Some fuzzy approaches to phytosociology: Ideals and instances
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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.
Keywords
Ideal types Numerical clustering Crisp clusters Nondeterministic clusters Fuzzy classes Bk clusters Typicality Allocation Ordination Two-parameter Additive clusters C-means Coding Transposed divisionPreview
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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.Google Scholar
- Arabie P. etCarroll J. D. (1980): MAPCLUS: a mathematical programming approach to fitting the ADCLUS model.—Psychometrika 45: 211–235.CrossRefGoogle Scholar
- Backer E. (1978): Cluster analysis by optimal decomposition of induced fuzzy sets.—Delft. Univ. Press. pp. 235.Google Scholar
- Ball G. H. etHall D. J. (1967): A clustering technique for summarising multivariate data.—Behav. Sci. 12: 153–155.CrossRefPubMedGoogle Scholar
- Bezdek J. C. (1974): Numerical taxonomy with fuzzy sets.—J. Math. Biol. 1: 57–71.CrossRefGoogle Scholar
- 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.CrossRefGoogle Scholar
- 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.Google Scholar
- Bray J. R. etCurtis J. T. (1957): An ordination of the upland forest communities of southern Wisconsin.—Ecol. Monogr. 27: 325–349.CrossRefGoogle Scholar
- Carroll J. B. (1953): An analytic solution for approximating simple structure.—Psychometrika 18: 23–38.CrossRefGoogle Scholar
- 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.CrossRefGoogle Scholar
- Dahl E., Prestvik O. etToftaker H. (1981): En kvantifiserung av karakterartbegrepet. —Det. Kgl. Norsk vidensk. Abers. Selskab, Musei Botaniskes Ser. 1981–5: 215–233.Google Scholar
- Dale M. B. etAnderson D. J. (1972): Qualitative and quantitative information analysis.— J. Ecol. 60: 639–653.CrossRefGoogle Scholar
- Dale M.-B. etAnderson D. J. (1973): Inosculate analysis of vegetation data.—Austral. J. Bot. 21: 253–276.CrossRefGoogle Scholar
- Dale M. B., Ferrari C., Beatrice M. etVenanzoni R. (1986): A comparison of some methods of species selection.—Coenoses 1: 35–51.Google Scholar
- Dale M. B. etWebb L. J. (1975): Numerical methods for the establishment of Associations.—Vegetatio 30: 77–87.CrossRefGoogle Scholar
- Dale M. B. etWilliams W. T. (1978): A new method of species reduction for ecological data.—Austral J. Ecol. 3: 1–5.CrossRefGoogle Scholar
- Diday E. etGovaert G. (1974): Classification avec distance adaptive.—C.R. Acad. Sci. Paris A, 993–995.Google Scholar
- Dunn, J. C. (1974): A fuzzy relative of ISODATA and its use in detecting compact well-separated clusters.—J. Cybernetics 3: 22–57.Google Scholar
- Flanagan P. A. (1986): An optimally data efficient isomorphism inference algorithm.—Information and Control 68: 207–222.CrossRefGoogle Scholar
- 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.CrossRefGoogle Scholar
- Goodall D. W. (1969): A procedure for recognition of uncommon species combinations in sets of vegetation samples.—Vegetatio 18: 19–35.CrossRefGoogle Scholar
- Gower J. (1966): Some distance properties of latent root and vector methods used in multivariate analysis.—Biometrika 53: 325–338.CrossRefGoogle Scholar
- Gunderson R. W. (1982): Choosing the r-dimension for the FCV family of clustering algorithms. —BIT 22: 140–149.CrossRefGoogle Scholar
- Gunderson R. W. (1983): An adaptive FCV clustering algorithm.—Interntl. J. Man-Mach. Stud. 19: 97–104.CrossRefGoogle Scholar
- 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.Google Scholar
- Harman H. H. (1967): Modern Factor Analysis..—Univ. Chicago Press, Chicago.Google Scholar
- Hill, M. O. (1973): Reciprocal averaging: an eigenvector method of ordination.—J. Ecol. 61: 237–249.CrossRefGoogle Scholar
- Horst P. (1965): Factor analysis of data matrices.—Holt, Rinehart et Winston, New York.Google Scholar
- 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.CrossRefGoogle Scholar
- Jardine N. etSibson R. (1968): The construction of hierarchic and nonhierarchic classifications. —Comput. J. 11: 177–184.CrossRefGoogle Scholar
- Kaiser H. F. (1958): The varimax criterion for analytic rotation in factor analysis.—Psychometrika 23: 187–200.CrossRefGoogle Scholar
- 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.CrossRefGoogle Scholar
- Kendall M. G. (1948): Rank correlation methods.—Griffin, London.Google Scholar
- Lance G. N. etWilliams W. T. (1966): A generalised sorting strategy for computer classifications. —Nature 212–218.Google Scholar
- Lance G. N. etWilliams W. T. (1967): Mixed-data classificatory programs. Agglomerative systems.—Aust. Comput. J. 1: 15–26.Google Scholar
- Lance G. N. etWilliams W. T. (1977): Attribute contributions to a classification.—Austral. Comput. J. 9: 128–129.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- McBratney A. B. etMooee A. W. (1985): Application of fuzzy sets to climatic classification.— Agric. For. Meteor. 35: 165–185.CrossRefGoogle Scholar
- Medis R. (1980): Unified analysis of variance by ranks.—Brit. J. Statist. Psychol. 33: 84–90.CrossRefGoogle Scholar
- 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.Google Scholar
- 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.CrossRefGoogle Scholar
- Molander P. (1986): Induction of categories: the problem of multiple equilibria.—J. Math. Psychol. 30: 42–54.CrossRefGoogle Scholar
- Pawlak Z. (1984): Rough classification.—Int. J. Man-Mach. Studies 20: 469–483.CrossRefGoogle Scholar
- Peay E. H. (1975): Nonmetric grouping: clusters and cliques.—Psychometrika 40: 297–313.CrossRefGoogle Scholar
- Ratkowsky D. etLance G. N. (1978): A criterion for determining the number of groups in a classification.—Austral. Comput. J. 10: 115–117.Google Scholar
- Roberts D. W. (1986): Ordination on the basis of fuzzy set theory.—Vegetatio 66: 123–131.CrossRefGoogle Scholar
- Rose M. J. (1965): Classification of a set of elements.—Comput. J. 7: 208–224.CrossRefGoogle Scholar
- Ross D. R. (1979): TAXON users manual, ed. P3.—CSIRO, Division Computing Research, Canberra, A. C. T.Google Scholar
- Selem, S. Z. etIsmail M. A. (1984): Soft clustering of multidimensional data: a semi-fuzzy aproach. —Patt. Recog. 17: 559–568.CrossRefGoogle Scholar
- Thurstone L. L. (1945): A multiple group method for factoring the correlation matrix.—Psychometrika 10: 73–78.CrossRefGoogle Scholar
- Thurstone L. L. (1947): Multiple factor analysis.—Univ. Chicago Press, Chicago.Google Scholar
- Wallace C. S. etBoulton D. A. (1968): An information measure for classification.—Comput. J. 11: 185–194.CrossRefGoogle Scholar
- 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.CrossRefGoogle Scholar
- Williams W. T. etTracey J. G. (1984): Network analysis of north Queensland rainforests.— Austral. J. Bot. 32: 109–116.CrossRefGoogle Scholar
- Wong A. K. C. etLiu T. S. (1975): Typicality, diversity and feature pattern of an ensemble.— IEEE. Trans. Comput. C-24: 158–181.CrossRefGoogle Scholar
- 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.CrossRefGoogle Scholar