Mathematical Classification And Clustering

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.

Classification and Clustering documents the proceedings of the Advanced Seminar on Classification and Clustering held in Madison, Wisconsin on May 3-5, 1976. This compilation discusses the relationship between multidimensional scaling and clustering, distribution problems in clustering, and botryology of botryology. The graph theoretic techniques for cluster analysis algorithms, data dependent clustering techniques, and linguistic approach to pattern recognition are also elaborated. This text likewise covers the discriminant analysis when scale contamination is present in the initial sample and statistical basis of computerized diagnosis using the electrocardiogram. Other topics include the simple histogram method for nonparametric classification and optimal smoothing of density estimates. This book is intended for mathematicians, biological scientists, social scientists, computer scientists, statisticians, and engineers interested in classification and clustering.

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 volume describes new methods with special emphasis on classification and cluster analysis. These methods are applied to problems in information retrieval, phylogeny, medical diagnosis, microarrays, and other active research areas.

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 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.

Clustering and classification: background and current directions; The relationship between multidimensional scaling and clustering; Distribution problems in clustering; The botryology of botryology; Graph theoretic techniques for cluster analysis algorithms; An empirical comparison of baseline models for goodness-of-fit in r-diameter hierarchical clustering; Data dependent clustering techniques; Cluster analysis applied to a study of race mixture in human populations; Linguistic approach to pattern recognition; Fuzzy sets and their application to pattern classification and clustering analysis; Discrimination, allocatory and separatory, linear aspects; Discriminant analysis when scale contamination is present in the initial sample; The statistical basis of computerrized diagnosis using the electrocardiogram; Linear discrimination some further results on best lower dimensional representations; A simple histogram method for nonparametric classification; Optimal smoothing of density estimates.