Seriation Frequency Ordering Tool

Produce deterministic type-frequency centroid seriation on a supplied type axis, input order breaking ties; not an optimal unimodal or independently dated ordering.

Description

Frequency-centroid seriation orders assemblages along a supplied type axis.

Frequency-centroid seriation orders assemblages along a supplied type axis. The axis is an explicit analytical choice and does not itself establish chronological age.^[1]

Produce deterministic type-frequency centroid seriation on a supplied type axis, input order breaking ties; not an optimal unimodal or independently dated ordering.

When to use Seriation Frequency Ordering Tool

Use this tool to produce deterministic type-frequency centroid seriation on a supplied type axis, input order breaking ties; not an optimal unimodal or independently dated ordering.

Prepare the artifact, site or survey measurements and any independently established calibration or model choices. Keep paired observations aligned and confirm units and coordinate conventions.

How to use Seriation Frequency Ordering Tool and understand its results

Prepare the artifact, site or survey measurements and any independently established calibration or model choices. Keep paired observations aligned and confirm units and coordinate conventions.
Enter assemblageTypeCounts, typeAxisCoordinates, assemblageIds using the field table and calculation rules, then run the tool.
Read frequencyCentroidCoordinates, orderedAssemblageIds. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
assemblageTypeCounts	Assemblage type counts	list of list of number	Required
typeAxisCoordinates	Type axis coordinates	list of number	Required
assemblageIds	Assemblage ids	list of number	Required

Supply a nonempty rectangular matrix of nonnegative integer counts, 1–128 distinct nonnegative integer assemblage IDs and one nonnegative strictly increasing type coordinate per column. There must be at least two types and a positive total in every assemblage. Return centroids and IDs ordered by centroid, breaking ties in original order.

Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.

centroid_i = Σ(count_ij axis_j)/Σcount_ij; order by increasing centroid then original position

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
frequencyCentroidCoordinates	Frequency centroid coordinates	list of number
orderedAssemblageIds	Ordered assemblage ids	list of number

json

{
  "input": {
    "assemblageTypeCounts": [
      [
        10,
        0,
        0
      ],
      [
        0,
        0,
        10
      ],
      [
        0,
        10,
        0
      ]
    ],
    "typeAxisCoordinates": [
      0,
      1,
      2
    ],
    "assemblageIds": [
      10,
      20,
      30
    ]
  },
  "output": {
    "frequencyCentroidCoordinates": [
      0,
      2,
      1
    ],
    "orderedAssemblageIds": [
      10,
      30,
      20
    ]
  }
}

Limitations and assumptions

This deterministic heuristic does not find an optimal unimodal seriation or independently date assemblages. Changing the supplied type axis changes the ordering.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other numeric lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Type Frequency Percent Per Phase: Normalize classified ceramic types within each phase and report excluded unclassified coverage on original denominators; not pooled across phases or a forced chronological classifier. For a complementary task, use Battleship Curve Fit Checker: Check each type-frequency column in a supplied ordering for nondecreasing-then-nonincreasing battleship shape under caller tolerance; monotone and plateau series are accepted, not proof of chronology.

References

Seriation Frequency Ordering Tool — tool.io

Similar or alternative tools

Type Frequency Percent Per Phase
Normalize classified ceramic types within each phase and report excluded unclassified coverage on original denominators; not pooled across phases or a forced chronological classifier.
Battleship Curve Fit Checker
Check each type-frequency column in a supplied ordering for nondecreasing-then-nonincreasing battleship shape under caller tolerance; monotone and plateau series are accepted, not proof of chronology.