Overview
- Comprehensive and in-depth treatment of the mathematical foundations of data science
- Guiding from general optimization approaches to finding structures in data
- Provides exercises for each chapter
- Elaborating the methodological intersection between data science and machine learning
- Providing material for a three hours per week course on data analytics for graduate students
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Table of contents (7 chapters)
Keywords
- dimensionality reduction
- principal component analysis
- multidimensional scaling
- classification
- machine learning
- data science
- supervised machine learning
- dimensionality reduction
- principal component analysis
- clustering
- diffusion maps
- ISOMAP
- spectral clustering
- matrix optimization and approximation
- support vector machines
- kernel methods
- Markov decision processes
- MapReduce
- artificial intelligence
- unsupervised machine learning
About this book
This book introduces the basic methodologies for successful data analytics. Matrix optimization and approximation are explained in detail and extensively applied to dimensionality reduction by principal component analysis and multidimensional scaling. Diffusion maps and spectral clustering are derived as powerful tools. The methodological overlap between data science and machine learning is emphasized by demonstrating how data science is used for classification as well as supervised and unsupervised learning.
Authors and Affiliations
About the authors
RUDOLF MATHAR received the Ph.D. degree from RWTH Aachen University in 1981. He held lecturer positions with Augsburg University and the European Business School. In 1989, he joined the Faculty of Natural Sciences, RWTH Aachen University as a professor for stochastics in computer science. In 2004, he was appointed full professor as the Head of the Institute for Theoretical Information Technology, RWTH Aachen University. Since 1994, he has held numerous visiting professor positions abroad. In 2011 he was elected Dean of the Faculty of Electrical Engineering and Information Technology. From 2014 to 2018 he served as Vice-rector for research and structure with RWTH Aachen University. His research interests include information theory and communication systems. Recently his research and teaching has focused on data science and machine learning. In 2019 he accepted the position of Associate Vice President (CIO) with the University of Cologne. In 2002, he was the recipient of the prestigious Vodafone Innovation Award. In 2010, he was elected member of the NRW Academy of Sciences and Arts. He is the co-founder of four spin-off enterprises, the last one aiXbrain GmbH, dealing with artificial intelligence for engineering processes.
GHOLAMREZA ALIREZAEI received the Ph.D. degree from RWTH Aachen University in 2014. He also received the habilitation degree from the same university in 2019. Currently he holds lecturer positions with RWTH Aachen University and Technical University of Munich. His research interests include signal processing, information theory and artificial intelligence. From 2008 to 2011 he was the head of the research and development (R&D) section at ATecoM GmbH. He received several awards and recognitions for his scientific research, among others he is the recipient of the ITG-Literature Prize and the Vodafone Young-Researcher Award.
EMILIO BALDA received the M.Sc. degree in communications and signal processing from Ilmenau University of Technology, Germany, in 2017. He obtained his Ph.D. degree from RWTH Aachen University in 2019. Since 2019, he has been an AI developer with aiXbrain GmbH. His research interests are machine learning, optimization and signal processing.
ARASH BEHBOODI received his Ph.D. degree in electrical engineering focused on information theory from École Supérieure délectricité (now CentraleSupélec), France in 2012, Masters in Philosophy from University of Paris 1- Pantheon Sorbonne in 2010 and Masters in electrical engineering from Sharif University of Technology in 2007. He has been co-recipient of multiple best paper awards in the field of machine learning and signal processing. He is currently a machine learning researcher with Qualcomm AI research. His research interests are focused on theory of information, communication, signal processing and machine learning.
Bibliographic Information
Book Title: Fundamentals of Data Analytics
Book Subtitle: With a View to Machine Learning
Authors: Rudolf Mathar, Gholamreza Alirezaei, Emilio Balda, Arash Behboodi
DOI: https://doi.org/10.1007/978-3-030-56831-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-56830-6Published: 16 September 2020
Softcover ISBN: 978-3-030-56833-7Published: 17 September 2021
eBook ISBN: 978-3-030-56831-3Published: 15 September 2020
Edition Number: 1
Number of Pages: XI, 127
Number of Illustrations: 13 b/w illustrations, 28 illustrations in colour
Topics: Statistical Theory and Methods, Big Data, Data Structures and Information Theory, Artificial Intelligence, Statistics and Computing/Statistics Programs