Optimal choice of prototypes for ceramic typology

A crucial step in any typological analysis is the determination of the prototypes according to which the assemblage is to be classified. Two conflicting requirements dictate this choice: the number of prototypes should be minimal to allow an efficient classification. At the same time, the set of prototypes should be comprehensive so that the essential variability of the original assemblage is reproduced by the prototypes. This problem is especially complex when the assemblage consists of ceramic vessels of the same genre such as e.g., storage jars, cooking pots or drinking cups. Here, we would like to present a computerized method to identify an optimal set of prototypes, which is based on the analysis of pottery profiles in terms of their curvature functions. The profiles are clustered according to their correlations (defined as the scalar products of the curvature functions). Averaging the curvature functions in each of the dominant branches yield a set of curvature functions, whose number is much smaller than the number of profiles in the original assemblage, and which is based on the dominant but distinct features in each of the branches. The next step in the process is to find the optimal subset of types, which satisfies the conflicting requirements mentioned above. In the present mathematical setting, one can define two "figures of merit" which quantify the two requirements. The optimal set of prototypes is the one which minimizes the number of types without affecting the quality of the description. The method will be illustrated by showing its application to an assemblage of a few hundreds of Early Bronze cooking pots and jars from Tel Arad (Southern Israel) and the Sinai peninsula (Egypt)