Nonlinear Dimensionality Reduction Techniques
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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.
Methods of dimensionality reduction provide a way to understand and visualize the structure of complex data sets. Traditional methods like principal component analysis and classical metric multidimensional scaling suffer from being based on linear models. Until recently, very few methods were able to reduce the data dimensionality in a nonlinear way. However, since the late nineties, many new methods have been developed and nonlinear dimensionality reduction, also called manifold learning, has become a hot topic. New advances that account for this rapid growth are, e.g. the use of graphs to represent the manifold topology, and the use of new metrics like the geodesic distance. In addition, new optimization schemes, based on kernel techniques and spectral decomposition, have lead to spectral embedding, which encompasses many of the recently developed methods. This book describes existing and advanced methods to reduce the dimensionality of numerical databases. For each method, the description starts from intuitive ideas, develops the necessary mathematical details, and ends by outlining the algorithmic implementation. Methods are compared with each other with the help of different illustrative examples. The purpose of the book is to summarize clear facts and ideas about well-known methods as well as recent developments in the topic of nonlinear dimensionality reduction. With this goal in mind, methods are all described from a unifying point of view, in order to highlight their respective strengths and shortcomings. The book is primarily intended for statisticians, computer scientists and data analysts. It is also accessible to other practitioners having a basic background in statistics and/or computational learning, like psychologists (in psychometry) and economists.
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.
Modern Multidimensional Scaling
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Author : I. Borg
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-04
Modern Multidimensional Scaling written by I. Borg 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 2005-08-04 with Social Science categories.
The first edition was released in 1996 and has sold close to 2200 copies. Provides an up-to-date comprehensive treatment of MDS, a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space. The authors have added three chapters and exercise sets. The text is being moved from SSS to SSPP. The book is suitable for courses in statistics for the social or managerial sciences as well as for advanced courses on MDS. All the mathematics required for more advanced topics is developed systematically in the text.
Data Analytics In Bioinformatics
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Author : Rabinarayan Satpathy
language : en
Publisher: John Wiley & Sons
Release Date : 2021-01-20
Data Analytics In Bioinformatics written by Rabinarayan Satpathy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-20 with Computers categories.
Machine learning techniques are increasingly being used to address problems in computational biology and bioinformatics. Novel machine learning computational techniques to analyze high throughput data in the form of sequences, gene and protein expressions, pathways, and images are becoming vital for understanding diseases and future drug discovery. Machine learning techniques such as Markov models, support vector machines, neural networks, and graphical models have been successful in analyzing life science data because of their capabilities in handling randomness and uncertainty of data noise and in generalization. Machine Learning in Bioinformatics compiles recent approaches in machine learning methods and their applications in addressing contemporary problems in bioinformatics approximating classification and prediction of disease, feature selection, dimensionality reduction, gene selection and classification of microarray data and many more.
Sufficient Dimension Reduction
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Author : Bing Li
language : en
Publisher: CRC Press
Release Date : 2018-04-27
Sufficient Dimension Reduction written by Bing Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-27 with Mathematics categories.
Sufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field. Features Provides comprehensive coverage of this emerging research field. Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion. Reflects most recent advances such as nonlinear sufficient dimension reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data. Includes a set of computer codes written in R that are easily implemented by the readers. Uses real data sets available online to illustrate the usage and power of the described methods. Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones. The author Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.
Condition Monitoring With Vibration Signals
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Author : Hosameldin Ahmed
language : en
Publisher: John Wiley & Sons
Release Date : 2020-01-07
Condition Monitoring With Vibration Signals written by Hosameldin Ahmed and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-07 with Technology & Engineering categories.
Provides an extensive, up-to-date treatment of techniques used for machine condition monitoring Clear and concise throughout, this accessible book is the first to be wholly devoted to the field of condition monitoring for rotating machines using vibration signals. It covers various feature extraction, feature selection, and classification methods as well as their applications to machine vibration datasets. It also presents new methods including machine learning and compressive sampling, which help to improve safety, reliability, and performance. Condition Monitoring with Vibration Signals: Compressive Sampling and Learning Algorithms for Rotating Machines starts by introducing readers to Vibration Analysis Techniques and Machine Condition Monitoring (MCM). It then offers readers sections covering: Rotating Machine Condition Monitoring using Learning Algorithms; Classification Algorithms; and New Fault Diagnosis Frameworks designed for MCM. Readers will learn signal processing in the time-frequency domain, methods for linear subspace learning, and the basic principles of the learning method Artificial Neural Network (ANN). They will also discover recent trends of deep learning in the field of machine condition monitoring, new feature learning frameworks based on compressive sampling, subspace learning techniques for machine condition monitoring, and much more. Covers the fundamental as well as the state-of-the-art approaches to machine condition monitoringguiding readers from the basics of rotating machines to the generation of knowledge using vibration signals Provides new methods, including machine learning and compressive sampling, which offer significant improvements in accuracy with reduced computational costs Features learning algorithms that can be used for fault diagnosis and prognosis Includes previously and recently developed dimensionality reduction techniques and classification algorithms Condition Monitoring with Vibration Signals: Compressive Sampling and Learning Algorithms for Rotating Machines is an excellent book for research students, postgraduate students, industrial practitioners, and researchers.
