Dimension 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.

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.

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.

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.

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.

Dimension Reduction Of Large Scale Systems

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Author : Peter Benner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Dimension Reduction Of Large Scale Systems written by Peter Benner 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 2006-03-30 with Technology & Engineering categories.

In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

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

Machine Learning Techniques For Multimedia

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Author : Matthieu Cord
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-07

Machine Learning Techniques For Multimedia written by Matthieu Cord 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 2008-02-07 with Computers categories.

Processing multimedia content has emerged as a key area for the application of machine learning techniques, where the objectives are to provide insight into the domain from which the data is drawn, and to organize that data and improve the performance of the processes manipulating it. Applying machine learning techniques to multimedia content involves special considerations – the data is typically of very high dimension, and the normal distinction between supervised and unsupervised techniques does not always apply. This book provides a comprehensive coverage of the most important machine learning techniques used and their application in this domain. Arising from the EU MUSCLE network, a program that drew together multidisciplinary teams with expertise in machine learning, pattern recognition, artificial intelligence, and image, video, text and crossmedia processing, the book first introduces the machine learning principles and techniques that are applied in multimedia data processing and analysis. The second part focuses on multimedia data processing applications, with chapters examining specific machine learning issues in domains such as image retrieval, biometrics, semantic labelling, mobile devices, and mining in text and music. This book will be suitable for practitioners, researchers and students engaged with machine learning in multimedia applications.

Dimensionality Reduction In Data Science

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Author : Max Garzon
language : en
Publisher: Springer Nature
Release Date : 2022-07-28

Dimensionality Reduction In Data Science written by Max Garzon and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-28 with Computers categories.

This book provides a practical and fairly comprehensive review of Data Science through the lens of dimensionality reduction, as well as hands-on techniques to tackle problems with data collected in the real world. State-of-the-art results and solutions from statistics, computer science and mathematics are explained from the point of view of a practitioner in any domain science, such as biology, cyber security, chemistry, sports science and many others. Quantitative and qualitative assessment methods are described to implement and validate the solutions back in the real world where the problems originated. The ability to generate, gather and store volumes of data in the order of tera- and exo bytes daily has far outpaced our ability to derive useful information with available computational resources for many domains. This book focuses on data science and problem definition, data cleansing, feature selection and extraction, statistical, geometric, information-theoretic, biomolecular and machine learning methods for dimensionality reduction of big datasets and problem solving, as well as a comparative assessment of solutions in a real-world setting. This book targets professionals working within related fields with an undergraduate degree in any science area, particularly quantitative. Readers should be able to follow examples in this book that introduce each method or technique. These motivating examples are followed by precise definitions of the technical concepts required and presentation of the results in general situations. These concepts require a degree of abstraction that can be followed by re-interpreting concepts like in the original example(s). Finally, each section closes with solutions to the original problem(s) afforded by these techniques, perhaps in various ways to compare and contrast dis/advantages to other solutions.

Factor Analysis And Dimension Reduction In R

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Author : G. David Garson
language : en
Publisher: Taylor & Francis
Release Date : 2022-12-16

Factor Analysis And Dimension Reduction In R written by G. David Garson and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-16 with Psychology categories.

Factor Analysis and Dimension Reduction in R provides coverage, with worked examples, of a large number of dimension reduction procedures along with model performance metrics to compare them. Factor analysis in the form of principal components analysis (PCA) or principal factor analysis (PFA) is familiar to most social scientists. However, what is less familiar is understanding that factor analysis is a subset of the more general statistical family of dimension reduction methods. The social scientist's toolkit for factor analysis problems can be expanded to include the range of solutions this book presents. In addition to covering FA and PCA with orthogonal and oblique rotation, this book’s coverage includes higher-order factor models, bifactor models, models based on binary and ordinal data, models based on mixed data, generalized low-rank models, cluster analysis with GLRM, models involving supplemental variables or observations, Bayesian factor analysis, regularized factor analysis, testing for unidimensionality, and prediction with factor scores. The second half of the book deals with other procedures for dimension reduction. These include coverage of kernel PCA, factor analysis with multidimensional scaling, locally linear embedding models, Laplacian eigenmaps, diffusion maps, force directed methods, t-distributed stochastic neighbor embedding, independent component analysis (ICA), dimensionality reduction via regression (DRR), non-negative matrix factorization (NNMF), Isomap, Autoencoder, uniform manifold approximation and projection (UMAP) models, neural network models, and longitudinal factor analysis models. In addition, a special chapter covers metrics for comparing model performance. Features of this book include: Numerous worked examples with replicable R code Explicit comprehensive coverage of data assumptions Adaptation of factor methods to binary, ordinal, and categorical data Residual and outlier analysis Visualization of factor results Final chapters that treat integration of factor analysis with neural network and time series methods Presented in color with R code and introduction to R and RStudio, this book will be suitable for graduate-level and optional module courses for social scientists, and on quantitative methods and multivariate statistics courses.

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.