A seriation involves a number of items (artifacts or assemblages) and a number of feaures. Mathematically, each feature can be considered as a separate dimension. Each item 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 is the shortest path.
Metrics are protocols or functions for measuring "distance" between artifacts. Choosing a proper metric can be important in getting a good seriation. OptiPath provides three metrics. It is possible to use different metrics on different features. Metrics can be assigned in the Features table. Right clicking on the column brings up a popup menu that allows you to set all features with one click.
Euclidean Distance - a distance function (metric) where the distance between two items (artifacts) is the square root of the sum of the squared differences in all of the dimensions (features) in which the items differ. This is the normal everyday "as the crow flies" way of computing distances that we are all used to.
Manhattan Distance - a distance function (metric) where the distance between two items (artifacts) is the sum of the absolute values of the differences in all of the dimensions (features) in which the items differ. This is the way we might think of distance in a city where we are constrained to travel along streets and avenues.
Hamming Distance - a distace function (metric) where the distance between two items (artifacts) is the number of dimensions (features) in which the items differ.