Zeroes
Zero values in the data are inherently ambiguous. Normally, zeroes indicate values of 0. However, a zero could also indicate that a feature is missing or absent for an artifact. Or, a zero might indicate both a value and an absence (for example, the feature might be the width of an ornamental band on pottery and a zero might indicate a band of zero width, or equivalently, the absence of a band on some artifacts). Alternatively, a zero could signify the absence of data rather than the absence of the feature - we simply don't know anything about this feature for this artifact. Whatever convention you are using, you need to let OptiPath know by setting the feature parameter Zeroes.
Zeroes can be interpreted four different ways: as absences, as values, as absences and values, or as unknowns.
If the feature parameter Zeroes is set to Unknown, zeroes are taken to mean that the true value of the feature for the artifact is unknown and the feature will have no effect in the computation of distance between artifacts. This means this feature's contribution to the distance, including any transition penalty, is zero.
If the feature parameter Zeroes is set to Value, zeroes will be considered a value in computing the feature's contribution to the distance between artifacts. However, features with the value zero will be considered to be present. Consequently in computing the distance to an artifact having any value (including zero) for this feature, the feature will incur no transition penalty; but a transition penalty will be incurred if the other artifact has a blank value for this feature and the Blanks parameter is set to Absent for this feature.
If the feature parameter Zeroes is set to Absent, zeroes are treated like absences and will affect the computation of transition penalties but otherwise they are treated like unknown values and have no effect in computing distance between artifacts.
If the feature parameter Zeroes is set to Value & Absent, zeroes will be treated as values and will affect the computation of transition penalties and distance between artifacts. If the other artifact has a non-zero value for this feature, then both the distance and the transition penalty will be computed; otherwise (when the other artifact's feature value is zero or blank) both the feature's contribution to the distance and transition penalty will be zero. When the features parameter Ranks = 1, you may want to avoid setting the Zeroes parameter to Value & Absent. This is because with Ranks = 1, all data values are assigned rank = 1 and absences of data are assigned rank = 0, resulting in a dilemma for OptiPath.
There is another issue concerning zeroes. Suppose, instead of 0/1 data we have the integer data presented in the table below, where the numbers represent frequencies, the number of times a feature appears in a collection or assemblage of artifacts. Conventional thinking on frequency seriation is to try to achieve lenticular or "battleship-shaped" curves. This would imply that feature B has a preferred ordering to feature A. To encourage the ordering in B, it is advisable to treat 0's as values (or values and absences). This way OptiPath will try to taper off a string of values gradually at both start and finish.
Features A B Assemblage 1 0 0 Assemblage 2 0 0 Assemblage 3 0 0 Assemblage 4 10 10 Assemblage 5 12 30 Assemblage 6 30 37 Assemblage 7 34 44 Assemblage 8 37 46 Assemblage 9 38 38 Assemblage 10 44 34 Assemblage 11 46 12 Assemblage 12 0 0 Assemblage 13 0 0 Assemblage 14 0 0
Each setting for Zeroes can lead to different results in seriation. For more information see Setting the Earlier, Later, Blanks, Zeroes and Transition Parameters.
4/14/08