Overview
- Reviews state-of-the-art methods in dimensionality reduction techniques, written in a clear but precise mathematical language
- Presents application of the methods to the representation of expert-designed fault indicators for smart buildings, I-V curves for photovoltaic systems and acoustic signals for Li-ion batteries
- Numerous appendices provide mathematical background to facilitate the understanding of the main text
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the authors
Benoit Colange graduated from the Ecole Centrale de Lyon and hte Universite Claude Bernard Lyon 1 in France. During his PhD training in collaboration between the CEA-INES and LAMA (Laboratory of Mathematics UMR 5127), he worked toward the connection of new methods for the analysis of metric data, including multidimensional data.The main purpose of this PhD was to provide innovative tools for the diagnosis of energy systems, such as photovoltaic power plants, electrochemical storage systems and smart buildings. His research interests mainly focus on dimensionality reduction and visual exploration of data.
Denys Dutykh completed his PhD at Ecole Normale Superieure de Cachan in 2007 on the topic of mathematical modelling of tsunami waves. He then joined CNRS (the French National Centre of Scientific Research) as afull-time researcher. In 2010 he defended his Habilitation thesis on the topic of mathematical modeling in the environment several years before it became mainstream. In 2012 and 2013 he lent the University College Dublin his expertise to the ERC AdG "Multiwave" project. Upon his return to CNRS in 2014 he started to diversify his research topics to include dimensionality reduction, building physics, electrochemistry, number theory and geometric approaches to Partial Differential Equations. Dr. Dutykh is the author of Numerical Methods for Diffusion Phenomena in Building Physics (Springer, 2019) and Dispersive Shallow Water Waves (Birkhauser, 2020) as well as many contributed book chapters, conference proceedings, and over 100 journal articles.
Bibliographic Information
Book Title: Nonlinear Dimensionality Reduction Techniques
Book Subtitle: A Data Structure Preservation Approach
Authors: Sylvain Lespinats, Benoit Colange, Denys Dutykh
DOI: https://doi.org/10.1007/978-3-030-81026-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-81025-2Published: 03 December 2021
Softcover ISBN: 978-3-030-81028-3Published: 04 December 2022
eBook ISBN: 978-3-030-81026-9Published: 02 December 2021
Edition Number: 1
Number of Pages: XLIII, 247
Number of Illustrations: 12 b/w illustrations, 88 illustrations in colour
Topics: Machine Learning, Data Structures and Information Theory, Artificial Intelligence, Computer Imaging, Vision, Pattern Recognition and Graphics, Signal, Image and Speech Processing