Abstract
Traditional procedures for clustering objects consist of two steps: measuring pairwise resemblance based on the attributes, and a clustering algorithm. The use of pairwise resemblances can be avoided; a set of objects can be represented as a set of lists of attribute states; an application of the Laplace indifference principle then allows an estimate to be made of the probability of each list as representative of an association of objects. By use of set-covering procedures, the object associations having maximum joint probability are found. The procedure is generalized to multistate unordered and ordered attributes, to frequencies, and to directly obtained relational data.
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References
Andersen, E.B. 1980. Discrete statistical models with social science applications. North-Holland, Amsterdam.
André, H.M. 1984. Overlapping recurrent groups: an extension of Fager’s concept and algorithm. Biometrié-Praximétrie 24: 49–65.
Chvatál, V. 1979. A greedy heuristic for the set covering problem. Mathematics of Operations Research 4: 233–235.
Dale, M.B. 1971. Information analysis of quantitative data. Statistical Ecology 3: 133–148.
Fine, T.L. 1973. Theories of probability. Academic, New York.
Garfinkel, R., and G.L. Nemhauser, 1972. Integer programming, Wiley, New York.
Gower, J.C. 1971. A general coefficient of similarity and some of its properties. Biometrics 27: 857–871.
Gower, J.C., and P. Legendre, 1986. Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification 3: 5–48.
Lefkovitch, L.P. 1976. Hierarchical clustering from principal coordinates: an efficient method for small to very large numbers of objects. Mathematical Biosciences 31: 157–174.
Lefkovitch, L.P. 1980. Conditional clustering. Biometrics 36: 43–58.
Lefkovitch, L.P. 1982. Conditional clusters, musters and probability. Mathematical Biosciences 60: 207–234.
Lefkovitch, L.P. 1984. A nonparametric method for comparing dissimilarity matrices, a general measure of biogeographical distance, and their application. American Naturalist 123: 484–499.
Lefkovitch, L.P. 1985. Entropy and set covering. Information Sciences 36: 283–294.
Lundy, M. 1985. Applications of the annealing algorithm to combinational problems in statistics. Biometrika 72: 191–198.
Rasch, G. 1960. Probabilistic models for some intelligence and attainment tests. Danmarks Paedagogistic Institut, Copenhagen.
Shore, J.E., and R.W. Johnson, 1980. Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross entropy. IEEE Trans. Inform. Theory IT-26:26–37.
Tjur, T. 1982. A connection between Rasch’s item analysis model and a multiplicative Poisson model. Scand. J. Statist. 9: 23–30.
Toussaint, G.T. 1980. The relative neighbourhood graph of a finite planar set. Pattern Recognition 12: 261–268.
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© 1987 Springer-Verlag Berlin Heidelberg
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Lefkovitch, L.P. (1987). Species Associations and Conditional Clustering: Clustering With or Without Pairwise Resemblances. In: Legendre, P., Legendre, L. (eds) Develoments in Numerical Ecology. NATO ASI Series, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70880-0_8
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DOI: https://doi.org/10.1007/978-3-642-70880-0_8
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