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Graphs as Structural Models : the Application of Graphs and Multigraphs in Cluster Analysis

Author: Erhard Godehardt
Publisher: Wiesbaden : Vieweg+Teubner Verlag : Imprint : Vieweg+Teubner Verlag, 1988.
Series: Advances in system analysis.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

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  Read more...

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Erhard Godehardt
ISBN: 9783322963109 3322963101
OCLC Number: 851823365
Description: 1 online resource (x, 214 pages).
Contents: 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! $$k, {\vec d̂T};s$$)-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 and Impaired Renal Function --
6.2 Pharmacokinetics of Lidocaine in Patients with Kidney or Liver Impairments --
6.3 Pregnancy-Induced Hypertension.
Series Title: Advances in system analysis.
Responsibility: by Erhard Godehardt.

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