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
Ehrenfeucht, A. Classification Theory (unpublished).
Ehrenfeucht, A. & Malitz, J. Problems in mathematical taxonomy (in preparation).
Elgueta, M. Unicity of cuts equalizing distances to centers of mass in convex regions (unpublished).
Chen, C. Statistical pattern recognition. Hayden Books, (1973) (See Chapter VIII in particular).
Murtagh, A. Survey of recent advances in hierarchical clustering algorithms, Comp.J., 26,no 4 (1983) pp.354–359.
Mauldin, R.D. ed., The Scottish Book. Birkhauser (1981) (See problem 19, p. 90 in particular).
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
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