Limits...
A theoretically-sufficient and computationally-practical technique for deterministic frequency seriation.

Lipo CP, Madsen ME, Dunnell RC - PLoS ONE (2015)

Bottom Line: This compression removes the ability to use all of the features of our data to fit to the seriation model, obscuring violations of the model, and thus lessens our ability to understand the degree to which the resulting order is chronological, spatial, or a mixture.Our initial implementation of IDSS does not solve all the problems of seriation, but begins to moves towards a resolution of a long-standing problem in archaeology while opening up new avenues of research into the study of cultural relatedness.We demonstrate the utility of IDSS using late prehistoric decorated ceramics from the Mississippi River Valley.

View Article: PubMed Central - PubMed

Affiliation: Department of Anthropology and IIRMES, California State University Long Beach, 1250 Bellflower Blvd., Long Beach, CA 90840, USA.

ABSTRACT
Frequency seriation played a key role in the formation of archaeology as a discipline due to its ability to generate chronologies. Interest in its utility for exploring issues of contemporary interest beyond chronology, however, has been limited. This limitation is partly due to a lack of quantitative algorithms that can be used to build deterministic seriation solutions. When the number of assemblages becomes greater than just a handful, the resources required for evaluation of possible permutations easily outstrips available computing capacity. On the other hand, probabilistic approaches to creating seriations offer a computationally manageable alternative but rely upon a compressed description of the data to order assemblages. This compression removes the ability to use all of the features of our data to fit to the seriation model, obscuring violations of the model, and thus lessens our ability to understand the degree to which the resulting order is chronological, spatial, or a mixture. Recently, frequency seriation has been reconceived as a general method for studying the structure of cultural transmission through time and across space. The use of an evolution-based framework renews the potential for seriation but also calls for a computationally feasible algorithm that is capable of producing solutions under varying configurations, without manual trial and error fitting. Here, we introduce the Iterative Deterministic Seriation Solution (IDSS) for constructing frequency seriations, an algorithm that dramatically constrains the search for potential valid orders of assemblages. Our initial implementation of IDSS does not solve all the problems of seriation, but begins to moves towards a resolution of a long-standing problem in archaeology while opening up new avenues of research into the study of cultural relatedness. We demonstrate the utility of IDSS using late prehistoric decorated ceramics from the Mississippi River Valley. The results compare favorably to previous analyses but add new details into the structure of cultural transmission of these late prehistoric populations.

No MeSH data available.


Related in: MedlinePlus

The ‘minmax’ graph produced for the Memphis and St. Francis area assemblages from the 97 valid DFS solutions generated the IDSS algorithm (as shown in Fig 11) using a continuity threshold of 0.30 and α = 0.05 confidence intervals for the comparison of frequencies. The “minmax” graph was generated using the procedure described in Fig 6.Significantly, the results show remarkable structure with a series of spatially clustered branches that are formed from overlapping but distinct sets of seriation solutions. Parkin (11-N-1) forms the center of a branch that extends in 3 different directions (to 11-N-9, 13-P-1 and 11-O-10). Assemblages 13-O-7 and 13-O-10 also have this same configuration. 13-O-7 has an extra branch leading to Holden Lake, a presumably earlier deposit. The branches are numbered and colored to correspond with the spatial groups in Fig 13.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4414518&req=5

pone.0124942.g012: The ‘minmax’ graph produced for the Memphis and St. Francis area assemblages from the 97 valid DFS solutions generated the IDSS algorithm (as shown in Fig 11) using a continuity threshold of 0.30 and α = 0.05 confidence intervals for the comparison of frequencies. The “minmax” graph was generated using the procedure described in Fig 6.Significantly, the results show remarkable structure with a series of spatially clustered branches that are formed from overlapping but distinct sets of seriation solutions. Parkin (11-N-1) forms the center of a branch that extends in 3 different directions (to 11-N-9, 13-P-1 and 11-O-10). Assemblages 13-O-7 and 13-O-10 also have this same configuration. 13-O-7 has an extra branch leading to Holden Lake, a presumably earlier deposit. The branches are numbered and colored to correspond with the spatial groups in Fig 13.

Mentions: Using the IDSS analysis we can systematically examine the full set of possible frequency seriation solutions (Figs 11–13). Despite the large number of possible solutions (N = 2.56 × 1018), iteratively finding the set of 97 possible solutions required less than two seconds of processing due to the fact that the largest possible seriations were composed of only 4 assemblages. No larger sets can be built without introducing violations of unimodality, so the algorithm did not need to continue its search and terminated. Using a confidence interval of α = 0.05 allowed us to generate a solution that included all assemblages. Fig 11 clearly shows how the traditional linear ordering breaks down as a visualization mechanism, especially in the presence of many valid solutions. A number of assemblages participate in multiple solutions, and it is impossible to get a sense of the overall nature of the solutions when confronted with many separate orderings. Thus, as described above, we focus here on the graph representation of results (Fig 12).


