11 – Cluster Analysis

Publisher Summary This chapter provides an overview of the uses of cluster methods and describes the procedures involved in conducting cluster analyses. Cluster analysis is a term used to describe a family of statistical procedures specifically designed to discover classifications within complex data sets. The objective of cluster analysis is to group objects into clusters such that objects within one cluster share more in common with one another than they do with the objects of other clusters. Thus, the purpose of the analysis is to arrange objects into relatively homogeneous groups based on multivariate observations. Furthermore, the chapter discusses the uses for cluster analysis. Clustering methods are useful whenever the researcher is interested in grouping together objects based on multivariate similarity. Cluster analysis can be employed as a data exploration tool as well as a hypothesis testing and confirmation tool. The most frequent use of cluster analysis is in the development of a typology or classification system. However, cluster analysis is not a single standardized procedure, and there are pitfalls associated with its improper use, therefore, care is required in its application.

[1]  R. Blong,et al.  A numerical classification of selected landslides of the débris slide-avalanche-flow type , 1973 .

[2]  G. N. Lance,et al.  A General Theory of Classificatory Sorting Strategies: 1. Hierarchical Systems , 1967, Comput. J..

[3]  R. Blashfield,et al.  A Nearest-Centroid Technique for Evaluating the Minimum-Variance Clustering Procedure. , 1980 .

[4]  D. Speece,et al.  Cluster Analysis in Perspective. , 1994 .

[5]  H. Skinner Dimensions and Clusters: A Hybrid Approach to Classification , 1979 .

[6]  H. P. Friedman,et al.  On Some Invariant Criteria for Grouping Data , 1967 .

[7]  Steven B. Robbins,et al.  Testing a Level Versus an Interactional View of Career Indecision , 1994 .

[8]  L. Cronbach,et al.  Assessing similarity between profiles. , 1953, Psychological bulletin.

[9]  G. W. Milligan,et al.  A Two-Stage Clustering Algorithm with Robust Recovery Characteristics , 1980 .

[10]  P. Green,et al.  An Empirical Comparison of Variable Standardization Methods in Cluster Analysis. , 1996, Multivariate behavioral research.

[11]  David Wishart,et al.  256 NOTE: An Algorithm for Hierarchical Classifications , 1969 .

[12]  W. T. Williams,et al.  Dissimilarity Analysis: a new Technique of Hierarchical Sub-division , 1964, Nature.

[13]  G. W. Milligan,et al.  Methodology Review: Clustering Methods , 1987 .

[14]  B. Everitt,et al.  A Monte Carlo Study of the Recovery of Cluster Structure in Binary Data by Hierarchical Clustering Techniques. , 1987, Multivariate behavioral research.

[15]  W. T. Williams,et al.  Multivariate Methods in Plant Ecology: VI. Comparison of Information-Analysis and Association-Analysis , 1966 .

[16]  G. W. Milligan,et al.  A Study of the Comparability of External Criteria for Hierarchical Cluster Analysis. , 1986, Multivariate behavioral research.

[17]  G. W. Milligan,et al.  A study of standardization of variables in cluster analysis , 1988 .

[18]  J. H. Ward Hierarchical Grouping to Optimize an Objective Function , 1963 .

[19]  D L Medin,et al.  Concepts and conceptual structure. , 1989, The American psychologist.

[20]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[21]  G. W. Milligan,et al.  A Review Of Monte Carlo Tests Of Cluster Analysis. , 1981, Multivariate behavioral research.

[22]  D Scheibler,et al.  Monte Carlo Tests of the Accuracy of Cluster Analysis Algorithms: A Comparison of Hierarchical and Nonhierarchical Methods. , 1985, Multivariate behavioral research.

[23]  G. W. Milligan,et al.  An examination of procedures for determining the number of clusters in a data set , 1985 .

[24]  L. Hubert,et al.  Measuring the Power of Hierarchical Cluster Analysis , 1975 .

[25]  Daniel M. Horn,et al.  A STUDY OF PERSONALITY SYNDROMES , 1944 .

[26]  W. T. Williams,et al.  Multivariate Methods in Plant Ecology: IV. Nodal Analysis , 1962 .

[27]  Joseph L. Fleiss,et al.  On the use of inverted factor analysis for generating typologies. , 1971 .

[28]  R. Cattell A note on correlation clusters and cluster search methods , 1944 .

[29]  H A Skinner,et al.  Toward the integration of classification theory and methods. , 1981, Journal of abnormal psychology.

[30]  Kurt F. Geisinger,et al.  Analyzing Test Content Using Cluster Analysis and Multidimensional Scaling , 1992 .

[31]  P. Paul Heppner,et al.  Presenting Problems of University Counseling Center Clients: A Snapshot and Multivariate Classification Scheme. , 1994 .

[32]  Roger K. Blashfield,et al.  Mixture model tests of cluster analysis: Accuracy of four agglomerative hierarchical methods. , 1976 .

[33]  R. Blashfield,et al.  Neuropsychology and cluster analysis: potentials and problems. , 1981, Journal of clinical neuropsychology.

[34]  G. W. Milligan,et al.  A monte carlo study of thirty internal criterion measures for cluster analysis , 1981 .

[35]  I. Gati,et al.  The Scale Structure of Multi-Scale Measures: Application of the Split-Scale Method to the Task- Specific Occupational Self-Efficacy Scale and the Career Decision-Making Self-Efficacy Scale , 1994 .

[36]  L. Mcquitty Elementary Linkage Analysis for Isolating Orthogonal and Oblique Types and Typal Relevancies , 1957 .

[37]  Lisa M. Larson,et al.  Applications of the Coping With Career Indecision Instrument With Adolescents , 1998 .

[38]  L. Hubert,et al.  A general statistical framework for assessing categorical clustering in free recall. , 1976 .

[39]  Robert S. Atlas,et al.  Comparative evaluation of two superior stopping rules for hierarchical cluster analysis , 1994 .

[40]  P. Sneath The application of computers to taxonomy. , 1957, Journal of general microbiology.

[41]  Roger K. Blashfield The equivalence of three statistical packages for performing hierarchical cluster analysis , 1977 .

[42]  R K Blashfield,et al.  Evaluative criteria for psychiatric classification. , 1976, Journal of abnormal psychology.

[43]  G. W. Milligan,et al.  An examination of the effect of six types of error perturbation on fifteen clustering algorithms , 1980 .

[44]  S. C. Johnson Hierarchical clustering schemes , 1967, Psychometrika.

[45]  John E. Overall,et al.  Replication as a Rule for Determining the Number of Clusters in Hierarchial Cluster Analysis , 1992 .

[46]  F. Borgen,et al.  Applying Cluster Analysis in Counseling Psychology Research. , 1987 .

[47]  Jacob Cohen A Coefficient of Agreement for Nominal Scales , 1960 .

[48]  Lydia J. Price Identifying cluster overlap with NORMIX population membership probabilities , 1993 .

[49]  J E Overall,et al.  Population recovery capabilities of 35 cluster analysis methods. , 1993, Journal of clinical psychology.