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This book begins with an introduction of pragmatic cluster randomized trials (PCTs) and reviews various pragmatic issues that need to be addressed by statisticians at the design stage. It discusses the advantages and disadvantages of each type of PCT, and provides sample size formulas, sensitivity analyses, and examples for sample size calculation. The generalized estimating equation (GEE) method will be employed to derive sample size formulas for various types of outcomes from the exponential family, including continuous, binary, and count variables. Experimental designs that have been frequently employed in PCTs will be discussed, including cluster randomized designs, matched-pair cluster randomized design, stratified cluster randomized design, stepped-wedge cluster randomized design, longitudinal cluster randomized design, and crossover cluster randomized design. It demonstrates that the GEE approach is flexible to accommodate pragmatic issues such as hierarchical correlation structures, different missing data patterns, randomly varying cluster sizes, etc. It has been reported that the GEE approach leads to under-estimated variance with limited numbers of clusters. The remedy for this limitation is investigated for the design of PCTs. This book can assist practitioners in the design of PCTs by providing a description of the advantages and disadvantages of various PCTs and sample size formulas that address various pragmatic issues, facilitating the proper implementation of PCTs to improve health care. It can also serve as a textbook for biostatistics students at the graduate level to enhance their knowledge or skill in clinical trial design.Key Features: Discuss the advantages and disadvantages of each type of PCTs, and provide sample size formulas, sensitivity analyses, and examples. Address an unmet need for guidance books on sample size calculations for PCTs; A wide variety of experimental designs adopted by PCTs are covered; The sample size solutions can be readily implemented due to the accommodation of common pragmatic issues encountered in real-world practice; Useful to both academic and industrial biostatisticians involved in clinical trial design; Can be used as a textbook for graduate students majoring in statistics and biostatistics.

This is the first technical book that considers tests as public tools and examines how to engineer and process test data, extract the structure within the data to be visualized, and thereby make test results useful for students, teachers, and the society. The author does not differentiate test data analysis from data engineering and information visualization. This monograph introduces the following methods of engineering or processing test data, including the latest machine learning techniques: classical test theory (CTT), item response theory (IRT), latent class analysis (LCA), latent rank analysis (LRA), biclustering (co-clustering), and Bayesian network model (BNM). CTT and IRT are methods for analyzing test data and evaluating students'abilities on a continuous scale. LCA and LRA assess examinees by classifying them into nominal and ordinal clusters, respectively, where the adequate number of clusters is estimated from the data. Biclustering classifies examinees into groups (latent clusters) while classifying items into fields (factors). Particularly, the infinite relational model discussed in this book is a biclustering method feasible under the condition that neither the number of groups nor the number of fields is known beforehand. Additionally, the local dependence LRA, local dependence biclustering, and bicluster network model are methods that search and visualize inter-item (or inter-field) network structure using the mechanism of BNM. As this book offers a new perspective on test data analysis methods, it is certain to widen readers'perspective on test data analysis.

With the development of Big Data platforms for managing massive amount of data and wide availability of tools for processing these data, the biggest limitation is the lack of trained experts who are qualified to process and interpret the results. This textbook is intended for graduate students and experts using methods of cluster analysis and applications in various fields.Suitable for an introductory course on cluster analysis or data mining, with an in-depth mathematical treatment that includes discussions on different measures, primitives (points, lines, etc.) and optimization-based clustering methods, Cluster Analysis and Applications also includes coverage of deep learning based clustering methods.With clear explanations of ideas and precise definitions of concepts, accompanied by numerous examples and exercises together with Mathematica programs and modules, Cluster Analysis and Applications may be used by students and researchers in various disciplines, working in data analysis or data science.

