Where does seriation collide?

In archaeology, seriation is a relative-dating method that arranges assemblages or artifact types into a chronological order from their changing frequencies or shared traits, on the assumption that styles rise, peak, and fade over time. Flinders Petrie's 1899 Sequences in prehistoric remains introduced the technique as sequence dating, ordering Egyptian predynastic graves by the pottery types they contained before any absolute dates were available. The referent is a one-dimensional time ordering recovered from undated material, and it is the historical root from which later matrix-reordering methods were generalized. It shares only its name with a child's growing ability to order objects by size.[1]

Unit

The inferred chronological ordering of undated assemblages or types

Recovery means

Not applicable

Measured by

Derived by ordering units so that each type's frequencies form a single peak (unimodal 'battleship' curves), historically by hand and later by matrix methods

In Piaget's developmental psychology, seriation is the cognitive ability to order a set of objects along a quantitative dimension such as length or size, and to insert new items into the correct place in that order. Piaget's The child's conception of number treats this operation as a marker of concrete-operational thinking, emerging when a child grasps that an item can be at once longer than those before it and shorter than those after. The referent is a mental operation in a developing person, assessed by having children arrange sticks or build staircases, not a chronology of objects or a reordered matrix. It carries the same word as archaeological and statistical seriation but names a stage of reasoning rather than a method.[2]

Unit

A child's capacity to construct and maintain a correct ordinal arrangement

Recovery means

Not applicable

Measured by

Assessed with ordering tasks (e.g., arranging sticks by length and inserting new items) scored for systematic, transitive ordering

In statistics and data mining, seriation is the problem of finding an ordering of the rows and columns of a data or similarity matrix that places similar elements near one another, revealing latent one-dimensional structure or gradients. Liiv's 2010 Seriation and matrix reordering methods: An historical overview traces the family of algorithms that optimize such an ordering across archaeology, ecology, and exploratory data analysis. The referent is a combinatorial ordering problem over a matrix, solved to maximize an arrangement criterion, and the archaeological case is one special application of it. It is unrelated to a child's reasoning, sharing only the term for putting things in a meaningful sequence.[3]

Unit

The permutation of rows and columns that optimizes a matrix-ordering criterion

Recovery means

Not applicable

Measured by

Evaluated by objective functions such as the Robinson form, anti-Robinson loss, or the bandwidth of nonzero entries after reordering