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Author: Nikita I. Lytkin
Publisher:
ISBN:
Category : Cluster analysis
Languages : en
Pages : 83
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Book Description
Two approaches have been proposed in statistical and machine learning communities in order to address the problem of uncovering clusters with complex structure. One approach relies on the development of clustering criteria that are able to accommodate increasingly complex characteristics of the data. The other approach is based on simplification of structure of data by mapping it to a different feature space via a non-linear function and then clustering in the new space. This dissertation covers three related studies: development of a novel multi-dimensional clustering method, development of non-linear mapping functions that leverage higher-order co-occurrences between features in boolean data, and applications of these mapping functions for improving the performance of clustering methods. In particular, we treat clustering as a combinatorial optimization problem of finding a partition of the data so as to minimize a certain criterion. We develop a novel multi-dimensional clustering method based on a statistically-motivated criterion proposed by J. Neyman for stratified sampling from one-dimensional data. We show that this criterion is more reflective of the underlying data structure than the seemingly similar K-means criterion when second order variability is not homogeneous between constituent subgroups. Furthermore, experimental results demonstrate that generalization of the Neyman's criterion to multi-dimensional spaces and development of the associated clustering algorithm allow for statistically efficient estimation of the grand mean vector of a population. In the framework of the mapping-based approach to discovering complex cluster structures, we introduced a novel adaptive non-linear data transformation termed Unsupervised Second Order Transformation (USOT). The novelties behind USOT are (a) that it leverages in a unsupervised manner, higher-order co-occurrences between features in boolean data, and (b) that it considers each feature in the context of probabilistic relationships with other features. In addition, USOT has two desirable properties. USOT adaptively selects features that would influence the mapping of a given feature, and preserves the interpretability of dimensions of the transformed space. Experimental results on text corpora and financial time series demonstrate that by leveraging higher-order co-occurrences between features, clustering methods achieved statistically significant improvements in USOT space over the original boolean space.
Author: Nikita I. Lytkin
Publisher:
ISBN:
Category : Cluster analysis
Languages : en
Pages : 83
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Book Description
Two approaches have been proposed in statistical and machine learning communities in order to address the problem of uncovering clusters with complex structure. One approach relies on the development of clustering criteria that are able to accommodate increasingly complex characteristics of the data. The other approach is based on simplification of structure of data by mapping it to a different feature space via a non-linear function and then clustering in the new space. This dissertation covers three related studies: development of a novel multi-dimensional clustering method, development of non-linear mapping functions that leverage higher-order co-occurrences between features in boolean data, and applications of these mapping functions for improving the performance of clustering methods. In particular, we treat clustering as a combinatorial optimization problem of finding a partition of the data so as to minimize a certain criterion. We develop a novel multi-dimensional clustering method based on a statistically-motivated criterion proposed by J. Neyman for stratified sampling from one-dimensional data. We show that this criterion is more reflective of the underlying data structure than the seemingly similar K-means criterion when second order variability is not homogeneous between constituent subgroups. Furthermore, experimental results demonstrate that generalization of the Neyman's criterion to multi-dimensional spaces and development of the associated clustering algorithm allow for statistically efficient estimation of the grand mean vector of a population. In the framework of the mapping-based approach to discovering complex cluster structures, we introduced a novel adaptive non-linear data transformation termed Unsupervised Second Order Transformation (USOT). The novelties behind USOT are (a) that it leverages in a unsupervised manner, higher-order co-occurrences between features in boolean data, and (b) that it considers each feature in the context of probabilistic relationships with other features. In addition, USOT has two desirable properties. USOT adaptively selects features that would influence the mapping of a given feature, and preserves the interpretability of dimensions of the transformed space. Experimental results on text corpora and financial time series demonstrate that by leveraging higher-order co-occurrences between features, clustering methods achieved statistically significant improvements in USOT space over the original boolean space.
Author: Michael R. Anderberg
Publisher: Academic Press
ISBN: 1483191397
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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.
