# lakhesis: Consensus Seriation for Binary Data

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

In brief, 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. In ecology, the distribution of a species may occur according to a preferred environmental condition that diminishes as that environment changes. There are a number of R functions and packages (especially seriation and vegan) that provide 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 for seriation. Moreover, not all “incidence matrices” (the matrix of 0/1s that record the joint incidence or occurrence for a row-column pairing) will necessarily be well seriated. The selection of row and column elements in the input is accordingly an intrinsic part of the task of seriation. In this respect, lakhesis seeks to complement existing methods in R, by focusing on binary data. It uses correspondence analysis, a mainstay technique for seriation, which is then fit to a reference curve that represents “ideally” seriated data. Multiple seriations can be run on partial subsets of the initial incidence matrix, which are then recompiled into a single consensus seriation. Critical measures are also provided.

While command line functions can be run in R, the functionality of lakhesis is primarily achieved via the Lakhesis Calculator, a graphical platform in shiny that enables investigators to explore datasets for potential seriated sequences, select them, and then harmonize them into a single consensus seriation. The four panels in the calculator include the following:

• Seriation Explorer (Top left) Displays the correspondence analysis of a dataset which has been fit to the curve an “ideal” seriation. Two plots are available, the biplot of the row and column CA scores as they have been fit to an ideally seriated curve, and a plot showing the orthogonal projection of the row and column scores as they have been fit to the reference curve. Selections can be made on either the biplot or the reference plot.
• Consensus Seriation (Top right) 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 which are harmonized via PCA, separately on row and column elements. The seriated incidence matrix is also displayed in this panel.
• Criteria (Bottom left) 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. Concentration expresses how well seriated the strand is with respect to both row and column values. 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 (Bottom right) Temporarily suppress row or column values from correspondence analysis, including recomputing the seriations from previously selected strands. 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 with 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.
• Recompute 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.curve() performs this task.
• Save Selection as Strand Record the displayed plot as a partial seriation, or “strand” (i.e., partial with respect to the initial data). Strands are sequenced according to their fit onto a reference curve which projects a sequence of ideally seriated data in the same dimensional space.
• Lakhesize Strands Constructs a consensus seriation of the selected strands using an iterative process of orthogonal and linear regression of partial rankings, with PCA to harmonize sequences. Results are displayed in the Consensus Seriation panel, which displays the PCA biplot of the row and column consensus seriations separately. The matrix plot displays the incidence matrix of the resulting consensus seriation, with its coefficient of concentration. The agreement of the seriation in each strand with that of the consensus seriation as well as its concentration coefficient is displayed in the Criteria 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 Criteria panel. The function element.eval() performs this task.
• Export Data Will download results in a single .rds file, which is a list containing the following objects:
• results The results of lakhesize(), itself a list which contains the consensus seriation, the row and column PCA, and coefficients of agreement and concentration.
• strands The strands selected to produce results.
• im.seriated The seriated incidence matrix (this matrix only includes row and column elements selected in the strands, not all rows and columns of the initial dataset).

## 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") 

## Usage

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

library(lakhesis)
LC()

Note that in uploading a csv file for analysis inside the Lakhesis Calculator, the file should consist of just two columms without headers. 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()).

## Bibliography

Hahsler M, Hornik K, Buchcta C (2008). “Getting Things in Order: An Introduction to the R Package seriation.” Journal of Statistical Software, 25, 1-34. doi:10.18637/jss.v025.i03.

Ihm P (2005). “A Contribution to the History of Seriation in Archaeology.” In Weihs C, Gaul W (eds.), Classification - The Ubiquitous Challenge, 307-16. Springer, Berlin.

Nenadic O, Greenacre MJ (2007). “Correspondence Analysis in R, with Two- and Three-dimensional Graphics: The ca Package.” Journal of Statistical Software, 20, 1-13. doi:10.18637/jss.v020.i03.

ter Braak CJF, Looman, CWN. (1986). “Weighted Averaging, Logistic Regression and the Gaussian Response Model.” Vegetatio 65, 3-11. doi:10.1007/BF00032121.