Skip to main content

Part of the book series: Perspectives on Individual Differences ((PIDF))

Abstract

Cluster analysis methods have a long history. The earliest known procedures were suggested by anthropologists (Czekanowski, 1911; Driver and Kroeber, 1932). Later, these ideas were picked up in psychology. For instance, Zubin (1938) proposed a rather simple method for sorting a correlation matrix which would yield clusters. About the same time, Stephenson (1936) suggested the use of inverted factor analysis to find clusters of people.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderberg, M. Cluster analysis for applications. New York: Academic Press, 1973.

    Google Scholar 

  • Anderson, T. W., Das Gupta, S., and Styan, G. P. H. A bibliography of multivariate statistical analysis. Edinburgh: Oliver & Boyd, 1972.

    Google Scholar 

  • Arabie, P., and Carroll, J. D. MAPCLUS: A mathematical programming approach to fitting the ADCLUS model. Psychometrika,1980, 45, 211–235.

    Google Scholar 

  • Bailey, T. A., and Dubes, R. Cluster validity profiles. Pattern Recognition 1982, 15, 61–83.

    Google Scholar 

  • Bartko, J. J. On various intraclass correlation reliability coefficients. Psychological Bulletin, 1976, 83, 762–765.

    Google Scholar 

  • Bartko, J. J., Strauss, J. S., and Carpenter, W. S. An evaluation of taxometric techniques for psychiatric data. Classification Society Bulletin,1971, 2, 2–28.

    Google Scholar 

  • Bass, B. M. Iterative inverse factor analysis—A rapid method for clustering persons. Psychometrika,1957, 22, 105–107.

    Google Scholar 

  • Bayne, R., Beauchamp, J., Begovich, C., and Kane, V. Monte Carlo comparisons of selected clustering procedures. Pattern Recognition, 1980, 12, 51–62.

    Google Scholar 

  • Bellman, R. E. Kalaha, R., and Zadeh, L. Abstraction and pattern classification. Journal of Mathematical Analysis and Applications,1966, 13, 1–7.

    Google Scholar 

  • Bezdek, J. C. Cluster validity with fuzzy sets. Journal of Cybernetics,1974, 3, 57–73.

    Google Scholar 

  • Bezdek, J. C. Mathematical models for taxonomy. Proceedings of the &h International Conference on Numerical Taxonomy,1975.

    Google Scholar 

  • Boake, C. Recovery of simulated MMPI mixtures by seven methods of cluster analysis. Paper presented to annual meeting of American Psychological Association, Anaheim, Calif., 1983.

    Google Scholar 

  • Bonacich, P., and Domhoff, G. W. Latent classes and group membership. Social Networks, 1981, 3, 175–196.

    Google Scholar 

  • Borgen, F. H., and Weiss, D. J. Cluster analysis and counseling research. Journal of Counseling Psychotherapy,1971, 18, 583–591.

    Google Scholar 

  • Burt, C. Correlations between persons. British Journal of Psychology,1937, 28,167–185.

    Google Scholar 

  • Carlson, K. A. Classes of adult offenders: A multivariate study. Journal of Abnormal Psychology, 1972, 79, 84–93.

    PubMed  Google Scholar 

  • Carmichael, J. W., George, J. A., and Julius, R. S. Finding natural clusters. Systematic Zoology, 1968, 17, 144–150.

    Google Scholar 

  • Carroll, J. D., and Arabie, P. INDCLUS: An individual differences generalization of the ADCLUS model and the MARCLUS algorithm. Psychometrika, 1983, 48, 157–169.

    Google Scholar 

  • Carroll, R. M., and Field, J. A comparison of the classific°qon accuracy of profile similarity measures. Multivariate Behavioral Research, 1974, 9, 373–380.

    Google Scholar 

  • Cattell, R. B. A note on correlation clusters and cluster search methods. Psychometrika, 1944, 9, 169–184.

    Google Scholar 

  • Cattell, R. B. rp and other coefficients of pattern similarity. Psychometrika, 1949, 14, 279–298.

