Cluster Analysis For Applications

Author: Michael R. Anderberg
Publisher: Academic Press
ISBN: 1483191397
Size: 32.25 MB
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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.

Graphs As Structural Models

Author: Erhard Godehardt
Publisher: Springer Science & Business Media
ISBN: 3322963101
Size: 14.33 MB
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The advent of the high-speed computer with its enormous storage capabilities enabled statisticians as well as researchers from the different topics of life sciences to apply mul tivariate statistical procedures to large data sets to explore their structures. More and more, methods of graphical representation and data analysis are used for investigations. These methods belong to a topic of growing popUlarity, known as "exploratory data analysis" or EDA. In many applications, there is reason to believe that a set of objects can be clus tered into subgroups that differ in meaningful ways. Extensive data sets, for example, are stored in clinical cancer registers. In large data sets like these, nobody would ex pect the objects to be homogeneous. The most commonly used terms for the class of procedures that seek to separate the component data into groups are "cluster analysis" or "numerical taxonomy". The origins of cluster analysis can be found in biology and anthropology at the beginning of the century. The first systematic investigations in cluster analysis are those of K. Pearson in 1894. The search for classifications or ty pologies of objects or persons, however, is indigenous not only to biology but to a wide variety of disciplines. Thus, in recent years, a growing interest in classification and related areas has taken place. Today, we see applications of cluster analysis not only to. biology but also to such diverse areas as psychology, regional analysis, marketing research, chemistry, archaeology and medicine.

Metastability

Author: Anton Bovier
Publisher: Springer
ISBN: 3319247778
Size: 80.77 MB
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This monograph provides a concise presentation of a mathematical approach to metastability, a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise, based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focuses on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hop dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.

Choice

Author: Richard K. Gardner
Publisher:
ISBN:
Size: 19.80 MB
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Combinatorial Data Analysis

Author: Lawrence Hubert
Publisher: SIAM
ISBN: 0898714788
Size: 52.70 MB
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Combinatorial data analysis refers to methods for the study of data sets where the arrangement of objects is central.