analysis (KPCA) is a popular nonlinear feature extraction method that uses eigendecomposition techniques to extract the principal components in the feature space. Most of the existing approaches are not feasible for analyzing large-scale data sets because of extensive storage needs and computation costs. To overcome these disadvantages, an efficient iterative method for computing kernel principal components is proposed. First, the power iteration is used to compute the first eigenvalue and the corresponding eigenvector. Then Schur-Weilandt deflation is repeatedly applied to obtain other higher order eigenvectors. No computation and storage of the kernel matrix is involved in this procedure. Instead, each row of the kernel matrix is calculated sequentially through the iterations. Thus, the kernel principal components can be computed without relying on the traditional eigendecomposition. The space complexity of the proposed method isO(m), and the time complexity is also greatly reduced. We illustrate the effectiveness of our approach through a series of real data experiments.
Download or read book Geometric Applications of Principal Component Analysis written by Darko Dimitrov and published by . This book was released on 2008 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Principal Component Analysis written by Yi Ma and published by Springer. This book was released on 2015-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to introduce a new method to study hybrid models, referred to as generalized principal component analysis. The general problems that GPCA aims to address represents a fairly general class of unsupervised learning problems— many data clustering and modeling methods in machine learning can be viewed as special cases of this method. This book provides a comprehensive introduction of the fundamental statistical, geometric and algebraic concepts associated with the estimation (and segmentation) of the hybrid models, especially the hybrid linear models.
Download or read book Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards written by and published by . This book was released on 2007 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Using Independent Component Analysis for Feature Extraction and Multivariate Data Projection written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Deriving low-dimensional perceptual spaces from data consisting of many variables is of crucial interest in strategic market planning. A frequently used method in this context is Principal Components Analysis, which finds uncorrelated directions in the data. This methodology which supports the identification of competitive structures can gainfully be utilized for product (re)positioning or optimal product (re)design. In our paper, we investigate the usefulness of a novel technique, Independent Component Analysis, to discover market structures. Independent Component Analysis is an extension of Principal Components Analysis in the sense that it looks for directions in the data that are not only uncorrelated but also independent. Comparing the two approaches on the basis of an empirical data set, we find that Independent Component Analysis leads to clearer and sharper structures than Principal Components Analysis. Furthermore, the results of Independent Component Analysis have a reasonable marketing interpretation. (author's abstract).
Download or read book A Neural Network for Non Linear Principal Component Analysis written by Tom Björkholm and published by . This book was released on 1992 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Non linear Principal Component Analysis for Process Monitoring written by Kamal Majed Shannak and published by . This book was released on 2004 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non linear principal component analysis technique using neural networks written by A. R. Perrino and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robust Extensions to Generalized Principal Component Analysis written by Shankar Ramamohan Rao and published by . This book was released on 2004 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
