Download or read book SOME RESULTS IN CLUSTER SET THEORY written by PHILIP THROOP CHURCH and published by . This book was released on 1958 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cluster Sets written by Kiyoshi Noshiro and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first systematic investigations of the theory of cluster sets of analytic functions, we are indebted to IVERSEN [1-3J and GROSS [1-3J about forty years ago. Subsequent important contributions before 1940 were made by SEIDEL [1-2J, DOOE [1-4J, CARTWRIGHT [1-3J and BEURLING [1]. The investigations of SEIDEL and BEURLING gave great impetus and interest to Japanese mathematicians; beginning about 1940 some contributions were made to the theory by KUNUGUI [1-3J, IRIE [IJ, TOKI [IJ, TUMURA [1-2J, KAMETANI [1-4J, TsuJI [4J and NOSHIRO [1-4J. Recently, many noteworthy advances have been made by BAGEMIHL, SEIDEL, COLLINGWOOD, CARTWRIGHT, HERVE, LEHTO, LOHWATER, MEIER, OHTSUKA and many other mathematicians. The main purpose of this small book is to give a systematic account on the theory of cluster sets. Chapter I is devoted to some definitions and preliminary discussions. In Chapter II, we treat extensions of classical results on cluster sets to the case of single-valued analytic functions in a general plane domain whose boundary contains a compact set of essential singularities of capacity zero; it is well-known that HALLSTROM [2J and TsuJI [7J extended independently Nevanlinna's theory of meromorphic functions to the case of a compact set of essential singUlarities of logarithmic capacity zero. Here, Ahlfors' theory of covering surfaces plays a funda mental role. Chapter III "is concerned with functions meromorphic in the unit circle.
Download or read book Some Results in Cluster Set Theory written by Harry Thomas Mathews and published by . This book was released on 1964 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Cluster Sets written by E. F. Collingwood and published by Cambridge University Press. This book was released on 2004-06-03 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of cluster sets, a branch of topological analysis.
Download or read book The Theory of Cluster Sets written by Edward F. Collingwood and published by . This book was released on with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Cluster Sets written by Ruth Ann Su and published by . This book was released on 1974 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Clustering Stability written by Ulrike Von Luxburg and published by Now Publishers Inc. This book was released on 2010 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are most stable. In recent years, a series of papers has analyzed the behavior of this method from a theoretical point of view. However, the results are very technical and difficult to interpret for non-experts. In this paper we give a high-level overview about the existing literature on clustering stability. In addition to presenting the results in a slightly informal but accessible way, we relate them to each other and discuss their different implications.
Download or read book Data Clustering written by Guojun Gan and published by SIAM. This book was released on 2007-01-01 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cluster analysis is an unsupervised process that divides a set of objects into homogeneous groups. This book starts with basic information on cluster analysis, including the classification of data and the corresponding similarity measures, followed by the presentation of over 50 clustering algorithms in groups according to some specific baseline methodologies such as hierarchical, center-based, and search-based methods. As a result, readers and users can easily identify an appropriate algorithm for their applications and compare novel ideas with existing results. The book also provides examples of clustering applications to illustrate the advantages and shortcomings of different clustering architectures and algorithms. Application areas include pattern recognition, artificial intelligence, information technology, image processing, biology, psychology, and marketing. Readers also learn how to perform cluster analysis with the C/C++ and MATLAB programming languages.