    Google Scholar 

  • Cattell, R. B. Factor analysis. New York: Harper, 1952.

    Google Scholar 

  • Cattell, R. B. A universal index of psychological factors. Psychologia,1957, 1,74–85.

    Google Scholar 

  • Cattell, R. B. The scientific analysis of personality. Chicago: Aldine, 1965.

    Google Scholar 

  • Cattell, R. B. The scientific use of factor analysis. New York: Academic Press, 1978.

    Google Scholar 

  • Cattell, R. B., Coulter, M. A., and Tsujioka, B. The taxonomic recognition of types and functional emergents. In R. B. Cattell (Ed.), Handbook of Multivariate Experimental Psychology. Chicago, Rand McNally, 1966.

    Google Scholar 

  • Clifford, H., and Stephenson, W. An introduction to numerical taxonomy. New York: Academic Press, 1975.

    Google Scholar 

  • Cohen, J. A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 1960, 20, 37–46.

    Google Scholar 

  • Cole, A. J. Numerical taxonomy. New York: Academic Press, 1969.

    Google Scholar 

  • Cormack, R. M. A review of classification. Journal of the Royal Statistical Society (Series A), 134,321–367.

    Google Scholar 

  • Cornell, J. A. Experiments with mixtures. Designs, models,and the analysis of mixture data. New York: Wiley, 1981.

    Google Scholar 

  • Cronbach, J. J., and Gleser, G. C. Assessing similarity between profiles. Psychological Bulletin, 1953, 50, 456–473.

    PubMed  Google Scholar 

  • Czekanowski, J. Objectiv kriterien in der ethnologie. Korrespondenzblatt der Deutschen Gesselschaft fur Anthropologie,Ethnologie, und Urgeschichte, 1911, 47, 1–5.

    Google Scholar 

  • Davies, D. L., and Bouldin, D. W. A cluster separation measure. IEEE Transactions in Pattern Analysis and Machine Intelligence,1979, PAMI-1,224–227.

    Google Scholar 

  • Delattre, M., and Hansen, P. Bicriterion cluster analysis. IEEE Transactions in Pattern Analysis, 1980, 2, 277–291.

    Google Scholar 

  • Driver, H. E., and Kroeber, A. L. Quantitative expression of cultural relationships. University of California Publications in Archaeology and Ethnology, 1932, 31, 211–216.

    Google Scholar 

  • Dubes, R., and Jain, A. K. Clustering methodologies in exploratory data analysis. Advances in Computers, 1980, 19, 113–228.

    Google Scholar 

  • Duda, R. O., and Hart, P. E. Pattern classification and scene analysis. New York: Wiley, 1973.

    Google Scholar 

  • Duran, B. S., and Odell, P. L. Cluster analysis: A survey. Berlin: Springer-Verlag, 1974.

    Google Scholar 

  • Edelbrock, C., and McLaughlin, B. Hierarchical cluster analysis using intraclass correlations: A mixture model study. Multivariate Behavioral Research,1980, 15,299–318.

    Google Scholar 

  • Edelbrock, C., and Reed, M. Inverse factor analysis: An evaluation using benchmark data sets. Unpublished, 1982.

    Google Scholar 

  • Edwards, A. W. F., and Cavalli-Sforza, L. L. A method for cluster analysis. Biometrics, 1965, 21, 362–375.

    PubMed  Google Scholar 

  • Everitt, B. S. Cluster analysis. London: Heinemann, 1974.

    Google Scholar 

  • Everitt, B. S. Unresolved problems in cluster analysis. Biometrics, 1979, 35, 169–181.

    Google Scholar 

  • Everitt, B. S. Cluster analysis (2nd ed.). New York: Wiley, 1980.

    Google Scholar 

  • Everitt, B. S., Gourlay, A. J., and Kendell, R. E. An attempt at validation of traditional psychiatric syndromes by cluster analysis. British Journal of Psychiatry,1971, 119,399–412.

    PubMed  Google Scholar 

  • Fisher, L., and van Ness, J. W. Admissible clustering procedures. Biometrika, 1971, 58, 91–104.