Author: Charu C. Aggarwal
Publisher: CRC Press
ISBN: 1466558229
Category : Business & Economics
Languages : en
Pages : 648
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Book Description
Research on the problem of clustering tends to be fragmented across the pattern recognition, database, data mining, and machine learning communities. Addressing this problem in a unified way, Data Clustering: Algorithms and Applications provides complete coverage of the entire area of clustering, from basic methods to more refined and complex data clustering approaches. It pays special attention to recent issues in graphs, social networks, and other domains. The book focuses on three primary aspects of data clustering: Methods, describing key techniques commonly used for clustering, such as feature selection, agglomerative clustering, partitional clustering, density-based clustering, probabilistic clustering, grid-based clustering, spectral clustering, and nonnegative matrix factorization Domains, covering methods used for different domains of data, such as categorical data, text data, multimedia data, graph data, biological data, stream data, uncertain data, time series clustering, high-dimensional clustering, and big data Variations and Insights, discussing important variations of the clustering process, such as semisupervised clustering, interactive clustering, multiview clustering, cluster ensembles, and cluster validation In this book, top researchers from around the world explore the characteristics of clustering problems in a variety of application areas. They also explain how to glean detailed insight from the clustering process—including how to verify the quality of the underlying clusters—through supervision, human intervention, or the automated generation of alternative clusters.
Author: Guojun Gan
Publisher: SIAM
ISBN: 1611976332
Category : Mathematics
Languages : en
Pages : 430
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Book Description
Data clustering, also known as cluster analysis, is an unsupervised process that divides a set of objects into homogeneous groups. Since the publication of the first edition of this monograph in 2007, development in the area has exploded, especially in clustering algorithms for big data and open-source software for cluster analysis. This second edition reflects these new developments, covers the basics of data clustering, includes a list of popular clustering algorithms, and provides program code that helps users implement clustering algorithms. Data Clustering: Theory, Algorithms and Applications, Second Edition will be of interest to researchers, practitioners, and data scientists as well as undergraduate and graduate students.
Author: Rudolf Scitovski
Publisher: Springer Nature
ISBN: 303074552X
Category : Computers
Languages : en
Pages : 277
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Book Description
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.
Author: Gérard Govaert
Publisher: John Wiley & Sons
ISBN: 1118649508
Category : Computers
Languages : en
Pages : 246
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Book Description
Cluster or co-cluster analyses are important tools in a variety of scientific areas. The introduction of this book presents a state of the art of already well-established, as well as more recent methods of co-clustering. The authors mainly deal with the two-mode partitioning under different approaches, but pay particular attention to a probabilistic approach. Chapter 1 concerns clustering in general and the model-based clustering in particular. The authors briefly review the classical clustering methods and focus on the mixture model. They present and discuss the use of different mixtures adapted to different types of data. The algorithms used are described and related works with different classical methods are presented and commented upon. This chapter is useful in tackling the problem of co-clustering under the mixture approach. Chapter 2 is devoted to the latent block model proposed in the mixture approach context. The authors discuss this model in detail and present its interest regarding co-clustering. Various algorithms are presented in a general context. Chapter 3 focuses on binary and categorical data. It presents, in detail, the appropriated latent block mixture models. Variants of these models and algorithms are presented and illustrated using examples. Chapter 4 focuses on contingency data. Mutual information, phi-squared and model-based co-clustering are studied. Models, algorithms and connections among different approaches are described and illustrated. Chapter 5 presents the case of continuous data. In the same way, the different approaches used in the previous chapters are extended to this situation. Contents 1. Cluster Analysis. 2. Model-Based Co-Clustering. 3. Co-Clustering of Binary and Categorical Data. 4. Co-Clustering of Contingency Tables. 