Cluster Analysis for Applications

Cluster Analysis for Applications

Probability and Mathematical Statistics: A Series of Monographs and Textbooks

1st Edition - November 28, 1973

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  • Author: Michael R. Anderberg
  • eBook ISBN: 9781483191393

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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.

Table of Contents

  • Preface


    Chapter 1. The Broad View of Cluster Analysis

    1.1 Category Sorting Problems

    1.2 Need for Cluster Analysis Algorithms

    1.3 Uses of Cluster Analysis

    1.4 Literature of Cluster Analysis

    1.5 Purpose of This Book

    Chapter 2. Conceptual Problems in Cluster Analysis

    2.1 Elements of a Cluster Analysis

    2.2 Illustrative Example

    2.3 Some Philosophical Observations

    2.4 A Note on Optimality and Intuition

    Chapter 3. Variables and Scales

    3.1 Classification of Variables

    3.2 Scale Conversions

    3.3 The Application of Scale Conversions

    Chapter 4. Measures of Association among Variables

    4.1 Measures between Ratio and Interval Variables

    4.2 Measures between Nominal Variables

    4.3 Measures between Binary Variables

    4.4 Strategies for Mixed Variable Data Sets

    Chapter 5. Measures of Association among Data Units

    5.1 Metric Measures for Interval Variables

    5.2 Nonmetric Measures for Interval Variables

    5.3 Measures Using Binary Variables

    5.4 Measures Using Nominal Variables

    5.5 Mixed Variable Strategies

    Chapter 6. Hierarchical Clustering Methods

    6.1 The Central Agglomerative Procedure

    6.2 The Stored Matrix Approach

    6.3 The Stored Data Approach

    6.4 The Sorted Matrix Approach

    6.5 Other Approaches

    Chapter 7. Nonhierarchical Clustering Methods

    7.1 Initial Configurations

    7.2 Nearest Centroid Sorting—Fixed Number of Clusters

    7.3 Nearest Centroid Sorting—Variable Number of Clusters

    7.4 Other Approaches to Nonhierarchical Clustering

    Chapter 8. Promoting Interpretation of Clustering Results

    8.1 Aids to Interpreting Hierarchical Classifications

    8.2 An Aid to Interpreting a Partition of Data Units into Clusters

    Chapter 9. Strategies for Using Cluster Analysis

    9.1 Sequential Clustering of Data Units

    9.2 Complementary Use of Several Clustering Methods

    9.3 Cluster Analysis as an Adjunct to Other Statistical Methods

    9.4 Clustering with Respect to an External Criterion

    9.5 The Need for Research on Strategies

    Chapter 10. Comparative Evaluation of Cluster Analysis Methods

    10.1 An Approach to the Evaluation of Clustering Methods

    10.2 Quantitative Assessment of Performance for Clustering Methods

    10.3 List of Candidate Characteristic for Problems and Methods

    10.4 The Evaluation Task Lying Ahead

    Appendix A. Correlation and Nominal Variables

    A.1 The Fundamental Analysis

    A.2 The Problem of Isolated Cells

    A.3 Deflating the Squared Correlation

    Appendix B. Programs for Scale Conversions

    B.1 Partitions of the Truncated Normal Distribution

    B.2 Iterative Improvement of a Partition

    Program CUTS

    Function ERF

    Program DIVIDE

    Subroutine TEST

    Subroutine SORT

    Function PSUMSQ

    Appendix C. Programs for Association Measures among Nominal and Interval Variables

    C.1 General Design Features

    C.2 Deck Setup and Utilization

    Subroutine GCORR

    Subroutine INPTR

    Subroutine NCAT

    Subroutine EIGEN

    Subroutine VSORT

    Function CORXX

    Function CORKX

    Function CORKK

    Appendix D. Programs for Association Measures Involving Binary Variables

    D.1 Bit-Level Storage

    D.2 Computing Association Measures

    D.3 Use of the Program

    Program BINARY

    Subroutine BDATA

    Function Subprogram KOUNT

    Function BASSN

    Appendix E. Programs for Hierarchical Cluster Analysis

    E.1 Stored Similarity Matrix Approach

    E.2 Stored Data Approach

    E.3 Sorted Matrix Approach

    Subroutine CNTRL

    Subroutine CLSTR

    Function LFIND

    Subroutine METHOD

    Subroutine MANAGE

    Subroutine GROUP

    Subroutine PROC

    Subroutine ALLINI

    Subroutine PREP

    Appendix F. Programs for Nonhierarchical Clustering

    Subroutine EXEC

    Subroutine RESULT

    Subroutine KMEAN

    Appendix G. Programs to Aid Interpretation of Clustering Results

    G.1 A Program for Manipulating Hierarchical Trees

    G.2 Permuting the Similarity Matrix

    G.3 Error Sum of Squares Analysis

    G.4 Analysis of a Given Partition

    Subroutine DETAIL

    Subroutine READCM

    Subroutine TREE

    Program PERMUTE

    Subroutine MTXIN

    Function LFIND

    Program ERROR

    Program POSTDU

    Appendix H. Relations Among Cluster Analysis Programs



Product details

  • No. of pages: 376
  • Language: English
  • Copyright: © Academic Press 1973
  • Published: November 28, 1973
  • Imprint: Academic Press
  • eBook ISBN: 9781483191393

About the Author

Michael R. Anderberg

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