Discrete Seriation

Discrete seriation is a special case of optimal path seriation where the feature values happen to be integral. The seriation technique can be set in the Seriations table.

In discrete seriation features are categorized into classes which are numbered discretely: 0, 1, 2, …, n for each feature. The objective is to order items keeping each class together and to progress gradually from one class to the next in nominal size. See Ranked Data.

The underlying assumption in discrete 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 values or measures 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 values. 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).

Discrete seriation is a special case of the Optimal Path seriation model. Setting the seriation parameter Technique to Discrete specifies OptiPath's standard implementation of discrete seriation. In this case OptiPath uses the Optimal Path seriation model with Manhattan distance. Data may take on any numerical values (fractions are rounded to the nearest whole number) but zeroes and blanks are both assumed to represent both the value zero and an absence of the feature (class or style) in question. 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 Discrete 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 discrete 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	=	Ranked
Ranks	=	0
Metric	=	Manhattan
Normalize	=	No
Transition	=	50
Earlier	=	Absent
Later	=	Absent
Blanks	=	Zero
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 blank or 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 the feature parameter Zeroes to Value (and the rest of the parameters as above). If you want blanks to be interpreted as unknown, you should set the seriation parameter Technique to Custom and the feature parameter Blanks to Unknown (and the rest of the parameters as above).  To see the effect of your settings, look at processed data in the Values table.

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