Numerical classification of proximity data with assignment measures
- 137 Downloads
An approach to numerical classification is described, which treats the assignment of objects to types as a continuous variable, called an assignment measure. Describing a classification by an assignment measure allows one not only to determine the types of objects, but also to see relationships among the objects of the same type and among the types themselves.
A classification procedure, the Assignment-Prototype algorithm, is described and evaluated. It is a numerical technique for obtaining assignment measures directly from one-mode, two-way proximity matrices.
KeywordsNumerical classification Cluster analysis Assignment measures Proximity data Dissimilarity data Assignment-Prototype Algorithm
Unable to display preview. Download preview PDF.
- ANDERSON, E. (1934), “The Irises of the Gaspe Peninsula,”Bulletin of the American Iris Society, 59, 2–5.Google Scholar
- BEZDEK, J.C. (1974), “Numerical Taxonomy with Fuzzy Sets,”Journal of Mathematical Biology, 1, 57–71.Google Scholar
- BEZDEK, J.C. (1981),Pattern Recognition with Fuzzy Objective Function Algorithms, New York: Plenum.Google Scholar
- LIBERT, G., and ROUBENS, M. (1982), “Non-metric Fuzzy Clustering Algorithms and Their Cluster Validity,” inFuzzy Information and Decision Processes, eds. R. Gupta and E. Sanchez, New York: Elsevier, 417–425.Google Scholar
- LUENBERGER, D.G. (1984),Introduction to Linear and Nonlinear Programming, (2nd ed), Reading: Addison-Wesley.Google Scholar
- ROUBENS, M. (1978), “Pattern Classification Problems and Fuzzy Sets,”Fuzzy Sets and Systems, 1, 239–253.Google Scholar
- RUSPINI, E. (1969), “A New Approach to Clustering,”Information and Control, 15, 22–32.Google Scholar
- RUSPINI, E. (1970), “Numerical Methods for Fuzzy Clustering,”Information Science, 2, 319–350.Google Scholar
- TUCKER, L.R. (1964), “The Extension of Factor Analysis to Three-dimensional Matrices,” inContributions to Mathematical Psychology, eds. N. Frederiksen and H. Gulliksen, New York: Holt, Rinehart & Winston.Google Scholar
- WOLFE, J.H. (1970), “Pattern Clustering by Multivariate Mixture Analysis,”Multivariate Behavioral Research, 5, 329–350.Google Scholar
- ZADEH, L.A. (1965), “Fuzzy Sets,”Information and Control, 8, 338–353.Google Scholar