    Google Scholar 

  • Fisher, R. A. The use of multiple measurements in taxonomic problems. Annals of Eugenics, 1936, 179–188.

    Google Scholar 

  • Fisher, W. D. Clustering and aggregation in economics. Baltimore: Johns Hopkins University Press, 1968.

    Google Scholar 

  • Fleiss, J., Lawlor, W., Platman, S., and Fieve, R. On the use of inverted factor analysis for generating typologies. Journal of Abnormal Psychology,1971, 77, 127–132.

    Google Scholar 

  • Florek, K., Lukaszewica, J., Perkal, J., Steinhaus, H., and Zubrzycki, S. Sur la liason et la devision des points d’un ensemble fini. Colloquia Mathmatica,1951, 2,282–285.

    Google Scholar 

  • Friedman, H. P., and Rubin, J. On some criteria for grouping data. Journal of the American Statistical Association,1967, 62,1159–1178.

    Google Scholar 

  • Golden, R. R., and Meehl, P. E. Detection of the schizoid taxon with MMPI indicators. Journal of Abnormal Psychology,1979, 88,217–233.

    PubMed  Google Scholar 

  • Golden, R. R., and Meehl, P. E. Detection of biological sex: An empirical test of cluster methods. Multivariate Behavioral Research,1981, 16,475–496.

    Google Scholar 

  • Goldstein, S. G., and Linden, J. D. A comparison of multivariate grouping techniques commonly used with profile data. Multivariate Behavioral Research,1969, 4,103–114.

    Google Scholar 

  • Gordon, A. D., and Henderson, J. T. An algorithm for Euclidean sum of squares classification. Biometrics, 1977, 33, 355–362.

    Google Scholar 

  • Cowda, K. C., and Krishna, G. Agglomerative clustering using the concept of mutual nearest neighborhood. Pattern Recognition,1978, 10,105–112.

    Google Scholar 

  • Gower, J. C. A comparison of some methods of cluster analysis. Biometrics, 1967, 23, 623–637.

    PubMed  Google Scholar 

  • Gower, J. C. Goodness-of-fit criteria for classification and other patterned structures. Proceedings of the &h International Conference on Numerical Taxonomy, 1975, pp. 38–62.

    Google Scholar 

  • Gower, J. C., and Ross, G. J. S. Minimum spanning trees and single-linkage cluster analysis. Applied Statistics,1969, 18,54–64.

    Google Scholar 

  • Gridgeman, N. T. A comparison of two methods of analysis of mixtures of normal distributions. Technometrics,1970, 12,823–833.

    Google Scholar 

  • Gross, A. L. A Monte Carlo study of the accuracy of the hierarchical grouping procedure. Multivariate Behavioral Research,1972, 7, 379–389.

    Google Scholar 

  • Guertin, W. H. The search for recurring patterns among individual profiles. Educational and Psychological Measurement,1966, 26,151–165.

    Google Scholar 

  • Hamer, R., and Cunningham, J. Cluster analyzing profile data confounded with interrater differences: Comparison of profile association measures. Applied Psychological Measurement, 1981, 5, 63–72.

    Google Scholar 

  • Hansen, P., and Delattre, M. Complete-link cluster analysis by graph coloring. Journal of the American Statistical Association, 1978, 73, 397–403.

    Google Scholar 

  • Hartigan, J. A. Representation of similarity matrices by trees. Journal of the American Statistical Association,1967, 62,1140–1158.

    Google Scholar 

  • Hartigan, J. A. Clustering algorithms. New York: Wiley, 1975.

    Google Scholar 

  • Hartigan, J. A. Distributional problems in clustering. In J. Van Ryzin (Ed.), Classification and clustering. New York: Academic Press, 1977.

    Google Scholar 

  • Hartigan, J. A. Consistency of single linkage for high-density clusters. Journal of the American Statistical Association,1981, 76, 388–394.

    Google Scholar 

  • Helmstadter, G. C. An empirical comparison of methods for estimating profile similarity. Educational and Psychological Measurement, 1957, 17, 71–82.