Download or read book An Introduction to Cluster Set Theory written by James Reid Calhoun and published by . This book was released on 1969 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fuzzy Sets their Application to Clustering Training written by Beatrice Lazzerini and published by CRC Press. This book was released on 2000-03-24 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy set theory - and its underlying fuzzy logic - represents one of the most significant scientific and cultural paradigms to emerge in the last half-century. Its theoretical and technological promise is vast, and we are only beginning to experience its potential. Clustering is the first and most basic application of fuzzy set theory, but forms the basis of many, more sophisticated, intelligent computational models, particularly in pattern recognition, data mining, adaptive and hierarchical clustering, and classifier design. Fuzzy Sets and their Application to Clustering and Training offers a comprehensive introduction to fuzzy set theory, focusing on the concepts and results needed for training and clustering applications. It provides a unified mathematical framework for fuzzy classification and clustering, a methodology for developing training and classification methods, and a general method for obtaining a variety of fuzzy clustering algorithms. The authors - top experts from around the world - combine their talents to lay a solid foundation for applications of this powerful tool, from the basic concepts and mathematics through the study of various algorithms, to validity functionals and hierarchical clustering. The result is Fuzzy Sets and their Application to Clustering and Training - an outstanding initiation into the world of fuzzy learning classifiers and fuzzy clustering.
Download or read book Finite Ordered Sets written by Nathalie Caspard and published by Cambridge University Press. This book was released on 2012-01-26 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate students and researchers in all of these areas. Beginning with definitions of key concepts and fundamental results (Dilworth's and Sperner's theorem, interval and semiorders, Galois connection, duality with distributive lattices, coding and dimension theory), the authors then present applications of these structures in fields such as preference modelling and aggregation, operational research and management, cluster and concept analysis, and data mining. Exercises are included at the end of each chapter with helpful hints provided for some of the most difficult examples. The authors also point to further topics of ongoing research.
Download or read book Introduction to Clustering Large and High Dimensional Data written by Jacob Kogan and published by Cambridge University Press. This book was released on 2007 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on a few of the important clustering algorithms in the context of information retrieval.
Download or read book Classification and Clustering written by John Van Ryzin and published by . This book was released on 1977 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Optimized Thresholding on Self Organizing Map for Cluster Analysis written by Ehsan Mohebi and published by LAP Lambert Academic Publishing. This book was released on 2012-03 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the popular tools in the exploratory phase of data mining and pattern recognition is the Kohonen Self Organizing Map (SOM). Recently, experiments have shown that to find the ambiguities involved in cluster analysis, it is not necessary to consider crisp boundaries in clustering operations. In this Book, the Incremental Leader algorithm for the thresholding of the SOM (Inc-SOM) is proposed to validate the potential of a crisp clustering algorithm. However, the performance deteriorates when there is overlap between clusters. To overcome the ambiguities in the results of cluster analysis, a rough thresholding for the SOM (Rough-SOM) is proposed. In Rough-SOM, the data is first trained by a SOM neural network, then the rough thresholding, which is a rough set based clustering approach, is applied on the neurons of the SOM. The optimal number of clusters can be found by rough set theory, which groups the neurons into a set of overlapping clusters. An optimization technique is applied during the last stage to assign the overlapped data to the true clusters.
Download or read book Fuzzy Approach to Hierarchical Clustering written by Martin Malcik and published by LAP Lambert Academic Publishing. This book was released on 2011-04 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we tried to extend the possibilities of hierarchical clustering methods to manipulate with fuzzy data both during preparing and clustering of data.The main aim was to apply some results of fuzzy sets theory and to develop new elements of hierarchical agglomerative clustering alforithms especially focused on manipulating with fuzzy data. The main goal consisted of the following parts - to prepare the fuzzy data for cluster analysis, to extend the definition of object dissimilarity for the case of fuzzy objects; to realize clustering of fuzzy data, to search of Tolerance coefficient for Definite hierarchical agglomerative clustering method and to find Partition optimality coefficient by means of fuzzy c-means algorithm.
Download or read book Topology and Approximate Fixed Points written by Afif Ben Amar and published by Springer Nature. This book was released on 2022-01-25 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory. This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces—and fundamental properties of their topologies—are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fréchet-Urysohn property. The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies. By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.
Download or read book Regents Proceedings written by University of Michigan. Board of Regents and published by . This book was released on 1957 with total page 1520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