This book introduces the basic concepts of fuzzy collaborative forecasting and clustering, including its methodology, system architecture, and applications. It demonstrates how dealing with disparate data sources is becoming more and more popular due to the increasing spread of internet applications. The book proposes the concepts of collaborative computing intelligence and collaborative fuzzy modeling, and establishes several so-called fuzzy collaborative systems. It shows how technical constraints, security issues, and privacy considerations often limit access to some sources. This book is a valuable source of information for postgraduates, researchers and fuzzy control system developers, as it presents a very effective fuzzy approach that can deal with disparate data sources, big data, and multiple expert decision making.

The purpose of this book is to thoroughly prepare the reader for applied research in clustering. Cluster analysis comprises a class of statistical techniques for classifying multivariate data into groups or clusters based on their similar features. Clustering is nowadays widely used in several domains of research, such as social sciences, psychology, and marketing, highlighting its multidisciplinary nature. This book provides an accessible and comprehensive introduction to clustering and offers practical guidelines for applying clustering tools by carefully chosen real-life datasets and extensive data analyses. The procedures addressed in this book include traditional hard clustering methods and up-to-date developments in soft clustering. Attention is paid to practical examples and applications through the open source statistical software R. Commented R code and output for conducting, step by step, complete cluster analyses are available. The book is intended for researchers interested in applying clustering methods. Basic notions on theoretical issues and on R are provided so that professionals as well as novices with little or no background in the subject will benefit from the book.

Covers everything readers need to know about clustering methodology for symbolic data—including new methods and headings—while providing a focus on multi-valued list data, interval data and histogram data This book presents all of the latest developments in the field of clustering methodology for symbolic data—paying special attention to the classification methodology for multi-valued list, interval-valued and histogram-valued data methodology, along with numerous worked examples. The book also offers an expansive discussion of data management techniques showing how to manage the large complex dataset into more manageable datasets ready for analyses. Filled with examples, tables, figures, and case studies, Clustering Methodology for Symbolic Data begins by offering chapters on data management, distance measures, general clustering techniques, partitioning, divisive clustering, and agglomerative and pyramid clustering. Provides new classification methodologies for histogram valued data reaching across many fields in data science Demonstrates how to manage a large complex dataset into manageable datasets ready for analysis Features very large contemporary datasets such as multi-valued list data, interval-valued data, and histogram-valued data Considers classification models by dynamical clustering Features a supporting website hosting relevant data sets Clustering Methodology for Symbolic Data will appeal to practitioners of symbolic data analysis, such as statisticians and economists within the public sectors. It will also be of interest to postgraduate students of, and researchers within, web mining, text mining and bioengineering.

The beginning of the age of artificial intelligence and machine learning has created new challenges and opportunities for data analysts, statisticians, mathematicians, econometricians, computer scientists and many others. At the root of these techniques are algorithms and methods for clustering and classifying different types of large datasets, including time series data.Time Series Clustering and Classification includes relevant developments on observation-based, feature-based and model-based traditional and fuzzy clustering methods, feature-based and model-based classification methods, and machine learning methods. It presents a broad and self-contained overview of techniques for both researchers and students.Features Provides an overview of the methods and applications of pattern recognition of time series Covers a wide range of techniques, including unsupervised and supervised approaches Includes a range of real examples from medicine, finance, environmental science, and more R and MATLAB code, and relevant data sets are available on a supplementary website

This book highlights the state of the art and recent advances in Big Data clustering methods and their innovative applications in contemporary AI-driven systems. The book chapters discuss Deep Learning for Clustering, Blockchain data clustering, Cybersecurity applications such as insider threat detection, scalable distributed clustering methods for massive volumes of data; clustering Big Data Streams such as streams generated by the confluence of Internet of Things, digital and mobile health, human-robot interaction, and social networks; Spark-based Big Data clustering using Particle Swarm Optimization; and Tensor-based clustering for Web graphs, sensor streams, and social networks. The chapters in the book include a balanced coverage of big data clustering theory, methods, tools, frameworks, applications, representation, visualization, and clustering validation.

