Nonlinear Dimensionality Reduction
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Nonlinear Dimensionality Reduction
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Author : John A. Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-31
Nonlinear Dimensionality Reduction written by John A. Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-31 with Mathematics categories.
This book describes established and advanced methods for reducing the dimensionality of numerical databases. Each description starts from intuitive ideas, develops the necessary mathematical details, and ends by outlining the algorithmic implementation. The text provides a lucid summary of facts and concepts relating to well-known methods as well as recent developments in nonlinear dimensionality reduction. Methods are all described from a unifying point of view, which helps to highlight their respective strengths and shortcomings. The presentation will appeal to statisticians, computer scientists and data analysts, and other practitioners having a basic background in statistics or computational learning.
Nonlinear Dimensionality Reduction Techniques
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Author : Sylvain Lespinats
language : en
Publisher: Springer Nature
Release Date : 2021-12-02
Nonlinear Dimensionality Reduction Techniques written by Sylvain Lespinats and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-02 with Computers categories.
This book proposes tools for analysis of multidimensional and metric data, by establishing a state-of-the-art of the existing solutions and developing new ones. It mainly focuses on visual exploration of these data by a human analyst, relying on a 2D or 3D scatter plot display obtained through Dimensionality Reduction. Performing diagnosis of an energy system requires identifying relations between observed monitoring variables and the associated internal state of the system. Dimensionality reduction, which allows to represent visually a multidimensional dataset, constitutes a promising tool to help domain experts to analyse these relations. This book reviews existing techniques for visual data exploration and dimensionality reduction such as tSNE and Isomap, and proposes new solutions to challenges in that field. In particular, it presents the new unsupervised technique ASKI and the supervised methods ClassNeRV and ClassJSE. Moreover, MING, a new approach for local map quality evaluation is also introduced. These methods are then applied to the representation of expert-designed fault indicators for smart-buildings, I-V curves for photovoltaic systems and acoustic signals for Li-ion batteries.
Elements Of Dimensionality Reduction And Manifold Learning
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Author : Benyamin Ghojogh
language : en
Publisher: Springer Nature
Release Date : 2023-02-02
Elements Of Dimensionality Reduction And Manifold Learning written by Benyamin Ghojogh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-02 with Computers categories.
Dimensionality reduction, also known as manifold learning, is an area of machine learning used for extracting informative features from data for better representation of data or separation between classes. This book presents a cohesive review of linear and nonlinear dimensionality reduction and manifold learning. Three main aspects of dimensionality reduction are covered: spectral dimensionality reduction, probabilistic dimensionality reduction, and neural network-based dimensionality reduction, which have geometric, probabilistic, and information-theoretic points of view to dimensionality reduction, respectively. The necessary background and preliminaries on linear algebra, optimization, and kernels are also explained to ensure a comprehensive understanding of the algorithms. The tools introduced in this book can be applied to various applications involving feature extraction, image processing, computer vision, and signal processing. This book is applicable to a wide audience who would like to acquire a deep understanding of the various ways to extract, transform, and understand the structure of data. The intended audiences are academics, students, and industry professionals. Academic researchers and students can use this book as a textbook for machine learning and dimensionality reduction. Data scientists, machine learning scientists, computer vision scientists, and computer scientists can use this book as a reference. It can also be helpful to statisticians in the field of statistical learning and applied mathematicians in the fields of manifolds and subspace analysis. Industry professionals, including applied engineers, data engineers, and engineers in various fields of science dealing with machine learning, can use this as a guidebook for feature extraction from their data, as the raw data in industry often require preprocessing. The book is grounded in theory but provides thorough explanations and diverse examples to improve the reader’s comprehension of the advanced topics. Advanced methods are explained in a step-by-step manner so that readers of all levels can follow the reasoning and come to a deep understanding of the concepts. This book does not assume advanced theoretical background in machine learning and provides necessary background, although an undergraduate-level background in linear algebra and calculus is recommended.
