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 Classification proposes different ways of visualizing high-dimensional data to unveil hidden internal structures, and nearly every chapter includes graphical explanations and computed examples using publicly available data sets to highlight similarities and differences among the algorithms. This self-contained book is geared toward advanced undergraduate and beginning graduate students in the mathematical sciences, engineering, and computer science and can be used as the main text in a semester course. Researchers in any application area where data science methods are used will also find the book of interest. No advanced mathematical or statistical background is assumed.

Colorful example-rich introduction to the state-of-the-art for students in data science, as well as researchers and practitioners.

I am very happy to have this opportunity to present the work of Boris Mirkin, a distinguished Russian scholar in the areas of data analysis and decision making methodologies. The monograph is devoted entirely to clustering, a discipline dispersed through many theoretical and application areas, from mathematical statistics and combina torial optimization to biology, sociology and organizational structures. It compiles an immense amount of research done to date, including many original Russian de velopments never presented to the international community before (for instance, cluster-by-cluster versions of the K-Means method in Chapter 4 or uniform par titioning in Chapter 5). The author's approach, approximation clustering, allows him both to systematize a great part of the discipline and to develop many in novative methods in the framework of optimization problems. The optimization methods considered are proved to be meaningful in the contexts of data analysis and clustering. The material presented in this book is quite interesting and stimulating in paradigms, clustering and optimization. On the other hand, it has a substantial application appeal. The book will be useful both to specialists and students in the fields of data analysis and clustering as well as in biology, psychology, economics, marketing research, artificial intelligence, and other scientific disciplines. Panos Pardalos, Series Editor.

At a moderately advanced level, this book seeks to cover the areas of clustering and related methods of data analysis where major advances are being made. Topics include: hierarchical clustering, variable selection and weighting, additive trees and other network models, relevance of neural network models to clustering, the role of computational complexity in cluster analysis, latent class approaches to cluster analysis, theory and method with applications of a hierarchical classes model in psychology and psychopathology, combinatorial data analysis, clusterwise aggregation of relations, review of the Japanese-language results on clustering, review of the Russian-language results on clustering and multidimensional scaling, practical advances, and significance tests.

This edited volume on the latest advances in data science covers a wide range of topics in the context of data analysis and classification. In particular, it includes contributions on classification methods for high-dimensional data, clustering methods, multivariate statistical methods, and various applications. The book gathers a selection of peer-reviewed contributions presented at the Fifteenth Conference of the International Federation of Classification Societies (IFCS2015), which was hosted by the Alma Mater Studiorum, University of Bologna, from July 5 to 8, 2015.

The book presents a long list of useful methods for classification, clustering and data analysis. By combining theoretical aspects with practical problems, it is designed for researchers as well as for applied statisticians and will support the fast transfer of new methodological advances to a wide range of applications.

This volume presents the latest advances in statistics and data science, including theoretical, methodological and computational developments and practical applications related to classification and clustering, data gathering, exploratory and multivariate data analysis, statistical modeling, and knowledge discovery and seeking. It includes contributions on analyzing and interpreting large, complex and aggregated datasets, and highlights numerous applications in economics, finance, computer science, political science and education. It gathers a selection of peer-reviewed contributions presented at the 16th Conference of the International Federation of Classification Societies (IFCS 2019), which was organized by the Greek Society of Data Analysis and held in Thessaloniki, Greece, on August 26-29, 2019.