Elements of dimensionality reduction and manifold learning / Benyamin Ghojogh, Mark Crowley, Fakhri Karray, Ali Ghodsi.
Ghojogh, Benyamin, author.; Crowley, Mark, author.; Karray, Fakhri, author.; Ghodsi, Ali, author.
2023
TA347.D5
Available Online

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Title Elements of dimensionality reduction and manifold learning / Benyamin Ghojogh, Mark Crowley, Fakhri Karray, Ali Ghodsi.
Author Ghojogh, Benyamin, author.
ISBN 9783031106026 (electronic bk.)
3031106024 (electronic bk.)
3031106016
9783031106019
DOI https://doi.org/10.1007/978-3-031-10602-6
Published Cham : Springer, [2023]
Copyright ©2023
Language English
Description 1 online resource (xxviii, 606 pages) : illustrations (some color)
Item Number 10.1007/978-3-031-10602-6 doi
Call Number TA347.D5
Dewey Decimal Classification 519.5/36
Summary 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 readers 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Crowley, Mark, author.
Karray, Fakhri, author.
Ghodsi, Ali, author.
Available in Other Form ELEMENTS OF DIMENSIONALITY REDUCTION AND MANIFOLD LEARNING.
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Chapter 1: Introduction
Part 1: Preliminaries and Background
Chapter 2: Background on Linear Algebra
Chapter 3: Background on Kernels
Chapter 4: Background on Optimization
Part 2: Spectral dimensionality Reduction
Chapter 5: Principal Component Analysis
Chapter 6: Fisher Discriminant Analysis
Chapter 7: Multidimensional Scaling, Sammon Mapping, and Isomap
Chapter 8: Locally Linear Embedding
Chapter 9: Laplacian-based Dimensionality Reduction
Chapter 10: Unified Spectral Framework and Maximum Variance Unfolding
Chapter 11: Spectral Metric Learning
Part 3: Probabilistic Dimensionality Reduction
Chapter 12: Factor Analysis and Probabilistic Principal Component Analysis
Chapter 13: Probabilistic Metric Learning
Chapter 14: Random Projection
Chapter 15: Sufficient Dimension Reduction and Kernel Dimension Reduction
Chapter 16: Stochastic Neighbour Embedding
Chapter 17: Uniform Manifold Approximation and Projection (UMAP)
Part 4: Neural Network-based Dimensionality Reduction
Chapter 18: Restricted Boltzmann Machine and Deep Belief Network
Chapter 19: Deep Metric Learning
Chapter 20: Variational Autoencoders
Chapter 21: Adversarial Autoencoders.

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