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Graphs as Structural Models

The Application of Graphs and Multigraphs in Cluster Analysis

Erhard Godehardt (Autor)

Buch | Softcover

X, 214 Seiten

1988 | 1988
Vieweg & Teubner (Verlag)
978-3-528-06312-2 (ISBN)

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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.

0 Mathematical Symbols and Notation.- 1 Introduction, Basic Concepts.- 1.1 Modelling in Medicine and Biology.- 1.2 Graphs as Tools in Mathematical Modelling.- 1.3 The Scope of Exploratory Data Analysis.- 1.4 The Basic Concepts of Cluster Analysis.- 2 Current Methods of Cluster Analysis: An Overview.- 2.1 The Aim of Cluster Analysis.- 2.2 The Different Steps of a Cluster Analysis.- 2.3 A Short Review of Classification Methods.- 2.4 Preparation and Presentation of Results.- 3 Graph-theoretic Methods of Cluster Analysis.- 3.1 Classification by Graphs.- 3.2 Classifications by Multigraphs.- 3.3 An Algorithm for the Construction of (% MathType!MTEF!2!1!+-% feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8% qacaWGRbGaaiilaiqadsgagaWca8aadaahaaWcbeqaa8qacaWGubaa% aOGaai4oaiaadohaaaa!3B95!$$k,{vec d^T};s$$)-Clusters.- 3.4 The Construction of Dendrograms of (k; s)-Clusters.- 4 Probability Models of Classification.- 4.1. Current Probability Models in Cluster Analysis.- 4.2. Graph-Theoretic Models of Classification.- 4.3. Discussion of the Graph-Theoretic Probability Models.- 5 Probability Theory of Completely Labelled Random Multigraphs.- 5.1 Definitions and Notation.- 5.2 A Probability Model of Random Multigraphs.- 5.3 Some Results for Random Graphs ?nN and Gnp.- 5.4 Limit Theorems for Random Multigraphs.- 5.5 Discussion of the Results.- 5.6 Hints for the Numerical Computation of the Expectations and Distributions.- 6 Classifications by Multigraphs: Three Examples from Medicine.- 6.1 Pharmacokinetics of Urapidil in Patients with Normal andImpaired Renal Function.- 6.2 Pharmacokinetics of Lidocaine in Patients with Kidney or Liver Impairments.- 6.3 Pregnancy-Induced Hypertension.

Erscheint lt. Verlag	1.1.1988
Reihe/Serie	Advances in System Analysis
Zusatzinfo	X, 214 p.
Verlagsort	Wiesbaden
Sprache	englisch
Gewicht	402 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	algorithms • Calculus • Chemistry • classification • Function • Graph • Graphs • Mathematica • Modeling • Optimization • Probability Theory • Theorem • Variable
ISBN-10	3-528-06312-2 / 3528063122
ISBN-13	978-3-528-06312-2 / 9783528063122
Zustand	Neuware