Frequency Seriation

Frequency seriation is a special case of optimal path seriation where the feature values for an artifact (or assemblage) are non-negative fractions and add up to zero or one. The seriation technique can be set in the Seriations table. If you choose frequency seriation, OptiPath will automatically convert your data to non-negative fractions summing to one (or zero, if all data for an artifact or assemblage are zero or blank). To see the effect on the raw data, look at processed data in the Values table. The seriation technique can be set in the Seriations table.

Frequency seriation is often used when you have raw data for individual artifacts that can be aggregated into assemblages. Feature data for the assemblage then reflect the fraction (percentage) of artifacts in the assemblage that share  a common trait (class or feature value). By treating each assemblage as an artifact, and each trait as a feature, frequency seriation is a special case of optimal path seriation. However, it is not necessary to use assemblages to use frequency seriation.

The underlying assumption in frequency seriation is that a feature will normally be introduced only once in the evolution of an artifact type - once the feature has appeared and then been absent in artifacts for a period of time it will not reappear, and that the frequencies of the individual features will tend to change slowly and smoothly over time. Most implementations of discrete seriation attempt to order the artifacts temporally so as to minimize the number of times that a distinct feature is introduced into the archaeological record (transitions from absent to present, and present to absent) and so as to minimize the number of reversals from increasing to decreasing, or vice versa, of the individual feature's frequency. If a perfect seriation exists, the total number of transitions will be two times the number of features (where each feature is assumed to be absent at some point both earlier and later than the artifacts in the sample being analyzed) and the frequency values for each feature will be unimodal.

Frequency seriation is a special case of the Optimal Path seriation model. Setting the seriation parameter Technique to Frequency specifies OptiPath's standard implementation of frequency seriation. In this case OptiPath uses the Optimal Path seriation model with Euclidean distance.  Data may take on any numerical values but zeroes are assumed to represent both the value zero and an absence of the feature (class or style) in question. Blanks are treated as unknowns. All other numerical values are taken to indicate the presence of the feature and non-numerical values are treated as unknowns. Setting the seriation parameter Technique to Frequency causes OptiPath to automatically set the feature parameters Data, Ranks, Metric, Normalize, Transition, Earlier, Later, Blanks and Zeroes to specific values.

The following are the default feature parameter settings for frequency seriation. To change them you must first select the Custom Seriation technique. With Custom seriation OptiPath allows you to simultaneously treat some features as occurrences/absences and others as classifications or as ranked or measured data - see Data in the Features table.

Data	=	Measured
Ranks	=	0
Metric	=	Euclidean
Normalize	=	No
Transition	=	0
Earlier	=	Unknown
Later	=	Unknown
Blanks	=	Unknown
Zeroes	=	Value & Absent

These settings result in any non-zero numerical entry in the Data being interpreted as indicating the presence of a feature (class or style) and any zero in the data being interpreted as the absence with the value of zero. If you do not want zeroes to be interpreted as values or the absence of the feature, you should set the seriation parameter Technique to Custom and reset the feature parameter Zeroes. If you do not want blanks to be interpreted as unknown, you should set the seriation parameter Technique to Custom and reset the feature parameter Blanks.  To see the effect of your settings, look at processed data in the Values table.

In frequency seriation, careful thought should be put into setting the feature parameters appropriately - see Setting the Earlier, Later, Blanks, Zeroes and Transition Parameters.