Abstract
Dale M. B. (1988): Some fuzzy approaches to phytosociology. Ideals and instances.—Folia Geobot. Phytotax., Praha, 23: 239–274.—In this paper I examine some differences between the ideals of systematic traditional phytosociology and pragmatic numerical ones, and identify a difference in their view of the role of a stand. Traditionally very few stands are regarded as typifying the Association, most stands being regarded as being composed of elements of several types. The approaches using numerical methods, by contrast, have generally regarded all stands as equally contributing to the definition of patterns. This difference is reflected in the methodologies regarded as appropriate for the two cases.
Attention is then given to eight classes of methods which relax the numerical insistence on crisp clusters in various ways, to permit the simultaneous presence of several types in a single stand. A stand may be assigned to one or to several clusters, and such assignment may be complete or partial. The methods are exemplified and their various possibilities and problems discussed.
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Literature Cited
Abel D. J. etWilliams W. T. (1981): NEBALL and FINGRP: new programs for multiple nearest neighbour analysis.—Austral. Comput. J. 13: 24–26.
Arabie P. etCarroll J. D. (1980): MAPCLUS: a mathematical programming approach to fitting the ADCLUS model.—Psychometrika 45: 211–235.
Backer E. (1978): Cluster analysis by optimal decomposition of induced fuzzy sets.—Delft. Univ. Press. pp. 235.
Ball G. H. etHall D. J. (1967): A clustering technique for summarising multivariate data.—Behav. Sci. 12: 153–155.
Bezdek J. C. (1974): Numerical taxonomy with fuzzy sets.—J. Math. Biol. 1: 57–71.
Bezdek J. C., Coray C., Gunderson R. etWatson J. (1983): Detection and characterization of cluster substructure 1. Linear structure: Fuzzy c-lines.—SIAM J. Appl. Math. 40: 339–357.
Bowman D. M. J. S. etWilson B. A. (1986): Wetland vegetation pattern on the Adelaide River flood plain, Northern Territory, Australis.—Proc. Roy. Soc. Old. 97: 69–77.
Bray J. R. etCurtis J. T. (1957): An ordination of the upland forest communities of southern Wisconsin.—Ecol. Monogr. 27: 325–349.
Carroll J. B. (1953): An analytic solution for approximating simple structure.—Psychometrika 18: 23–38.
Cattell R. B. etCattell A. K. S. (1955): Factor rotation for parallel proportion profiles; analytical solutions and an example.—Brit. J. Statist. Psychol. 8: 83–91.
Dahl E., Prestvik O. etToftaker H. (1981): En kvantifiserung av karakterartbegrepet. —Det. Kgl. Norsk vidensk. Abers. Selskab, Musei Botaniskes Ser. 1981–5: 215–233.
Dale M. B. etAnderson D. J. (1972): Qualitative and quantitative information analysis.— J. Ecol. 60: 639–653.
Dale M.-B. etAnderson D. J. (1973): Inosculate analysis of vegetation data.—Austral. J. Bot. 21: 253–276.
Dale M. B., Ferrari C., Beatrice M. etVenanzoni R. (1986): A comparison of some methods of species selection.—Coenoses 1: 35–51.
Dale M. B. etWebb L. J. (1975): Numerical methods for the establishment of Associations.—Vegetatio 30: 77–87.
Dale M. B. etWilliams W. T. (1978): A new method of species reduction for ecological data.—Austral J. Ecol. 3: 1–5.
Diday E. etGovaert G. (1974): Classification avec distance adaptive.—C.R. Acad. Sci. Paris A, 993–995.
Dunn, J. C. (1974): A fuzzy relative of ISODATA and its use in detecting compact well-separated clusters.—J. Cybernetics 3: 22–57.
Flanagan P. A. (1986): An optimally data efficient isomorphism inference algorithm.—Information and Control 68: 207–222.
Gitman I. etLevine M. (1970): An algoritm, for detecting unimodal fuzzy sets and its appliation as a clustering technique.—IEEE Trans. Comput. C-19: 583–593.
Goodall D. W. (1969): A procedure for recognition of uncommon species combinations in sets of vegetation samples.—Vegetatio 18: 19–35.
Gower J. (1966): Some distance properties of latent root and vector methods used in multivariate analysis.—Biometrika 53: 325–338.
Gunderson R. W. (1982): Choosing the r-dimension for the FCV family of clustering algorithms. —BIT 22: 140–149.
Gunderson R. W. (1983): An adaptive FCV clustering algorithm.—Interntl. J. Man-Mach. Stud. 19: 97–104.
Gustafson D. E. etKessel W. E. (1978): Fuzzy clustering with a fuzzy covariance matrix.—In:D. S. Fu [ed.]: IEEE Conf. Decision Contrib. pp. 761–76.
Harman H. H. (1967): Modern Factor Analysis..—Univ. Chicago Press, Chicago.