    Google Scholar 

  • Holgerson, M. The limited value of the cophenetic correlation as a clustering criterion. Pattern Recognition,1978, 10,287–295.

    Google Scholar 

  • Horst, P. Factor analysis of data matrices. New York: Holt, Rinehart & Winston, 1965.

    Google Scholar 

  • Hosmer, D. W. A comparison of interative maximum likelihood estimates of the parametrics of a mixture of two normal distributions under three different types of samples. Biometrics,1973, 29,761–770.

    Google Scholar 

  • Hubert, L. J. Some applications of graph theory to clustering. Psychometrika, 1974b, 39, 283–309.

    Google Scholar 

  • Hudson, H. C. (Ed.) Classifying social data: New applications of analytic methods for social science research. San Francisco: Jossey—Bass, 1982.

    Google Scholar 

  • Jambu, M., and Lebeaux, M. O. Cluster analysis and data analysis. Amsterdam: North-Holland, 1983.

    Google Scholar 

  • Jardine, N., and Sibson, R. The construction of hierarchic and nonhierarchic classification. Computer Journal, 1968, 11, 117–184.

    Google Scholar 

  • Jardine, N., and Sibson, R. Mathematical taxonomy. New York: Wiley, 1971.

    Google Scholar 

  • Johnson, S. Hierarchical clustering schemes. Psychometrika, 1967, 38, 241–254.

    Google Scholar 

  • Krus, D. J. Logical basis of dimensionality. Applied Psychological Measurement, 1978, 2, 321–329.

    Google Scholar 

  • Kuiper, F., and Fisher, L. A Monte Carlo comparison of six clustering procedures. Biometrics,1975, 31,777–783.

    Google Scholar 

  • Lance, G., and Williams, W. A general theory of classificatory sorting strategies. Computer Journal, 1967, 9,373–380.

    Google Scholar 

  • Ling, R. F. A probability theory of cluster analysis. Journal of the American Statistical Association, 1973a, 68,159–169.

    Google Scholar 

  • Ling, R. F. The expected number of components in random linear graphs. Annals of Probability, 1973b, 1, 876–881.

    Google Scholar 

  • Lorr, M. (Ed.) Explorations in typing psychotics. Elmsford, N.Y.: Pergamon Press, 1966.

    Google Scholar 

  • Lorr, M. Cluster analysis for social scientists. San Francisco: Jossey—Bass, 1983.

    Google Scholar 

  • McNaughton-Smith, P. Some statistical and other numerical techniques for classifying individuals. London: Her Majesty’s Stationery Office, 1965.

    Google Scholar 

  • McQuitty, L. L. Elementary linkage analysis for isolating orthogonal and oblique types and typal relevancies. Educational and Psychological Measurement, 1957, 17, 207–22.

    Google Scholar 

  • McQuitty, L. L. Capabilities and improvements in linkage analysis as a clustering method. Educational and Psychological Measurements,1964, 24,441–456.

    Google Scholar 

  • Mahalanobis, P. C. On the generalized distance in statistics. Proceedings of the National Institute of Sciences of India,1936, 2,49–55.

    Google Scholar 

  • Matthews, A. Standardization of measures prior to clustering. Biometrics, 1980, 35, 892–897.

    Google Scholar 

  • May, K. O. The growth and quality of the mathematical literature. Isis, 1969, 59, 363–371.

    Google Scholar 

  • Meehl, P. E. Psychodiagnosis: Selected papers. Minneapolis: University of Minnesota Press, 1973.

    Google Scholar 

  • Meehl, P. E. A funny thing happened to us on the way to latent entities. Journal of Personality Assessment,1979, 43, 563–581.

    Google Scholar 

  • Meehl, P. E., and Golden, R. R. Taxonmetric methods. In P. C. Kendal and J. N. Butcher (Eds.), Handbook of research methods in clinical psychology. New York: Wiley, 1982.

