The arkhe package provides a set of S4 classes for archaeological data matrices. These new classes represent different special types of matrix.
CountMatrix
represents absolute frequency data,AbundanceMatrix
represents relative frequency data,OccurrenceMatrix
represents a co-occurrence matrix,SimilarityMatrix
represents a (dis)similarity matrix,IncidenceMatrix
represents presence/absence data,StratigraphicMatrix
represents stratigraphic relationships.It assumes that you keep your data tidy: each variable (taxon/type) must be saved in its own column and each observation (assemblage/sample) must be saved in its own row. Note that missing values are not allowed.
The internal structure of S4 classes implemented in arkhe is depicted in the UML class diagram in the following figure.
UML class diagram of the S4 classes structure.
CountMatrix
)We denote the \(m \times p\) count matrix by \(A = \left[ a_{ij} \right] ~\forall i \in \left[ 1,m \right], j \in \left[ 1,p \right]\) with row and column sums:
AbundanceMatrix
)A frequency matrix represents relative abundances.
We denote the \(m \times p\) frequency matrix by \(B = \left[ b_{ij} \right] ~\forall i \in \left[ 1,m \right], j \in \left[ 1,p \right]\) with row and column sums:
OccurrenceMatrix
)A co-occurrence matrix is a symmetric matrix with zeros on its main diagonal, which works out how many times (expressed in percent) each pairs of taxa occur together in at least one sample.
The \(p \times p\) co-occurrence matrix \(D = \left[ d_{i,j} \right] ~\forall i,j \in \left[ 1,p \right]\) is defined over an \(m \times p\) abundance matrix \(A = \left[ a_{x,y} \right] ~\forall x \in \left[ 1,m \right], y \in \left[ 1,p \right]\) as:
\[ d_{i,j} = \sum_{x = 1}^{m} \bigcap_{y = i}^{j} a_{xy} \]
with row and column sums:
Many familiar methods and group generic functions are available for all *Matrix
classes (such as length
, dim
, rowSums
, rowMeans
, sum
, any
, all
…). In addition, all functions that call as.matrix
first on their main argument should work (e. g. apply
).
These new classes are of simple use, on the same way as the base matrix
:
set.seed(12345) ## Create a count data matrix ## Data are rounded to zero decimal places, then coerced with as.integer CountMatrix(data = sample(0:10, 100, TRUE), nrow = 10, ncol = 10) #> <CountMatrix: 10 x 10> #> col1 col2 col3 col4 col5 col6 col7 col8 col9 col10 #> row1 2 6 2 3 9 7 9 3 3 6 #> row2 9 9 8 7 9 10 6 8 9 0 #> row3 7 0 3 10 2 3 6 10 3 2 #> row4 9 7 9 5 2 1 4 0 8 1 #> row5 10 6 6 8 2 2 6 2 1 4 #> row6 7 5 1 4 0 5 9 9 7 9 #> row7 1 0 3 2 9 2 7 6 9 5 #> row8 5 3 10 0 7 6 2 9 0 6 #> row9 10 7 8 0 10 9 4 9 8 8 #> row10 5 9 8 4 8 6 10 6 5 9 ## Create an incidence (presence/absence) matrix ## Data are coerced to logical as by as.logical IncidenceMatrix(data = sample(0:1, 100, TRUE), nrow = 10, ncol = 10) #> <IncidenceMatrix: 10 x 10> #> col1 col2 col3 col4 col5 col6 col7 col8 col9 col10 #> row1 TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE TRUE #> row2 TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE #> row3 TRUE TRUE TRUE FALSE TRUE FALSE TRUE FALSE TRUE TRUE #> row4 TRUE FALSE TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE #> row5 FALSE FALSE TRUE FALSE TRUE TRUE FALSE FALSE TRUE TRUE #> row6 TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE TRUE #> row7 TRUE FALSE TRUE FALSE FALSE TRUE FALSE FALSE TRUE TRUE #> row8 FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE #> row9 FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE #> row10 TRUE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE
Note that an AbundanceMatrix
can only be created by coercion (see below).
arkhe uses coercing mechanisms (with validation methods) for data type conversions:
## Create a count matrix A0 <- matrix(data = sample(0:10, 100, TRUE), nrow = 10, ncol = 10) ## Coerce to absolute frequencies A1 <- as_count(A0) ## Coerce to relative frequencies B <- as_abundance(A1) ## Row sums are internally stored before coercing to a frequency matrix ## (use get_totals() to get these values) ## This allows to restore the source data A2 <- as_count(B) all(A1 == A2) #> [1] TRUE ## Coerce to presence/absence C <- as_incidence(A1) ## Coerce to a co-occurrence matrix D <- as_occurrence(A1)