5. Co-Clustering of Continuous Data. About the Authors Gérard Govaert is Professor at the University of Technology of Compiègne, France. He is also a member of the CNRS Laboratory Heudiasyc (Heuristic and diagnostic of complex systems). His research interests include latent structure modeling, model selection, model-based cluster analysis, block clustering and statistical pattern recognition. He is one of the authors of the MIXMOD (MIXtureMODelling) software. Mohamed Nadif is Professor at the University of Paris-Descartes, France, where he is a member of LIPADE (Paris Descartes computer science laboratory) in the Mathematics and Computer Science department. His research interests include machine learning, data mining, model-based cluster analysis, co-clustering, factorization and data analysis. Cluster Analysis is an important tool in a variety of scientific areas. Chapter 1 briefly presents a state of the art of already well-established as well more recent methods. The hierarchical, partitioning and fuzzy approaches will be discussed amongst others. The authors review the difficulty of these classical methods in tackling the high dimensionality, sparsity and scalability. Chapter 2 discusses the interests of coclustering, presenting different approaches and defining a co-cluster. The authors focus on co-clustering as a simultaneous clustering and discuss the cases of binary, continuous and co-occurrence data. The criteria and algorithms are described and illustrated on simulated and real data. Chapter 3 considers co-clustering as a model-based co-clustering. A latent block model is defined for different kinds of data. The estimation of parameters and co-clustering is tackled under two approaches: maximum likelihood and classification maximum likelihood. Hard and soft algorithms are described and applied on simulated and real data. Chapter 4 considers co-clustering as a matrix approximation. The trifactorization approach is considered and algorithms based on update rules are described. Links with numerical and probabilistic approaches are established. A combination of algorithms are proposed and evaluated on simulated and real data. Chapter 5 considers a co-clustering or bi-clustering as the search for coherent co-clusters in biological terms or the extraction of co-clusters under conditions. Classical algorithms will be described and evaluated on simulated and real data. Different indices to evaluate the quality of coclusters are noted and used in numerical experiments.
Author: Chao Xu
Publisher: Frontiers Media SA
ISBN: 2889714365
Category : Science
Languages : en
Pages : 136
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Book Description
Author: G. De Giacomo
Publisher: IOS Press
ISBN: 164368101X
Category : Computers
Languages : en
Pages : 3122
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Book Description
This book presents the proceedings of the 24th European Conference on Artificial Intelligence (ECAI 2020), held in Santiago de Compostela, Spain, from 29 August to 8 September 2020. The conference was postponed from June, and much of it conducted online due to the COVID-19 restrictions. The conference is one of the principal occasions for researchers and practitioners of AI to meet and discuss the latest trends and challenges in all fields of AI and to demonstrate innovative applications and uses of advanced AI technology. The book also includes the proceedings of the 10th Conference on Prestigious Applications of Artificial Intelligence (PAIS 2020) held at the same time. A record number of more than 1,700 submissions was received for ECAI 2020, of which 1,443 were reviewed. Of these, 361 full-papers and 36 highlight papers were accepted (an acceptance rate of 25% for full-papers and 45% for highlight papers). The book is divided into three sections: ECAI full papers; ECAI highlight papers; and PAIS papers. The topics of these papers cover all aspects of AI, including Agent-based and Multi-agent Systems; Computational Intelligence; Constraints and Satisfiability; Games and Virtual Environments; Heuristic Search; Human Aspects in AI; Information Retrieval and Filtering; Knowledge Representation and Reasoning; Machine Learning; Multidisciplinary Topics and Applications; Natural Language Processing; Planning and Scheduling; Robotics; Safe, Explainable, and Trustworthy AI; Semantic Technologies; Uncertainty in AI; and Vision. The book will be of interest to all those whose work involves the use of AI technology.
Author: Krzystof Jajuga
Publisher: Springer Science & Business Media
ISBN: 3642561810
Category : Computers
Languages : en
Pages : 468
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Book Description
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.
Author: Petra Perner
Publisher: Springer
ISBN: 354073435X
Category : Computers
Languages : en
Pages : 362
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Book Description
The papers in this volume represent the proceedings of the 7th Industrial Conference on Data Mining. They are organized into topical sections on aspects of classification and prediction, clustering, web mining, data mining in medicine, applications of data mining, time series and frequent pattern mining, and association rule mining. Readers gain new insights into theories underlying data mining and discover state-of-the-technology applications.