A theoretically-sufficient and computationally-practical technique for deterministic frequency seriation.

Lipo CP, Madsen ME, Dunnell RC - PLoS ONE (2015)

The ‘minmax’ graph produced for the Memphis and St. Francis area assemblages from the 97 valid DFS solutions generated the IDSS algorithm (as shown in Fig 11) using a continuity threshold of 0.30 and α = 0.05 confidence intervals for the comparison of frequencies. The “minmax” graph was generated using the procedure described in Fig 6.Significantly, the results show remarkable structure with a series of spatially clustered branches that are formed from overlapping but distinct sets of seriation solutions. Parkin (11-N-1) forms the center of a branch that extends in 3 different directions (to 11-N-9, 13-P-1 and 11-O-10). Assemblages 13-O-7 and 13-O-10 also have this same configuration. 13-O-7 has an extra branch leading to Holden Lake, a presumably earlier deposit. The branches are numbered and colored to correspond with the spatial groups in Fig 13.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4414518&req=5

pone.0124942.g012: The ‘minmax’ graph produced for the Memphis and St. Francis area assemblages from the 97 valid DFS solutions generated the IDSS algorithm (as shown in Fig 11) using a continuity threshold of 0.30 and α = 0.05 confidence intervals for the comparison of frequencies. The “minmax” graph was generated using the procedure described in Fig 6.Significantly, the results show remarkable structure with a series of spatially clustered branches that are formed from overlapping but distinct sets of seriation solutions. Parkin (11-N-1) forms the center of a branch that extends in 3 different directions (to 11-N-9, 13-P-1 and 11-O-10). Assemblages 13-O-7 and 13-O-10 also have this same configuration. 13-O-7 has an extra branch leading to Holden Lake, a presumably earlier deposit. The branches are numbered and colored to correspond with the spatial groups in Fig 13.
Mentions: Using the IDSS analysis we can systematically examine the full set of possible frequency seriation solutions (Figs 11–13). Despite the large number of possible solutions (N = 2.56 × 1018), iteratively finding the set of 97 possible solutions required less than two seconds of processing due to the fact that the largest possible seriations were composed of only 4 assemblages. No larger sets can be built without introducing violations of unimodality, so the algorithm did not need to continue its search and terminated. Using a confidence interval of α = 0.05 allowed us to generate a solution that included all assemblages. Fig 11 clearly shows how the traditional linear ordering breaks down as a visualization mechanism, especially in the presence of many valid solutions. A number of assemblages participate in multiple solutions, and it is impossible to get a sense of the overall nature of the solutions when confronted with many separate orderings. Thus, as described above, we focus here on the graph representation of results (Fig 12).

Bottom Line: This compression removes the ability to use all of the features of our data to fit to the seriation model, obscuring violations of the model, and thus lessens our ability to understand the degree to which the resulting order is chronological, spatial, or a mixture.Our initial implementation of IDSS does not solve all the problems of seriation, but begins to moves towards a resolution of a long-standing problem in archaeology while opening up new avenues of research into the study of cultural relatedness.We demonstrate the utility of IDSS using late prehistoric decorated ceramics from the Mississippi River Valley.

View Article: PubMed Central - PubMed

Affiliation: Department of Anthropology and IIRMES, California State University Long Beach, 1250 Bellflower Blvd., Long Beach, CA 90840, USA.

ABSTRACT
Frequency seriation played a key role in the formation of archaeology as a discipline due to its ability to generate chronologies. Interest in its utility for exploring issues of contemporary interest beyond chronology, however, has been limited. This limitation is partly due to a lack of quantitative algorithms that can be used to build deterministic seriation solutions. When the number of assemblages becomes greater than just a handful, the resources required for evaluation of possible permutations easily outstrips available computing capacity. On the other hand, probabilistic approaches to creating seriations offer a computationally manageable alternative but rely upon a compressed description of the data to order assemblages. This compression removes the ability to use all of the features of our data to fit to the seriation model, obscuring violations of the model, and thus lessens our ability to understand the degree to which the resulting order is chronological, spatial, or a mixture. Recently, frequency seriation has been reconceived as a general method for studying the structure of cultural transmission through time and across space. The use of an evolution-based framework renews the potential for seriation but also calls for a computationally feasible algorithm that is capable of producing solutions under varying configurations, without manual trial and error fitting. Here, we introduce the Iterative Deterministic Seriation Solution (IDSS) for constructing frequency seriations, an algorithm that dramatically constrains the search for potential valid orders of assemblages. Our initial implementation of IDSS does not solve all the problems of seriation, but begins to moves towards a resolution of a long-standing problem in archaeology while opening up new avenues of research into the study of cultural relatedness. We demonstrate the utility of IDSS using late prehistoric decorated ceramics from the Mississippi River Valley. The results compare favorably to previous analyses but add new details into the structure of cultural transmission of these late prehistoric populations.

No MeSH data available.


Related in: MedlinePlus