Hill, M. O. (1973): Reciprocal averaging: an eigenvector method of ordination.—J. Ecol. 61: 237–249.
Horst P. (1965): Factor analysis of data matrices.—Holt, Rinehart et Winston, New York.
Horst P. etSchaie K. W. (1956): The multiple group method of factor analysis and rotation to a simple structure hypothesis.—J. Exp. Ed. 24: 231–237.
Jardine N. etSibson R. (1968): The construction of hierarchic and nonhierarchic classifications. —Comput. J. 11: 177–184.
Kaiser H. F. (1958): The varimax criterion for analytic rotation in factor analysis.—Psychometrika 23: 187–200.
Keller J. M., Gray M. R. etGivens J. A. Jr.: (1985): A fuzzy k-nearest neighbour algorithm. —IEEE Trans. Syst. Man Cyber. SMC-15: 580–585.
Kendall M. G. (1948): Rank correlation methods.—Griffin, London.
Lance G. N. etWilliams W. T. (1966): A generalised sorting strategy for computer classifications. —Nature 212–218.
Lance G. N. etWilliams W. T. (1967): Mixed-data classificatory programs. Agglomerative systems.—Aust. Comput. J. 1: 15–26.
Lance G. N. etWilliams W. T. (1977): Attribute contributions to a classification.—Austral. Comput. J. 9: 128–129.
Libert G. etRoubens M. (1983): New experimental results in cluster validity of fuzzy clustering algorithms.—In:J. Janssen, J.-P. Marcotorchino etJ.-M. Proth [eds.]: New trends in data analysis and applications.—Elsevier (North Holland), pp. 205–218.
McBratney A. B. etde Gruijter J. (1987): Estimation and spatial prediction of continuous soil classes using fuzzy sets and generalized co-kriging.—Internatl. Fed. Classif. Soc. Conf. 1987, Aachen in prep.
McBratney A. B. etMooee A. W. (1985): Application of fuzzy sets to climatic classification.— Agric. For. Meteor. 35: 165–185.
Medis R. (1980): Unified analysis of variance by ranks.—Brit. J. Statist. Psychol. 33: 84–90.
Michalski S. etStepp R. E. (1985): Automated construction of classifications: conceptual clustering versus numerical taxonomy.—IEEE Trans. Patt. Anal. Mach. Intel. PAMI-5: 396–410.
Miyamoto S. etNakayama K. (1986): Similarity measures based on a fuzzy set model and application to hierarchical clustering.—IEEE Trans. Syst. Man Cyber. SMC-16: 479–482.
Molander P. (1986): Induction of categories: the problem of multiple equilibria.—J. Math. Psychol. 30: 42–54.
Pawlak Z. (1984): Rough classification.—Int. J. Man-Mach. Studies 20: 469–483.
Peay E. H. (1975): Nonmetric grouping: clusters and cliques.—Psychometrika 40: 297–313.
Ratkowsky D. etLance G. N. (1978): A criterion for determining the number of groups in a classification.—Austral. Comput. J. 10: 115–117.
Roberts D. W. (1986): Ordination on the basis of fuzzy set theory.—Vegetatio 66: 123–131.
Rose M. J. (1965): Classification of a set of elements.—Comput. J. 7: 208–224.
Ross D. R. (1979): TAXON users manual, ed. P3.—CSIRO, Division Computing Research, Canberra, A. C. T.
Selem, S. Z. etIsmail M. A. (1984): Soft clustering of multidimensional data: a semi-fuzzy aproach. —Patt. Recog. 17: 559–568.
Thurstone L. L. (1945): A multiple group method for factoring the correlation matrix.—Psychometrika 10: 73–78.
Thurstone L. L. (1947): Multiple factor analysis.—Univ. Chicago Press, Chicago.
Wallace C. S. etBoulton D. A. (1968): An information measure for classification.—Comput. J. 11: 185–194.
Whitfield J. W. (1953): The distribution of total rank values for one particular object in m rankings of n objects.—Brit. J. Statist. Psychol. 6: 35–40.
Williams W. T. etTracey J. G. (1984): Network analysis of north Queensland rainforests.— Austral. J. Bot. 32: 109–116.
Wong A. K. C. etLiu T. S. (1975): Typicality, diversity and feature pattern of an ensemble.— IEEE. Trans. Comput. C-24: 158–181.
Yamamoto S., Ushio K., Tazawa S., Ikeda H., Tamari F. etHamada N. (1977): Partitions of a query set into minimal number of subsets having the consecutive retrieval property.— J. Statist. Planning Infer. 1: 41–51.
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Present address: Division of Tropical Crops and Pastures, C. S. I. R. O., St. Lucia, 4067, Australia
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Dale, M.B. Some fuzzy approaches to phytosociology: Ideals and instances. Folia geobot. phytotax. 23, 239–274 (1988). https://doi.org/10.1007/BF02854819
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DOI: https://doi.org/10.1007/BF02854819