lakhesis: Consensus Seriation for Binary Data

The R package lakhesis provides an interactive platform and critical measures for seriating binary data matrices through the exploration, selection, and consensus of partially seriated sequences.

Seriation (sequencing, ordination) involves putting a set of things in an optimal order. In archaeology, seriation can be used to establish a chronological order of contexts and find-types on the basis of their similarity, i.e, that things come into and go out of fashion with a peak moment of popularity (Ihm 2005). In ecology, the distribution of a species may occur according to a preferred environmental condition that diminishes as that environment changes (ter Braak and Looman 1986). There are a number of R functions and packages, especially seriation (Hahsler, Hornik, and Buchcta 2008) and vegan (Oksanen et al. 2024) that provide the means to seriate or ordinate matrices, especially for frequency or count data. While binary (presence/absence) data are often viewed as a reductive case of frequency data, they can also present their own challenges. Moreover, not all incidence matrices (the matrix of 0/1s that record the joint incidence or occurrence for a row-column pairing) will be well seriated. The selection of which row and column elements to inlcude in the input is accordingly an intrinsic part of the task of seriation. In this respect, lakhesis seeks to complement existing methods in R, focusing on binary data, by providing an interactive, graphical means of selecting seriated sequences. It relies correspondence analysis (CA), a mainstay technique for seriation, and offers a method of Procrustes-fit CA to align scores with an ideal reference curve. Multiple seriations can be rerun on partial subsets, called “strands,” of the initial incidence matrix, which are then recompiled into a single consensus seriation using an optimality criterion. The process of harmonizing different strands of sequential elements via iterative linear regression is called a lakhesis technique, after the fate from ancient Greek mythology who measured the strand of one’s life. The package relies on Rcpp and RcppArmadillo (Eddelbuettel and Sanderson 2014; Eddelbuettel and Balamuta 2018).

While command line functions can be run in R, the functionality of lakhesis is primarily achieved via the Lakhesis Calculator, a graphical interface in shiny (Chang et al. 2024) that enables investigators to explore datasets, select strands, and harmonize them into a single consensus seriation. Panels in the calculator include:

• Seriation Explorer displays the correspondence analysis plot of a datase, including Procrustes-fit CA (both as they have been fit to the curve and their orthogonal projection along the curve). Selections can be made on any plot.
  • Map options. Users can choose either a symmetric or an asymmetric CA plot.
• Save Strand records the displayed plot as a partial seriation, or “strand” (i.e., partial with respect to the initial data matrix).
  • Strands can be sequenced according to different projections:
    • CA1 / CA2 Projection of scores along the first or second principal CA axis.
    • Procrustes1 / Procrustes2 Projection of scores along the first or second axis after Procrustes fitting.
    • Curve Projection along the reference curve of an ideal seriation.
  • Lakhesize Produce a consensus seriation (must have saved at least two strands). Constructs a consensus seriation of the selected strands using an iterative process of linear regression of partial rankings in an agglomerative fashion. The matrix plot displays the incidence matrix of the resulting consensus seriation, with optimality criteria. The agreement of the seriation in each strand with that of the consensus seriation as well as its criterion is displayed in the Diganostics panel. The function lakhesize() performs this task.
  • Run Deviance Test performs a goodness-of-fit test using deviance, treating the distribution of the row and column incidences with a quadratic-logistic model. The largest $p$ values of the row and column elements is contained in the Diganostics panel. The function element_eval() performs this task.
• Consensus Seriation displays the results of harmonizing selected partial seriations, which have been identified as “strands.” The process of deriving a consensus seriation entails a process of iterative regressions on partially seriated sequences, optimized using the concentration measure. The seriated incidence matrix is also displayed in this panel.
• Diagnostics show critical coefficients to determine whether discordant strands should be removed and/or row or column elements should be suppressed from consideration.
  • Agreement expresses whether a strand agrees with consensus seriation.
  • Criteria expresses how well seriated the strand is. Options for optimality criteria are those which are used in Lakhesis, comprising:
    • Squared correlation coefficient (cor_sq).
    • Weighted row-column concentration (conc_wrc).
  • Tabs marked Deviance report on the goodness-of-fit of row and column elements in the consensus seriation using deviance with a quadratic-logistic model. Higher $p$ values will indicate poorer fit for a particular row or column element.
• Modify temporarily suppress row or column elements from correspondence analysis. Strands which have low agreement or high concentration may also be deleted in this panel.

The sidebar contains the following commands:

• Choose CSV – data must be without a header in a two-column “long” format of occurring pairs of row and column elements, where the first column contains a row element and the second column contains a column element of the incidence matrix.
• Reinitialize resets the plots to their original, starting condition.
• Replot with Selection – upon the selection of row and column points from the Seriation Explorer panel, this command will perform and fit CA only on the selection. To return to the initial dataset, press the Reinitialize button. The function ca_procrustes_ser() performs this task.
• Export Data will download results in a single .rds file, which is a list class object containing the following:
  • consensus The results of lakhesize(), a lakhesis class object containing row and column consensus seriations, coefficients of agreement and concentration, and the seriated incidence matrix.
  • strands The strands selected to produce consensus.

Installation

To obtain the current development version of lakhesis from GitHub, install from GitHub in the R command line with:

library(devtools)
install_github("scollinselliott/lakhesis", dependencies = TRUE, build_vignettes = TRUE) 

Usage

To start the Lakhesis Calculator, execute the function LC():

library(lakhesis)
LC()

In uploading a csv file for analysis inside the Lakhesis Calculator, the incidence matrix should be in “long” format. That is, the file should consist of just two columns without headers, in which each row represents the incidence of a row-column pair. For example, an incidence matrix of

$$\begin{array} , & C_1 & C_2 & C_3 \\ R_1 & 1 & 0 & 0 \\ R_2 & 0 & 1 & 1 \\ R_3 & 0 & 0 & 1 \end{array}$$

will have a corresponding long format of

R1, C1
R2, C2 
R2, C3 
R3, C3

If characters are not displaying properly in the plot, make sure to check font encoding (UTF-8 is recommended).

Row and column elements must be unique (a row element cannot have the same name as a column element).

The Lakhesis Calculator enables the temporary suppression of row or column elements from the plots, with zero rows/columns automatically removed. As such, unexpected results may be elicited if key elements are suppressed. All elements can easily be re-added and the starting incidence matrix re-initialized.

Incidence Matrices

If data are already in incidence matrix format, the im_long() function in lakhesis can be used to convert an incidence matrix to be exported into the necessary long format, using the write.table() function to export (see documentation on im_long()):

# x is a matrix of 0/1 values with unique row/column names
y <- im_long(x)
write.table(y, file = "im.csv", sep = ",")

The file im.csv can then be loaded into the Lakhesis Calculator.

Consensus Seriations

Establishing a consensus seriation via a lakhesis technique can be done in the calculator, but if one has seriations, whether derived by Procustes-fit CA or by another method, one can perform a consensus seriation in the console by creating a strands object and then executing the lakhesize() function.

The console can also be used to perform consensus seriations. For example, using the built-in selection of three strands in the data object qf_strands, a consensus seriation is performed using the lakhesize() function:

x <- lakhesize(qf_strands)
summary(x)

The vignette “A Guide to Lakhesis” contains more information on usage.

Citation

To cite lakhesis, please use the following reference:

• Collins-Elliott, S.A. 2026. “Lakhesis: Consensus Seriation via Iterative Regression of Partial Rankings for Binary Data.” Journal of Applied Statistics. doi:10.1080/02664763.2026.2672564.

References