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Problems in taxonomy, a floating log

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1130)

Abstract

Given a region R in an n-dimensional normed linear space, is there a partition of R into k pieces R1,Rj,…,Rk with centers of mass c1,c2,…,ck respectively such that for each i ≤ k and each x × Ri we have |x-ci| ≤ |x-cj| for all j ≤ k. The problem is open even for n=2 and k=2 but some partial results are known.

The problem is highly relevant to the foundations of taxonomy, medical diagnosis and classification in general.

Keywords

  • Medical Diagnosis
  • Classification Theory
  • Heuristic Argument
  • Good Partition
  • Perpendicular Bisector

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Ehrenfeucht, A. Classification Theory (unpublished).

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  2. Ehrenfeucht, A. & Malitz, J. Problems in mathematical taxonomy (in preparation).

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  3. Elgueta, M. Unicity of cuts equalizing distances to centers of mass in convex regions (unpublished).

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  4. Chen, C. Statistical pattern recognition. Hayden Books, (1973) (See Chapter VIII in particular).

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  5. Murtagh, A. Survey of recent advances in hierarchical clustering algorithms, Comp.J., 26,no 4 (1983) pp.354–359.

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  6. Mauldin, R.D. ed., The Scottish Book. Birkhauser (1981) (See problem 19, p. 90 in particular).

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  7. Steinhaus, H. Mathematical Snapshots. Oxford University Press (1969) (See p. 50).

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© 1985 Springer-Verlag

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Malitz, J.I. (1985). Problems in taxonomy, a floating log. In: Di Prisco, C.A. (eds) Methods in Mathematical Logic. Lecture Notes in Mathematics, vol 1130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075315

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  • DOI: https://doi.org/10.1007/BFb0075315

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15236-1

  • Online ISBN: 978-3-540-39414-3

  • eBook Packages: Springer Book Archive