Open Problems In Spectral Dimensionality Reduction
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Author : Harry Strange
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-07
Open Problems In Spectral Dimensionality Reduction written by Harry Strange and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-07 with Computers categories.
The last few years have seen a great increase in the amount of data available to scientists, yet many of the techniques used to analyse this data cannot cope with such large datasets. Therefore, strategies need to be employed as a pre-processing step to reduce the number of objects or measurements whilst retaining important information. Spectral dimensionality reduction is one such tool for the data processing pipeline. Numerous algorithms and improvements have been proposed for the purpose of performing spectral dimensionality reduction, yet there is still no gold standard technique. This book provides a survey and reference aimed at advanced undergraduate and postgraduate students as well as researchers, scientists, and engineers in a wide range of disciplines. Dimensionality reduction has proven useful in a wide range of problem domains and so this book will be applicable to anyone with a solid grounding in statistics and computer science seeking to apply spectral dimensionality to their work.
Principal Manifolds For Data Visualization And Dimension Reduction
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Author : Alexander N. Gorban
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-11
Principal Manifolds For Data Visualization And Dimension Reduction written by Alexander N. Gorban and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-11 with Technology & Engineering categories.
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.
Multi Label Dimensionality Reduction
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Author : Liang Sun
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Multi Label Dimensionality Reduction written by Liang Sun and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Business & Economics categories.
Similar to other data mining and machine learning tasks, multi-label learning suffers from dimensionality. An effective way to mitigate this problem is through dimensionality reduction, which extracts a small number of features by removing irrelevant, redundant, and noisy information. The data mining and machine learning literature currently lacks
Geometric Structure Of High Dimensional Data And Dimensionality Reduction
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Author : Jianzhong Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-28
Geometric Structure Of High Dimensional Data And Dimensionality Reduction written by Jianzhong Wang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-28 with Computers categories.
"Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists. Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A.
Materials Science And Engineering
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Author : S. Samudrala
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-07-10
Materials Science And Engineering written by S. Samudrala and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-10 with Technology & Engineering categories.
Materials science research has witnessed an increasing use of data-mining techniques in establishing structure–process–property relationships. Significant advances in high-throughput experiments and computational capability have resulted in the generation of huge amounts of data. Various statistical methods are currently employed to reduce the noise, redundancy, and dimensionality of the data to make analysis more tractable. Popular methods for reduction (such as principal component analysis) assume a linear relationship between the input and output variables. Recent developments in nonlinear reduction (neural networks, self-organizing maps), though successful, have computational issues associated with convergence and scalability. This chapter reviews various spectral-based techniques that efficiently unravel linear and nonlinear structures in the data, which can subsequently be used to tractably investigate structure–property–process relationships. We compare and contrast the advantages and disadvantages of these techniques and discuss the mathematical and algorithmic underpinning of these methods. In addition, we describe techniques (based on graph-theoretic analysis) to estimate the optimal dimensionality of the low-dimensional parametric representation. We show how these techniques can be packaged into a modular, computationally scalable software framework with a graphical user interface – Scalable Extensible Toolkit for Dimensionality Reduction (SETDiR). This interface helps to separate out the mathematics and computational aspects from the material science applications, thus significantly enhancing utility to the materials science community. The applicability of the framework in constructing reduced order models of complicated materials data sets is illustrated.
Nonlinear Principal Component Analysis And Its Applications
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Author : Yuichi Mori
language : en
Publisher: Springer
Release Date : 2016-12-09
Nonlinear Principal Component Analysis And Its Applications written by Yuichi Mori and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-09 with Mathematics categories.
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.
Evolutionary Multi Criterion Optimization
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Author : Shigeru Obayashi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-12
Evolutionary Multi Criterion Optimization written by Shigeru Obayashi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-12 with Computers categories.
This book constitutes the refereed proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2007, held in Matsushima, Japan in March 2007. The 65 revised full papers presented together with 4 invited papers are organized in topical sections on algorithm design, algorithm improvements, alternative methods, applications, engineering design, many objectives, objective handling, and performance assessments.