Название: Elements of Dimensionality Reduction and Manifold Learning
Автор: Benyamin Ghojogh, Mark Crowley, Fakhri Karray
Издательство: Springer
Год: 2023
Страниц: 617
Язык: английский
Формат: pdf (true), epub
Размер: 36.06 MB

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. With the explosion of interest and advances in Machine Learning (ML), there has been a corresponding increased need for educational and reference books to explain various aspects of Machine Learning. However, there has not been a comprehensive text tackling the various methods in dimensionality reduction, Manifold Learning, and feature extraction that integrate with modern Machine Learning theory and practice.

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. This book delves into basic concepts and recent developments in the field of dimensionality reduction and Manifold Learning, providing the reader with a comprehensive understanding. The necessary background and preliminaries on linear algebra, optimization, and kernels are also highlighted 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.

Targeted Readers:

This book provides the required understanding to extract, transform, and interpret the structure of data. It is intended for 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 for both technical and applied concepts. 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.

This book is structured as a reference textbook so that it can be used for advanced courses, as an in-depth supplementary resource or for researchers or practitioners who want to learn about dimensionality reduction and Manifold Learning. 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 an advanced theoretical background in Machine Learning and provides the necessary background, although an undergraduate-level background in linear algebra and calculus is recommended.

Contents:
1. Introduction
Part I. Preliminaries and Background
Part II. Spectral Dimensionality Reduction
Part III. Probabilistic Dimensionality Reduction
Part IV. Neural Network-Based Dimensionality Reduction