This book provides the reader with a basic understanding of the formal concepts of the cluster, clustering, partition, cluster analysis etc. The book explains feature-based, graph-based and spectral clustering methods and discusses their formal similarities and differences. Understanding the related formal concepts is particularly vital in the epoch of Big Data; due to the volume and characteristics of the data, it is no longer feasible to predominantly rely on merely viewing the data when facing a clustering problem. Usually clustering involves choosing similar objects and grouping them together. To facilitate the choice of similarity measures for complex and big data, various measures of object similarity, based on quantitative (like numerical measurement results) and qualitative features (like text), as well as combinations of the two, are described, as well as graph-based similarity measures for (hyper) linked objects and measures for multilayered graphs. Numerous variants demonstrating how such similarity measures can be exploited when defining clustering cost functions are also presented. In addition, the book provides an overview of approaches to handling large collections of objects in a reasonable time. In particular, it addresses grid-based methods, sampling methods, parallelization via Map-Reduce, usage of tree-structures, random projections and various heuristic approaches, especially those used for community detection.

Partitioning data sets into disjoint groups is a problem arising in many domains. The theory of cluster analysis aims to find groups that are both homogeneous (entities in the same group that are similar) and well separated (entities in different groups that are dissimilar). There has been rapid expansion in the axiomatic foundations and the computational complexity of such problems and in the design and analysis of exact or heuristic algorithms to solve them. Applications have burgeoned in psychology, computer vision, target tracking, and other areas. This book contains papers presented at the workshop Partioning Data Sets held at DIMACS in April 1993. Some of the papers cover the main paradigms of the field of cluster analysis methods and algorithms. Other topics include partitioning problems arising from multitarget tracking and surveillance and from computer and human vision. The multiplicity of approaches, methods, problems, and algorithms make for lively and informative reading.

Cluster Randomised Trials, Second Edition discusses the design, conduct, and analysis of trials that randomise groups of individuals to different treatments. It explores the advantages of cluster randomisation, with special attention given to evaluating the effects of interventions against infectious diseases. Avoiding unnecessary mathematical detail, the book covers basic concepts underlying the use of cluster randomisation, such as direct, indirect, and total effects.In the time since the publication of the first edition, the use of cluster randomised trials (CRTs) has increased substantially, which is reflected in the updates to this edition. There are greatly expanded sections on randomisation, sample size estimation, and alternative designs, including new material on stepped wedge designs. There is a new section on handling ordinal outcome data, and an appendix with descriptions and/or generating code of the example data sets.Although the book mainly focuses on medical and public health applications, it shows that the rigorous evidence of intervention effects provided by CRTs has the potential to inform public policy in a wide range of other areas. The book encourages readers to apply the methods to their own trials, reproduce the analyses presented, and explore alternative approaches.

Handbook of Cluster Analysis provides a comprehensive and unified account of the main research developments in cluster analysis. Written by active, distinguished researchers in this area, the book helps readers make informed choices of the most suitable clustering approach for their problem and make better use of existing cluster analysis tools.The

Clustering remains a vibrant area of research in statistics. Although there are many books on this topic, there are relatively few that are well founded in the theoretical aspects. This book presents an overview of the theory and applications of probabilistic clustering and variable selection, synthesizing the key research results of the last 50 years. It includes all the important theoretical details, and covers the probabilistic models and inference, robustness issues, optimization algorithms, validation techniques and variable selection methods. The book illustrates the different methods with simulated data and applies them to real-world data sets that can be easily downloaded from the web.

Cluster Analysis for Applications deals with methods and various applications of cluster analysis. Topics covered range from variables and scales to measures of association among variables and among data units. Conceptual problems in cluster analysis are discussed, along with hierarchical and non-hierarchical clustering methods. The necessary elements of data analysis, statistics, cluster analysis, and computer implementation are integrated vertically to cover the complete path from raw data to a finished analysis. Comprised of 10 chapters, this book begins with an introduction to the subject of cluster analysis and its uses as well as category sorting problems and the need for cluster analysis algorithms. The next three chapters give a detailed account of variables and association measures, with emphasis on strategies for dealing with problems containing variables of mixed types. Subsequent chapters focus on the central techniques of cluster analysis with particular reference to computational considerations; interpretation of clustering results; and techniques and strategies for making the most effective use of cluster analysis. The final chapter suggests an approach for the evaluation of alternative clustering methods. The presentation is capped with a complete set of implementing computer programs listed in the Appendices to make the use of cluster analysis as painless and free of mechanical error as is possible. This monograph is intended for students and workers who have encountered the notion of cluster analysis.

