Data Science – serie

This textbook provides a solid mathematical basis for understanding popular data science algorithms for clustering and classification and shows that an in-depth understanding of the mathematics powering these algorithms gives insight into the underlying data. It presents a step-by-step derivation of these algorithms, outlining their implementation from scratch in a computationally sound way.Mathematics of Data Science: A Computational Approach to Clustering and Classificationproposes different ways of visualizing high-dimensional data to unveil hidden internal structures, andincludes graphical explanations and computed examples using publicly available data sets in nearly every chapter to highlight similarities and differences among the algorithms.

Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully.Nonnegative Matrix Factorization is accessible to a wide audience and is ideal for anyone interested in the workings of NMF. It discusses some new results on the nonnegative rank and the identifiability of NMF and makes available MATLAB codes for readers to run the numerical examples presented in the book. Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization.

The goal of Algorithmic Mathematics in Machine Learning is to explore several well-known machine learning and data analysis algorithms from a mathematical and programming perspective. In this unique book, the authors:Present machine learning methods, review the underlying mathematics, and provide programming exercises intended to deepen the reader's understanding.Accompany application areas with exercises that explore the unique characteristics of real-world data sets (e.g. pedestrian detection image data, biological cell data).Highlight new terminology and background information on mathematical concepts, as well as exercises, in "info-boxes" throughout the text.