By Ingo Balderjahn (auth.), Prof. Dr. Otto Optiz (eds.)

ISBN-10: 3540516417

ISBN-13: 9783540516415

ISBN-10: 3642750400

ISBN-13: 9783642750403

The thirteenth convention of the Gesellschaft fUr Klassifikation e. V. happened on the Universitat Augsburg from April 10 to twelve, 1989, with the' neighborhood association by way of the Lehrstuhl fUr Mathematische Me­ thoden der Wirtschaftswissenschaften. The vast ranged topic of the convention Conceptual and Numerical research of knowledge used to be obliged to point the range of the ideas of information and data in addition to the manifold tools of analysing and structuring. in response to the acquired bulletins of papers 4 sections were prepared: 1. facts research and class: simple strategies and techniques 2. functions in Library Sciences, Documentation and knowledge Sciences three. purposes in Economics and Social Sciences four. purposes in usual Sciences and desktop Sciences This class does not separate strictly, however it indicates that theo­ retic and utilizing researchers of such a lot diverse disciplines have been disposed to provide a paper. In 60 survey and particular lectures the audio system suggested on advancements in conception and purposes en­ couraging the interdisciplinary discussion of all members. This quantity includes forty two chosen papers grouped based on the 4 sections. Now we provide a brief perception into the offered papers. x numerous difficulties of suggestion research, cluster research, information research and multivariate information are thought of in 18 pa­ pers of part 1. The geometric illustration of an idea lattice is a set of figures within the aircraft similar to the given thoughts in this type of manner that the subconcept-superconcept-relation corresponds to the containment relation among the figures. R.

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Extra info for Conceptual and Numerical Analysis of Data: Proceedings of the 13th Conference of the Gesellschaft für Klassifikation e. V., University of Augsburg, April 10–12, 1989

Example text

More- 29 over, it may be doubtful to use them as tests for unimodality HI since even under HI there may be large gaps in the tails ·of the distribution (a weighted version of the test statistics may be used in this case, see Henze 1983). In particular, the occurrence of large gaps must be interpreted very carefully in cluster analysis since they may point to non-uniform, but non-clustering structures as well due to the complex topological structure of RP for p 2: 2. , I F~(w)dw, and Schilling (1983) considers a weighted version of Fn in order to improve on the power properties from the order 1/ log n to the order n- I / 2 .

Goodness of fit testing in R m based on the weighted empirical distribution of certain nearest neighbor statistics. Ann. Statist. 11 (1983) 1-12. Schroeder, A. ~nalyse d'un melange de distributions de probabilire de meme type. 1, 39-62. Schweder, T. On the dispersion of mixtures. Scand. J. , Theory and Applications 9 (1982) 165-170. Sclove, S. L. Population mixture models and clustering algorithms. Communications in Statistics, Theory and Methods A 6 (1977) 417-434. Scott, A. , Knott, M. A cluster analysis method for grouping means in the analysis of variance.

3 MuItimodality It is generally understood that a unimodal (possibly: symmetric) distribution density I (x), x E RP, corresponds to a homogeneous, unclustered population. In contrast, the existence of several modes 6, ... , E RP (local maxima of f) is considered as a strong indication of a heterogeneous, clustered population with m classes, the more if they are separated by regions of very low values of I (valleys). Evidently, this is a non-parametric clustering model with no precise definition of the class concept: All points x E RP which can reach, by iterative relocation, the same mode by a hillclimbing walk are generally considered to belong to the same cluster (mode cluster).

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Conceptual and Numerical Analysis of Data: Proceedings of the 13th Conference of the Gesellschaft für Klassifikation e. V., University of Augsburg, April 10–12, 1989 by Ingo Balderjahn (auth.), Prof. Dr. Otto Optiz (eds.)

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