seriate_* computes a permutation order for rows and/or columns.

permute rearranges a data matrix according to a permutation order.

get_order returns the seriation order for rows and columns.

seriate_rank(object, ...)

seriate_correspondence(object, subset, ...)

permute(object, order, ...)

get_order(object)

# S4 method for PermutationOrder
get_order(object)

# S4 method for CountMatrix,PermutationOrder
permute(object, order)

# S4 method for IncidenceMatrix,PermutationOrder
permute(object, order)

# S4 method for CountMatrix,missing
seriate_correspondence(object, margin = c(1, 2), ...)

# S4 method for IncidenceMatrix,missing
seriate_correspondence(object, margin = c(1, 2), ...)

# S4 method for CountMatrix,BootCA
seriate_correspondence(object, subset, margin = c(1, 2), ...)

# S4 method for CountMatrix
seriate_rank(object, EPPM = FALSE, margin = c(1, 2), stop = 100)

# S4 method for IncidenceMatrix
seriate_rank(object, margin = c(1, 2), stop = 100)

## Arguments

object An $$m \times p$$ data matrix (typically an object of class CountMatrix or IncidenceMatrix. Further arguments to be passed to internal methods. A BootCA object giving the subset of object to be used. A PermutationOrder object giving the permutation order for rows and columns. A numeric vector giving the subscripts which the rearrangement will be applied over: 1 indicates rows, 2 indicates columns, c(1, 2) indicates rows then columns, c(2, 1) indicates columns then rows. A logical scalar: should the seriation be computed on EPPM instead of raw data? An integer giving the stopping rule (i.e. maximum number of iterations) to avoid infinite loop.

## Value

seriate_* returns a PermutationOrder object.

permute returns either a CountMatrix or an IncidenceMatrix (the same as object).

## Seriation

The matrix seriation problem in archaeology is based on three conditions and two assumptions, which Dunell (1970) summarizes as follows.

The homogeneity conditions state that all the groups included in a seriation must:

1. Be of comparable duration.

2. Belong to the same cultural tradition.

3. Come from the same local area.

The mathematical assumptions state that the distribution of any historical or temporal class:

1. Is continuous through time.

2. Exhibits the form of a unimodal curve.

Theses assumptions create a distributional model and ordering is accomplished by arranging the matrix so that the class distributions approximate the required pattern. The resulting order is inferred to be chronological.

The following seriation methods are available:

correspondence

Correspondence analysis-based seriation. Correspondence analysis (CA) is an effective method for the seriation of archaeological assemblages. The order of the rows and columns is given by the coordinates along one dimension of the CA space, assumed to account for temporal variation. The direction of temporal change within the correspondence analysis space is arbitrary: additional information is needed to determine the actual order in time.

reciprocal

Reciprocal ranking seriation. These procedures iteratively rearrange rows and/or columns according to their weighted rank in the data matrix until convergence. Note that this procedure could enter into an infinite loop. If no convergence is reached before the maximum number of iterations, it stops with a warning.

## Correspondence Analysis Refining

refine_ca allows to identify samples that are subject to sampling error or samples that have underlying structural relationships and might be influencing the ordering along the CA space.

This relies on a partial bootstrap approach to CA-based seriation where each sample is replicated n times. The maximum dimension length of the convex hull around the sample point cloud allows to remove samples for a given cutoff value.

According to Peebles and Schachner (2012), "[this] point removal procedure [results in] a reduced dataset where the position of individuals within the CA are highly stable and which produces an ordering consistent with the assumptions of frequency seriation."

If the results of refine is used as an input argument in seriate, a correspondence analysis is performed on the subset of object which matches the samples to be kept. Then excluded samples are projected onto the dimensions of the CA coordinate space using the row transition formulae. Finally, row coordinates onto the first dimension give the seriation order.

## References

Desachy, B. (2004). Le sériographe EPPM: un outil informatisé de sériation graphique pour tableaux de comptages. Revue archéologique de Picardie, 3(1), 39-56. DOI: 10.3406/pica.2004.2396.

Dunnell, R. C. (1970). Seriation Method and Its Evaluation. American Antiquity, 35(03), 305-319. DOI: 10.2307/278341.

Ihm, P. (2005). A Contribution to the History of Seriation in Archaeology. In C. Weihs & W. Gaul (Eds.), Classification: The Ubiquitous Challenge. Berlin Heidelberg: Springer, p. 307-316. DOI: 10.1007/3-540-28084-7_34.

Peeples, M. A., & Schachner, G. (2012). Refining correspondence analysis-based ceramic seriation of regional data sets. Journal of Archaeological Science, 39(8), 2818-2827. DOI: 10.1016/j.jas.2012.04.040.

N. Frerebeau

## Examples

## Replicates Desachy 2004 results
## Coerce dataset to abundance matrix
compiegne_count <- as_count(compiegne)

## Get seriation order for columns on EPPM using the reciprocal averaging method
## Expected column order: N, A, C, K, P, L, B, E, I, M, D, G, O, J, F, H
(compiegne_indices <- seriate_rank(compiegne_count, EPPM = TRUE, margin = 2))#> <PermutationOrder>
#> Permutation order for matrix seriation:
#> - Row order: 1 2 3 4 5...
#> - Column order: 14 1 3 11 16 12 2 5 9 13 4 7 15 10 6 8...
#> - Method: reciprocal ranking
## Permute columns
compiegne_new <- permute(compiegne_count, compiegne_indices)

## Plot new matrix
plot_ford(compiegne_new, EPPM = FALSE)
## See the vignette:
# \donttest{
utils::vignette("seriation", package = "tabula")#> Warning: vignette ‘seriation’ not found# }