Nonlinear Dimensionality Reduction Techniques: A Data Structure Preservation Approach (Paperback)

Nonlinear Dimensionality Reduction Techniques: A Data Structure Preservation Approach By Sylvain Lespinats, Benoit Colange, Denys Dutykh Cover Image

Nonlinear Dimensionality Reduction Techniques: A Data Structure Preservation Approach (Paperback)

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This book proposes tools for analysis of multidimensional and metric data, by establishing a state-of-the-art of the existing solutions and developing new ones. It mainly focuses on visual exploration of these data by a human analyst, relying on a 2D or 3D scatter plot display obtained through Dimensionality Reduction.
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.


After his PhD degree in biomathematics from Pierre and Marie Curie University, Sylvain Lespinats held postdoc positions at several institutions, including INSERM (the French National Institute of Medical Reseach), INREST (the French National Insistute of Transport and Security Research), and some universities and research institutes. He is currently a permanent researcher at CEA-INES (the French National Institute of Solar Energy) near Chambery. He is the author or co-author of about 50 papers and more then ten patents. His work is dedicated to providing ad hoc approaches for data mining and knowledge discovery to his colleagues in various fields, including genomics, virology, quantitiative sociology, transport security, solar energy forecasting, solar plang security, and battery diagnosis. Dr. Lespinats's scientific interests include the exhibition of spatial structures in high dimensional data. In that framework, he developed several non-linear mapping methods and worked on the local evaluation of mappings. Recently he mainly focuses on renewable data to contribute to energy transition.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 a full-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.
Product Details ISBN: 9783030810283
ISBN-10: 3030810283
Publisher: Springer
Publication Date: December 4th, 2022
Pages: 247
Language: English