Cluster Analysis (2版)

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【簡介】 Cluster analysis is a fundamental data analysis task that aims to group similar data points together, revealing the inherent structure and patterns within complex datasets. This book serves as a comprehensive and accessible guide, taking readers on a captivating journey through the foundational principles of cluster analysis. At its core, the book delves deeply into various clustering algorithms, covering partitioning methods, hierarchical methods, and advanced techniques such as mixture density-based clustering, graph clustering, and grid-based clustering. Each method is presented with clear, concise explanations, supported by illustrative examples and hands-on implementations in the R programming language — a popular and powerful tool for data analysis and visualization. Recognizing the importance of cluster validation and evaluation, the book devotes a dedicated chapter to exploring a wide range of internal and external quality criteria, equipping readers with the necessary tools to assess the performance of clustering algorithms. For those eager to stay at the forefront of the field, the book also presents deep learning-based clustering methods, showcasing the remarkable capabilities of neural networks in uncovering hidden structures within complex, high-dimensional data. Whether you are a student seeking to expand your knowledge, a data analyst looking to enhance your toolbox, or a researcher exploring the frontiers of data analysis, this book will provide you with a solid foundation in cluster analysis and empower you to tackle a wide range of data-driven problems. 【目錄】 Introduction to Data Clustering Similarity Measures Partitioning Methods for Minimizing Distance Measures Hierarchical Methods Clustering Visualization Cluster Validity: Evaluation of Clustering Algorithms Mixture Densities-Based Clustering Graph Clustering Grid-Based Clustering Methods Deep Learning for Clustering Spectral Clustering

The Theory of Cluster Sets Vol:56

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The book provides an introduction to the theory of cluster sets, a branch of topological analysis which has made great strides in recent years. The cluster set of a function at a particular point is the set of limit values of the function at that point which may be either a boundary point or (in the case of a non-analytic function) an interior point of the function's domain. In topological analysis, its main application is to problems arising in the theory of functions of a complex variable, with particular reference to boundary behaviour such as the theory of prime ends under conformal mapping. An important and novel feature of the book is the discussion of more general applications to non-analytic functions, including arbitrary functions. The authors assume a general familiarity with classical function theory but include the more specialised material required for the development of the theory of cluster sets, so making the treatment accessible to graduate students.