Often considered more of an art than a science, books on clustering have been dominated by learning through example with techniques chosen almost through trial and error. Even the two most popular, and most related, clustering methods-K-Means for partitioning and Ward's method for hierarchical clustering-have lacked the theoretical underpinning req

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.

In the last few years, the tremendous growth in the use of clustered survey methods in data mining in the presence of cluster effects has dichotomized the subject of econometrics due to the nature and problems in the way the data is being gathered. This book develops and investigates diagnostic tests for such cluster effects. In addition, this book also considers several aspects of hypothesis testing problems associated with the testing for cluster effects using the multi-stage model, stochastic model and testing for change point problem in more complex data.

With a DVD of color figures, Clustering in Bioinformatics and Drug Discovery provides an expert guide on extracting the most pertinent information from pharmaceutical and biomedical data. It offers a concise overview of common and recent clustering methods used in bioinformatics and drug discovery.Setting the stage for subsequent material, the firs

This book provides a theoretical foundation for the analysis of discrete data such as count and binary data in the longitudinal setup. Unlike the existing books, this book uses a class of auto-correlation structures to model the longitudinal correlations for the repeated discrete data that accommodates all possible Gaussian type auto-correlation models as special cases including the equi-correlation models. This new dynamic modelling approach is utilized to develop theoretically sound inference techniques such as the generalized quasi-likelihood (GQL) technique for consistent and efficient estimation of the underlying regression effects involved in the model, whereas the existing ‘working'correlations based GEE (generalizedestimating equations) approach has serious theoretical limitations both for consistent and efficient estimation, and the existing random effects based correlations approach is not suitable to model the longitudinal correlations. The book has exploited the random effects carefully only to model the correlations of the familial data. Subsequently, this book has modelled the correlations of the longitudinal data collected from the members of a large number of independent families by using the class of auto-correlation structures conditional on the random effects. The book also provides models and inferences for discrete longitudinal data in the adaptive clinical trial set up.The book is mathematically rigorous and provides details for the development of estimation approaches under selected familial and longitudinal models. Further, while the book provides special cares for mathematics behind the correlation models, it also presents theillustrations of the statistical analysis of various real life data. This book will be of interest to the researchers including graduate students in biostatistics and econometrics, among other applied statistics research areas. Brajendra Sutradhar is a University ResearchProfessor at Memorial University in St. John's, Canada. He is an elected member of the International Statistical Institute and a fellow of the American Statistical Association. He has published about 110 papers in statistics journals in the area of multivariate analysis, time series analysis including forecasting, sampling, survival analysis for correlated failure times, robust inferences in generalized linear mixed models with outliers, and generalized linear longitudinal mixed models with bio-statistical and econometric applications. He has served as an associate editor for six years for Canadian Journal of Statistics and for four years for the Journal of Environmental and Ecological Statistics. He has served for 3 years as a member of the advisory committee on statistical methods in Statistics Canada. Professor Sutradhar was awarded 2007 distinguished service award of Statistics Society of Canada for his many years of services to thesociety including his special services for society's annual meetings.