    Google Scholar 

  • Mezzich, J. E. Evaluating clustering methods for psychiatric diagnosis. Biological Psychiatry, 1978, 13, 265–281.

    PubMed  Google Scholar 

  • Mezzich, J. E. Comparing cluster analysis methods. In H. C. Hudson (Ed.), Classifying social data: New applications of analytic methods for social science research. San Frnacisco: Jossey—Bass, 1982.

    Google Scholar 

  • Mezzich, J. E., and Solomon, H. Taxonomy and behavioral science. New York: Academic Press, 1980.

    Google Scholar 

  • Milligan, G. W. An examination of the effect of six types of error perturbation of fifteen clustering algorithms. Psychometrika,1980, 45,325–342.

    Google Scholar 

  • Milligan, G. W. A review of Monte Carlo tests of cluster analysis. Multivariate Behavioral Research,1981, 16,379–407.

    Google Scholar 

  • Milligan, G. W., and Cooper, M. C. An examination of procedures for determining the number of clusters in a data set. Unpublished report, 1983.

    Google Scholar 

  • Mojena, R. Hierarchical grouping methods and stopping rules—An evaluation. Computer Journal, 1977, 20, 359–363.

    Google Scholar 

  • Nowakowska, M. Epidemical spread of scientific objects: An empirical approach to some problems of meta-science. Theory and Decision, 1973, 3, 262–297.

    Google Scholar 

  • Nunnally, J. C. The analysis of profile data. Psychological Bulletin,1962, 59,311–319.

    PubMed  Google Scholar 

  • Overall, J. and Klett, C. Applied multivariate analysis. New York: McGraw–Hill, 1972.

    Google Scholar 

  • Paykel, E. S. Classification of depressed patients: A cluster analysis derived grouping. British Journal of Psychiatry, 1971, 118, 275–288.

    PubMed  Google Scholar 

  • Rand, W. M. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association,1971, 66,846–850.

    Google Scholar 

  • Rohlf, F. J. Single-link clustering algorithms. In P. R. Krishnaiah and L. N. Kanal (Eds.), Handbook of Statistics. Vol. 2. Amsterdam: North-Holland, 1982.

    Google Scholar 

  • Rucci, A. J., and Tweney, R. D. Analysis of variance—the “second discipline” of scientific psychology: A historical account. Psychological Bulletin, 1980, 87,166–184.

    Google Scholar 

  • Scoltock, J. A survey of the literature of cluster analysis. Computer Journal, 1982, 25, 130–134.

    Google Scholar 

  • Scolve, S. Population mixture models and clustering algorithms. Communications in Statistical Theories and Methods,1977, A6, 417–434.

    Google Scholar 

  • Shepard, R. N., and Arabie, P. Additive clustering: Representation of similarities as combination of discrete overlapping properties. Psychological Review, 1979, 86, 87–123.

    Google Scholar 

  • Skinner, H. A. Differentiating the contribution of elevation, scatter, and shape in profile similarity. Educational and Psychological Measurement, 1978, 38, 297–308.

    Google Scholar 

  • Skinner, H. A. Dimensions and clusters: A hybrid approach to classification. Applied Psychological Measurement,1979, 3,327–341.

    Google Scholar 

  • Skinner, H. A., and Lei, H. Model profile analysis: A computer program for classification research. Educational and Psychological Measurement, 1980, 40, 769–772.

    Google Scholar 

  • Skinner, H. A., Jackson, D. N., and Hoffman, H. Alcoholic personality types: Identification and correlates. Journal of Abnormal Psychology, 1974, 83, 658–666.

    PubMed  Google Scholar 

  • Sneath, P. H. A. The application of computers to taxonomy. Journal of General Microbiology, 1957, 17, 201–226.

    PubMed  Google Scholar 

  • Sneath, P. H. A. A method for testing the distinctiveness of clusters: A test for the disjunction of two clusters in Euclidean space as measured by their overlap. Mathematical Geology, 1977, 9, 123–143.

    Google Scholar 

  • Sneath, P., and Sokal, R. Numerical taxonomy. San Francisco: Freeman, 1973.

