Unimodality is a mathematical concept – there can be only one peak in a graph of a unimodal function. In archaeology the concept has been expressed in terms of "lenticularity" and "battleship shaped curves". For archaeologists, the concept expresses the idea that a style appears in the archaeological record, gains in popularity over time and then loses popularity until it vanishes from the record.
It has often been argued that seriation can only be meaningfully applied to stylistic, as opposed to functional, features. However, technological innovation has often shown the same pattern - paradigm changing innovation which introduces a new style which becomes more popular until replaced by a new functional refinements and adustments significant enough to be considerd a new style.
Unimodality has long been the basis for archaeological seriation, providing archaeologists a pattern to replicate in an attempt to order data chronologically. Mathematically, unimodality is all-or-nothing. The temporal distribution of artifacts or assemblages rarely exhibits strict unimodality and it is rarely possible to order artifacts to achieve perfect unimodality for multiple features or styles. The lack of an objective measure of unimodality when perfect unimodality is not attainable has precluded consistently independently reproducible seriations.
It can be shown that, under reasonable assumptions, unimodality is the natural outcome of gradual change (paper in preparation by the authors). Gradualness is actually the more general of the two concepts. There are situations where it is reasonable to assume that a style may come into vogue then lose popularity only later to see a resurgence in its popularity. In this case forcing a seriation to be unimodal would likely be inferior to making the rate of stylistic change as gradual as possible. Neither is perfect. OptiPath allows you to choose not just one or the other (gradualness or unimodality) but there is also the option of optimizing a combination of the two.
To optimize either unimodality or gradualness we need objective measures of each. To do that we have developed indices of each. They are mathematically derived and depend only on the data, not on a user's assumptions or techinque.
The unimodal index is a measure of the unimodality of a seriation or an ordered sequence of numbers. The unimodal index is scaled from -1 to 1. If each feature's data values were plotted against their assigned dates, a graph showing a single peak would be perfectly unimodal and have a Unimodal Index of 1. A graph with a single valley would be perfectly anti-unimodal and would have a Unimodal Index of -1. A random ordering of the data would have an expected Unimodal Index of 0. The overall Unimodal Index for the seriation is the weighted average (using the Weights in the Features table) of the individual feature indices.
The unimodal index was developed by the authors in a paper in preparation for submission to an academic journal.