A culmination of the authors'years of extensive research on this topic, Relational Data Clustering: Models, Algorithms, and Applications addresses the fundamentals and applications of relational data clustering. It describes theoretic models and algorithms and, through examples, shows how to apply these models and algorithms to solve real-world problems.After defining the field, the book introduces different types of model formulations for relational data clustering, presents various algorithms for the corresponding models, and demonstrates applications of the models and algorithms through extensive experimental results. The authors cover six topics of relational data clustering:Clustering on bi-type heterogeneous relational dataMulti-type heterogeneous relational data Homogeneous relational data clusteringClustering on the most general case of relational dataIndividual relational clustering frameworkRecent research on evolutionary clusteringThis book focuses on both practical algorithm derivation and theoretical framework construction for relational data clustering. It provides a complete, self-contained introduction to advances in the field.

This book is intended to provide a text on statistical methods for detecting clus ters and/or clustering of health events that is of interest to?nal year undergraduate and graduate level statistics, biostatistics, epidemiology, and geography students but will also be of relevance to public health practitioners, statisticians, biostatisticians, epidemiologists, medical geographers, human geographers, environmental scien tists, and ecologists. Prerequisites are introductory biostatistics and epidemiology courses. With increasing public health concerns about environmental risks, the need for sophisticated methods for analyzing spatial health events is immediate. Further more, the research area of statistical tests for disease clustering now attracts a wide audience due to the perceived need to implement wide ranging monitoring systems to detect possible health related bioterrorism activity. With this background and the development of the geographical information system (GIS), the analysis of disease clustering of health events has seen considerable development over the last decade. Therefore, several excellent books on spatial epidemiology and statistics have re cently been published. However, it seems to me that there is no other book solely focusing on statistical methods for disease clustering. I hope that readers will?nd this book useful and interesting as an introduction to the subject.

This is the first book to take a truly comprehensive look at clustering. It begins with an introduction to cluster analysis and goes on to explore: proximity measures; hierarchical clustering; partition clustering; neural network-based clustering; kernel-based clustering; sequential data clustering; large-scale data clustering; data visualization and high-dimensional data clustering; and cluster validation. The authors assume no previous background in clustering and their generous inclusion of examples and references help make the subject matter comprehensible for readers of varying levels and backgrounds.

Design of water control structures, reservoir management, economic evaluation of flood protection projects, land use planning and management, flood insurance assessment, and other projects rely on knowledge of magnitude and frequency of floods. Often, estimation of floods is not easy because of lack of flood records at the target sites. Regional flood frequency analysis (RFFA) alleviates this problem by utilizing flood records pooled from other watersheds, which are similar to the watershed of the target site in flood characteristics. Clustering techniques are used to identify group(s) of watersheds which have similar flood characteristics. This book is a comprehensive reference on how to use these techniques for RFFA and is the first of its kind. It provides a detailed account of several recently developed clustering techniques, including those based on fuzzy set theory and artificial neural networks. It also documents research findings on application of clustering techniques to RFFA that remain scattered in various hydrology and water resources journals. The optimal number of groups defined in an area is based on cluster validation measures and L-moment based homogeneity tests. These form the bases to check the regions for homogeneity. The subjectivity involved and the effort needed to identify homogeneous groups of watersheds with conventional approaches are greatly reduced by using efficient clustering techniques discussed in this book. Furthermore, better flood estimates with smaller confidence intervals are obtained by analysis of data from homogeneous watersheds. Consequently, the problem of over- or under-designing by using these flood estimates is reduced. This leads to optimal economic design of structures. The advantages of better regionalization of watersheds and their utility are entering into hydrologic practice. Audience:This book will be of interest to researchers in stochastic hydrology, practitioners in hydrology and graduate students.

Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.