    Google Scholar 

  • Sokal, R., and Michener, C. D. A statistical method for evaluating systematic relationships. University of Kansas Scientific Bulletin,1958, 38, 1409–1438.

    Google Scholar 

  • Sokal, R. R., and Rohlf, F. J. The comparison of dendrograms by objective methods. Taxon,1962, 11, 33–40.

    Google Scholar 

  • Sokal, R. R., and Rohlf, F. J. An experiment in taxonomic judgement. Systematic Botany, 1980, 5, 341–365.

    Google Scholar 

  • Sokal, R. R., and Sneath, P. Principles of numerical taxonomy. San Francisco: Freeman, 1963.

    Google Scholar 

  • Spath, H. Cluster analysis algorithms. New York: Wiley, 1980.

    Google Scholar 

  • Stephenson, W. Introduction of inverted factor analysis with some applications to studies in orexia. Journal of Educational Psychology,1936, 5, 353–367.

    Google Scholar 

  • Tryon, R. Cluster analysis. New York: McGraw–Hill, 1939.

    Google Scholar 

  • Tryon, R. C. Identification of social areas by cluster analysis. Berkeley: University of California Press, 1955.

    Google Scholar 

  • Tryon, R. C., and Bailey, D. E. Cluster analysis. New York: McGraw–Hill, 1970.

    Google Scholar 

  • Tversky, A. Features of similarity. Psychological Review,1977, 84, 327–352.

    Google Scholar 

  • Van Ryzin, J. (Ed.) Classification and clustering. New York: Academic Press, 1977.

    Google Scholar 

  • Ward, J. H. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association,1963, 58, 236–244.

    Google Scholar 

  • Williams, W. T., Lance, G. N., Dale, M. B., and Clifford, H. T. Controversy concerning the criteria for taxometric strategies. Computer Journal, 1971, 14, 162–165.

    Google Scholar 

  • Wishart, D. Mode analysis: A generalization of nearest neighbor which reduces chaining effects. In A. Cole (Ed.), Numerical taxonomy. New York: Academic Press, pp. 282–311.

    Google Scholar 

  • Wolfe, J. H. Pattern clustering by multivariate mixture analysis. Multivariate Behavioral Research, 1970, 5, 329–350.

    Google Scholar 

  • Wolfe, J. H. A Monte Carlo study of the sampling distribution of the likelihood ratio for mixtures of multinormal distributions. Naval Personnel and Training Research Laboratory Technical Bulletin STB 72–2, San Diego, Calif., 1971.

    Google Scholar 

  • Wong, M. A., and Lane, T. A Rth nearest neighbor clustering procedure. Unpublished manuscript, 1981.

    Google Scholar 

  • Woodbury, M. A., and Clive, J. Clinical pure types as a fuzzy partition. Journal of Cybernetics,1974, 4, 111–121.

    Google Scholar 

  • Yahil, A., and Brown, M. B. On separating clusters from background. Technometrics, 1976, 18, 55–58.

    Google Scholar 

  • Yau, S. S., and Chang, S. C. A direct method for cluster analysis. Pattern Recognition, 1975, 7, 215–224.

    Google Scholar 

  • Zadeh, L. A. Similarity relations and fuzzy orderings. Information Sciences 1971, 3, 177–200.

    Google Scholar 

  • Zahn, C. T. Graph-theoretic methods for detecting and describing Gestalt clusters. IEEE Transactions in Computers, 1971, C-20, 68–86.

    Google Scholar 

  • Zubin, J. A technique for measuring likemindedness. Journal of Abnormal Psychology,1938, 33, 508–516.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Plenum Press, New York

About this chapter

Cite this chapter

Blashfield, R.K., Aldenderfer, M.S. (1988). The Methods and Problems of Cluster Analysis. In: Nesselroade, J.R., Cattell, R.B. (eds) Handbook of Multivariate Experimental Psychology. Perspectives on Individual Differences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0893-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-0893-5_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8232-7

  • Online ISBN: 978-1-4613-0893-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics