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Measuring Cultural Relatedness Using Multiple Seriation Ordering Algorithms
Seriation is a long-standing archaeological method for relative dating that has proven effective in probing regional-scale patterns of inheritance, social networks, and cultural contact in their full spatiotemporal context. The orderings produced by seriation are produced by the continuity of class distributions and unimodality of class frequencies, properties that are related to social learning and transmission models studied by evolutionary archaeologists. Linking seriation to social learning and transmission enables one to consider ordering principles beyond the classic unimodal curve. Unimodality is a highly visible property that can be used to probe and measure the relationships between assemblages, and it was especially useful when seriation was accomplished with simple algorithms and manual effort. With modern algorithms and computing power, multiple ordering principles can be employed to better understand the spatiotemporal relations between assemblages. Ultimately, the expansion of seriation to additional ordering algorithms allows us an ability to more thoroughly explore underlying models of cultural contact, social networks, and modes of social learning. In this paper, we review our progress to date in extending seriation to multiple ordering algorithms, with examples from Eastern North America and Oceania.
Archaeological seriation extracts an ordering from a set of class descriptions, usually rendered as type frequencies within assemblages, by reordering those descriptions until each type displays a continuous and unimodal distribution. This combination of criteria dates from the earliest days of seriation, and appears to originate in empirical generalizations concerning both archaeological distributions and the behavior of object “styles” in contemporary populations.
Those empirical generalizations are easy to tie to the ideas behind cultural transmission and other diffusion models in a broad, descriptive way. It is clear, for example, that in many cases, a new cultural variant is introduced, spreads within a population, increasing in prevalence relative to other variants, and eventually declines in frequency as other, perhaps newer, variants are introduced and themselves grow. But it is also clear to anyone who has studied the behavior of diffusion and transmission models that unimodal growth and decline is far from the only pattern that variants display. Especially in diffusion models with no selection, many classes display complex multimodal distributions.
Similarly, we expect most cultural variants to display relatively “smooth” distributions, where the prevalence of a trait is similar among points close in space or time, without major discontinuities. We also expect culture-historical “styles” or types to display a single spacetime distribution without recurrence – this is the basis of occurrence seriation, and of course is an unspoken corollary of the unimodal frequency criterion.
In classical seriation methods, the major ordering principles are unimodality and nonrecurrence (i.e., no holes). Neither of these, however, are the deep ordering principle which allow us to order descriptions into a full spatiotemporal map of a diffusion process. That principle, for underlying processes which are relatively continuous, is given by the “smoothness” principle, which requires that diffusion makes no major “jumps” and thus is continuous in the mathematical, analytic sense of the term.
We call this the “analytic continuity” principle, and it is constructed in empirical cases by finding the ordering of assemblage descriptions which globally minimize the inter-assemblage distance, where distance is measured by an appropriate vector distance (e.g., cosine or angular distance).
Why was this principle not employed earlier in archaeological seriation? After all, practitioners like James A. Ford fully understood the spatiotemporal nature of the cultural diffusion process which underlay seriation results (ref to the 1938 diagram). We believe that it was not used in real seriations because there is no way to accomplish such orderings in real cases without significant computational support, and by the time computer support for seriation was available, the nature of the problem had been recast as one of matrix ordering of similiarity coefficients, with significiant changes in the nature of the solutions accepted as a result. The difference is one of detail, but the details are significant.
The other ordering principles – unimodality and “topological continuity” (or the “no holes” principle) – relate to smoothness continuity in a global/local fashion. The latter provides a global view of diffusion, while the latter allow us to find structure within the field of assemblages, and find groups of assemblages which fit together more than they fit with surrounding groups.
We propose, therefore, extensions to the seriation method which employ all three ordering principles: analytic continuity, to provide the global map of diffusion across all of the assemblage descriptions in a given data set, and the use of unimodality and non-recurrence (“no holes”) to help probe smaller-scale or “mesoscopic” structure within the data set.
This redescription of the overall seriation method provides a way to link the method to both to an overall cultural transmission model, as well as a principled way to describe the internal structure of solutions at smaller scales, and is ideally suited to analysis at scales ranging from a few assemblages to large regional surveys. In a future paper, we intend to explore the extension of this method between regional and larger scales by exploring the interface between seriation and cladistics, which we believe extends the mesoscopic scale to macroscopic large scale analysis of cultural relatedness.