Optimal path is a seriation methodology used in OptiPath and described in a paper by Brett Shepardson and Fred Shepardson which is being prepared for publication. The OptiPath software implements Shortest Path seriation described in the same paper. OptiPath also includes additional traditional seriation techniques such as Occurrence seriation, Nominal seriation, Discrete seriation and Frequency seriation. All of these take advantage of OptiPath's heuristic optimization algorithms. There is also an option to build your own Custom seriation technique using OptiPath's algorithms. We actually recommend the Custom approach (if you don't want to use the Optimal Path technique). The seriation technique can be set in the Seriations table.
The goal of seriation is to determine an ordering of a number of items (artifacts or assemblages) that replicates as closely as possible the historical order of events they represent. Seriation relies on the assumption that the artifacts to be seriated share characteristics or features (attributes or styles) whose measures evolve in a predictable fashion over time. The ordering of artifacts that best conforms to the pattern of that prediction for all features and all artifacts is considered to be the optimal seriation.
There are many predictions that may be made and OptiPath allows users a choice among a few, represented by objectives available in the Seriations table and on the Seriate menu. Given an objective, OptiPath seeks the seriation that optimizes that objective. Most of the predictions about the evolution of features or styles used in seriation boil down to two broad categories: unimodality and gradual change of the features involved. It can be shown that these two are often equivalent (paper in preparation by the authors). OptiPath provides five objectives to choose from: maximize unimodality and four others that all minimize some aspect of the rate of change from one item to the next.
Optimal Path Seriation is a mathematically based seriation methodology which considers items (artifacts or assemblages) to be seriated to be defined by the features (attributes or styles) they have in common. Each feature is considered a separate dimension and the values of the n features for an item determine a point in n-dimensional feature space. A seriation is an ordering of the items which determines a path through these points in feature space. The seriation problem is to find the path that optimizes a given objective. Many objectives have been proposed over the years including unimodularity (battleship shaped curves), uninterrupted occurrence, similarity and gradualness. These objectives have led to differing techniques of seriation including frequency seriation, occurrence seriation, similarity seriation, shortest path seriation and even component analysis. All of them, however, can be considered special cases of optimal path seriation.
Shortest Path seriation is a special case of optimal path seriation. Each item in a seriation is defined by its feature values which determine a unique point in feature space. A seriation determines a path connecting these points (items) in feature space. The distance from one point to the next in the seriation is a measure of the change in features from one item to the next. The path with the least overall change will be the shortest path through all the points. The ordering of artifacts that produces the most gradual evolution of all features for all artifacts over a given time interval is the shortest path. This is appropriate when the user has not restricted the dates on any individual item. When dates on individual items are restricted, an alternative objective, such as minimizing the average or maximum rate of change, is more appropriate. An advantage of shortest path seriation is that it can work with object level data. That is, it can work with objective measurements of individual features of individual items, rather than with the often subjective assignment of styles and collections (assemblages).
Optimal path seriation is not a specific technique; it is a methodology which embraces all seriation techniques (every seriation determines a path through feature space). They all have in common that they are seeking the path through the items in feature space that minimizes a chosen objective. It is possible to conceive of objectives in addition to the ones included in OptiPath (for example, the objectives used in component analysis). Although most traditional seriation techniques maximize unimodality rather than maximize gradualness, the two are often the same (for example, occurrence seriation) (paper in preparation by the authors).