Dataclusteringisacommontechniqueforstatisticaldataanalysis,whichisusedin many?elds, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the classi?cation of similar objects into di?erent groups, or more precisely, the partitioning of a data set into subsets (clusters), so that the data in each subset (ideally) share some common trait – often proximity according to some de?ned distance measure. The aim of this book is to illustrate that advanced fuzzy clustering algorithms can be used not only for partitioning of the data, but it can be used for visuali- tion,regression,classi?cationandtime-seriesanalysis,hence fuzzy cluster analysis is a good approach to solve complex data mining and system identi?cation pr- lems. Overview In the last decade the amount of the stored data has rapidly increased related to almost all areas of life. The most recent survey was given by Berkeley University of California about the amount of data. According to that, data produced in 2002 and stored in pressed media,?lms and electronics devices only are about 5 - abytes. For comparison, if all the 17 million volumes of Library of Congress of the UnitedStatesofAmericaweredigitalized,itwouldbeabout136terabytes. Hence, 5 exabytes is about 37,000 Library of Congress. If this data mass is projected into 6. 3 billion inhabitants of the Earth, then it roughly means that each contem- rary generates 800 megabytes of data every year. It is interesting to compare this amount with Shakespeare's life-work, which can be stored even in 5 megabytes.

Clustering is one of the most fundamental and essential data analysis techniques. Clustering can be used as an independent data mining task to discern intrinsic characteristics of data, or as a preprocessing step with the clustering results then used for classification, correlation analysis, or anomaly detection. Kogan and his co-editors have put together recent advances in clustering large and high-dimension data. Their volume addresses new topics and methods which are central to modern data analysis, with particular emphasis on linear algebra tools, opimization methods and statistical techniques. The contributions, written by leading researchers from both academia and industry, cover theoretical basics as well as application and evaluation of algorithms, and thus provide an excellent state-of-the-art overview. The level of detail, the breadth of coverage, and the comprehensive bibliography make this book a perfect fit for researchers and graduate students in data mining and in many other important related application areas.

It is a great privilege and pleasure to write a foreword for a book honor­ ing Wolfgang Gaul on the occasion of his sixtieth birthday. Wolfgang Gaul is currently Professor of Business Administration and Management Science and the Head of the Institute of Decision Theory and Management Science, Faculty of Economics, University of Karlsruhe (TH), Germany. He is, by any measure, one of the most distinguished and eminent scholars in the world today. Wolfgang Gaul has been instrumental in numerous leading research initia­ tives and has achieved an unprecedented level of success in facilitating com­ munication among researchers in diverse disciplines from around the world. A particularly remarkable and unique aspect of his work is that he has been a leading scholar in such diverse areas of research as graph theory and net­ work models, reliability theory, stochastic optimization, operations research, probability theory, sampling theory, cluster analysis, scaling and multivariate data analysis. His activities have been directed not only at these and other theoretical topics, but also at applications of statistical and mathematical tools to a multitude of important problems in computer science (e.g., w- mining), business research (e.g., market segmentation), management science (e.g., decision support systems) and behavioral sciences (e.g., preference mea­ surement and data mining). All of his endeavors have been accomplished at the highest level of professional excellence.

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.'Cluster analysis is the increasingly important and practical subject of finding groupings in data. The authors set out to write a book for the user who does not necessarily have an extensive background in mathematics. They succeed very well.'—Mathematical Reviews'Finding Groups in Data [is] a clear, readable, and interesting presentation of a small number of clustering methods. In addition, the book introduced some interesting innovations of applied value to clustering literature.'—Journal of Classification'This is a very good, easy-to-read, and practical book. It has many nice features and is highly recommended for students and practitioners in various fields of study.'—Technometrics An introduction to the practical application of cluster analysis, this text presents a selection of methods that together can deal with most applications. These methods are chosen for their robustness, consistency, and general applicability. This book discusses various types of data, including interval-scaled and binary variables as well as similarity data, and explains how these can be transformed prior to clustering.

Often considered more as an art than a science, the field of clustering has been dominated by learning through examples and by techniques chosen almost through trial-and-error. Even the most popular clustering methods--K-Means for partitioning the data set and Ward's method for hierarchical clustering--have lacked the theoretical attention that wou

Research has generated a number of advances in methods for spatial cluster modelling in recent years, particularly in the area of Bayesian cluster modelling. Along with these advances has come an explosion of interest in the potential applications of this work, especially in epidemiology and genome research. In one integrated volume, this b