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Elements of Dimensionality Reduction and Manifold Learning (Hardcover, 1st ed. 2023)
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Elements of Dimensionality Reduction and Manifold Learning (Hardcover, 1st ed. 2023)
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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.
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