Unsupervised Learning Approaches For Dimensionality Reduction And Data Visualization
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Author : B.K. Tripathy
language : en
Publisher: CRC Press
Release Date : 2021-09-01
Unsupervised Learning Approaches For Dimensionality Reduction And Data Visualization written by B.K. Tripathy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-01 with Business & Economics categories.
Unsupervised Learning Approaches for Dimensionality Reduction and Data Visualization describes such algorithms as Locally Linear Embedding (LLE), Laplacian Eigenmaps, Isomap, Semidefinite Embedding, and t-SNE to resolve the problem of dimensionality reduction in the case of non-linear relationships within the data. Underlying mathematical concepts, derivations, and proofs with logical explanations for these algorithms are discussed, including strengths and limitations. The book highlights important use cases of these algorithms and provides examples along with visualizations. Comparative study of the algorithms is presented to give a clear idea on selecting the best suitable algorithm for a given dataset for efficient dimensionality reduction and data visualization. FEATURES Demonstrates how unsupervised learning approaches can be used for dimensionality reduction Neatly explains algorithms with a focus on the fundamentals and underlying mathematical concepts Describes the comparative study of the algorithms and discusses when and where each algorithm is best suitable for use Provides use cases, illustrative examples, and visualizations of each algorithm Helps visualize and create compact representations of high dimensional and intricate data for various real-world applications and data analysis This book is aimed at professionals, graduate students, and researchers in Computer Science and Engineering, Data Science, Machine Learning, Computer Vision, Data Mining, Deep Learning, Sensor Data Filtering, Feature Extraction for Control Systems, and Medical Instruments Input Extraction.
Dimensionality Reduction In Machine Learning
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Author : Jamal Amani Rad
language : en
Publisher: Morgan Kaufmann
Release Date : 2025-02-04
Dimensionality Reduction In Machine Learning written by Jamal Amani Rad and has been published by Morgan Kaufmann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-04 with Computers categories.
Dimensionality Reduction in Machine Learning covers both the mathematical and programming sides of dimension reduction algorithms, comparing them in various aspects. Part One provides an introduction to Machine Learning and the Data Life Cycle, with chapters covering the basic concepts of Machine Learning, essential mathematics for Machine Learning, and the methods and concepts of Feature Selection. Part Two covers Linear Methods for Dimension Reduction, with chapters on Principal Component Analysis and Linear Discriminant Analysis. Part Three covers Non-Linear Methods for Dimension Reduction, with chapters on Linear Local Embedding, Multi-dimensional Scaling, and t-distributed Stochastic Neighbor Embedding.Finally, Part Four covers Deep Learning Methods for Dimension Reduction, with chapters on Feature Extraction and Deep Learning, Autoencoders, and Dimensionality reduction in deep learning through group actions. With this stepwise structure and the applied code examples, readers become able to apply dimension reduction algorithms to different types of data, including tabular, text, and image data. - Provides readers with a comprehensive overview of various dimension reduction algorithms, including linear methods, non-linear methods, and deep learning methods - Covers the implementation aspects of algorithms supported by numerous code examples - Compares different algorithms so the reader can understand which algorithm is suitable for their purpose - Includes algorithm examples that are supported by a Github repository which consists of full notebooks for the programming code
Dimension Reduction
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Author : Christopher J. C. Burges
language : en
Publisher: Now Publishers Inc
Release Date : 2010
Dimension Reduction written by Christopher J. C. Burges and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
We give a tutorial overview of several foundational methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the data lies. For projective methods, we review projection pursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, canonical correlation analysis (CCA), kernel CCA, Fisher discriminant analysis, oriented PCA, and several techniques for sufficient dimension reduction. For the manifold methods, we review multidimensional scaling (MDS), landmark MDS, Isomap, locally linear embedding, Laplacian eigenmaps, and spectral clustering. Although the review focuses on foundations, we also provide pointers to some more modern techniques. We also describe the correlation dimension as one method for estimating the intrinsic dimension, and we point out that the notion of dimension can be a scale-dependent quantity. The Nystr m method, which links several of the manifold algorithms, is also reviewed. We use a publicly available dataset to illustrate some of the methods. The goal is to provide a self-contained overview of key concepts underlying many of these algorithms, and to give pointers for further reading.