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Optimal choice of prototypes for ceramic typology

Optimal choice of prototypes for ceramic typology. Uzy Smilansky (WIS) Avshalom Karasik (WIS) M. Bietak (Vienna) V. Mueller(Vienna). Acknowledge support from : Bikura (ISF), Kimmel center for archaeological studies (WIS). Tel – el – Daba = Abidos The capital of the Hyksos (1800-1600 bc).

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Optimal choice of prototypes for ceramic typology

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  1. Optimal choice of prototypes for ceramic typology Uzy Smilansky (WIS) Avshalom Karasik (WIS) M. Bietak (Vienna) V. Mueller(Vienna) Acknowledge support from : Bikura (ISF), Kimmel center for archaeological studies (WIS). Tel – el – Daba = Abidos The capital of the Hyksos (1800-1600 bc) Assemblage - 190 drinking cups w/o clear stratigraphical assignment.

  2. Typological analysis with a single index: (D. Arnold, M. Bietak)

  3. Various equivalent ways to characterize a curve (profile) s : arc length, Total length = L x(s) : distance from the symmetry axis. (s) : tangent angle. (s) : curvature. s 2 [0,L] Formally:

  4. Profiles of two cups and their characteristic functions

  5. The distance between the curves i and j can be defined in different ways using any of the characteristic functions Measure arc-length in units of L. Thus, s 2 [0,1]. The corresponding scaler products The correlation matrices Similarly: and Per definition:

  6. An abstract approach to typology We consider each profile as a “vector” is a multi-dimensional space. If the profiles are “similar” - their corresponding vectors occupy only a subspace of the space of profiles. Typology = Identification the relevant subspace and its basis vectors. The basis vectors are the “prototypes”. Criterion: maximum detail using a subspace spanned of minimal dimension.

  7. Sorting branches (correlated groups) using the correlation matrix 8 prototypes Constructed as means of The 8 branches. Generate the prototype correlation matrix Eigenvalues : 3.39 ; 2.61 ; 1.40 0.34 ; 0.21 ; 0.02 ; 0.00 ; 0.00 Projection on the two eigenvectors Corresponding to the largest eigenvalues

  8. Cluster analysis in terms of the Correlation matrix Eigenvalues : 3.4342 .39030; .15690 ; .01860 Hence- a single parameter is sufficient To characterize the assemblage !

  9. I m Good correlation between typology and chronology

  10. Conclusions: • The optimal mathematical characterization of the • profiles depends primarily on the nature of the features • of importance. • The best set of independent prototypes is created by • the eigenvectors of the prototype correlation matrix which • correspond to the dominant eigenvalues. • The chosen set of prototypes presents the best possible • compromise which minimizes the number of prototypes, • while maximizing the amount of preserved details. • For further details on the method and other applications: • visit- • http://www.weizmann.ac.il/complex/uzy/archaeomath/research.html

  11. The End חזק חזק ונתחזק

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