Art historians are well aware that styles tend to change gradually over time. Although this may be a self-fulfilling prophecy - drastic and sudden changes are often simply labeled as new styles - it is often true enough that it can be used as a criterion for successful seriation. An arrangement of items that makes the overall change in style as gradual as possible can be considered a good guess of their chronological ordering.
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, followed by gradual stylistic as well as functional refinements and adustments.
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 gradualness or unimodality 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 gradual index is a measure of the gradualness of a seriation or an ordered sequence of numbers. The gradual index is scaled from -1 to 1. A seriation with a Gradual Index of 1 cannot be made more gradual by reordering. A seriation with a Gradual Index of -1 could not be less gradual. The overall Gradual 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.