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Optimal Prototypes Selection for Ceramic Typology Analysis

Explore the methodology of selecting prototypes for ceramic typology analysis. Learn about curve characterization, correlation matrices, and prototype selection to efficiently identify groups within an assemblage. Details at http://www.weizmann.ac.il/complex/uzy/archaeomath/research.html

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Optimal Prototypes Selection for Ceramic Typology Analysis

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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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