Epigraphic Networks using R¶
This post is about Epigraphic Networks based on measures of similarity of artefact assemblages and geographic proximity.
Measuring similarity of artefact assemblages and geographic proximity¶
To measure similarity of artefact assemblages and geographic proximity, [R] package
sdam provides the function simil(), which allows assesing similarity by comparing
columns representing –in this case– different attributes for epigraphic inscriptions.
Function usage¶
-
simil()¶
# arguments supported (currently)
R> simil(x, vars, type=c("sm","ja","ra"), uniq, diag.incl)
Which returns a square and valued matrix with similarity meassures based on simple match among variables.
Parameters¶
Formal arguments of simil() are:
x:
a data frame with an id column
vars:
(vector) column(s) in
xrepresenting attributes or variablestype:
whether the similarity measure is by simple matching
"sm", Jaccard"ja", or Rand index"ra"
Optional parameters¶
uniq:
(optional and logical) only unique elements?
diag.incl:
include entries in the matrix diagonal?
Note that at this point the ID column represents the labels of the nodes. In
case that an ID column does not exists, then the first column is taken
as id provided that there are not duplicated entry names in x.
Similarity measures¶
For cases where duplication does not matter, a good option is Jaccard similarity whose index is the proportion of the number of observations in both sets to the number in either set. This index is formally expressed as \(J(A,B)= \left| A \cap B \right| / \left| A \cup B \right|\). (Otherwise
Todo
Rand index plain and corrected by chance.
Structures of similarity in the EDH dataset¶
We illustrate the use of the simil() function with ancient inscriptions from
the Epigraphic Database Heidelberg, and we first follow the entry Epigraphic Database Heidelberg
to see how accessing the EDH dataset using sdam [R] package.
# devtools::install_github("mplex/cedhar", subdir="pkg/sdam")
# devtools::install_github("sdam-au/sdam")
R> library("sdam")
# load the EDH data from this package
R> data("EDH")
Epigraphic network data¶
Creating epigraphic network data list with variables measures of similarity of artefact assemblages and geographic proximity.
For example, a list object named epinet with the ID of the inscription plus seven other characteristics from
the EDH dataset is produced by edhw().
# choose variables of interest and record it as a data frame
R> epinet <- edhw(vars=c("type_of_inscription", "language", "material", "country",
"findspot_ancient", "not_after", "not_before"), as="df")
Take a look at this data:
# first eight entries in the data frame
R> head(epinet, 8)
# id type_of_inscription not_before not_after material language findspot_ancient country
#1 HD000001 epitaph 0071 0130 Marmor, geädert / farbig Latin Cumae, bei Italy
#2 HD000002 epitaph 0051 0200 marble: rocks - metamorphic rocks Latin Roma Italy
#3 HD000003 honorific inscription 0131 0170 marble: rocks - metamorphic rocks Latin <NA> Spain
#4 HD000004 votive inscription 0151 0200 limestone: rocks - clastic sediments Latin Ipolcobulcula Spain
#5 HD000005 epitaph 0001 0200 <NA> Latin Roma Italy
#6 HD000006 epitaph 0071 0150 limestone: rocks - clastic sediments Latin Sabora, bei Spain
#7 HD000007 epitaph -0100 -0051 travertine: rocks - chemische Sedimente Latin Roma Italy
#8 HD000008 epitaph 0101 0200 marble: rocks - metamorphic rocks Latin Roma? Italy
For instance, entry 8 indicates that this ancient findspot is uncertain.
Function cln()
R> epinet2 <- cln(epinet)
And then we take a look at epinet2 again, and we assume the questioned entries.
# first eight entries in the new data frame
R> head(epinet2, 8)
# id type_of_inscription not_before not_after material language findspot_ancient country
#1 HD000001 epitaph 0071 0130 Marmor, geädert / farbig Latin Cumae, bei Italy
#2 HD000002 epitaph 0051 0200 marble: rocks - metamorphic rocks Latin Roma Italy
#3 HD000003 honorific inscription 0131 0170 marble: rocks - metamorphic rocks Latin NA Spain
#4 HD000004 votive inscription 0151 0200 limestone: rocks - clastic sediments Latin Ipolcobulcula Spain
#5 HD000005 epitaph 0001 0200 NA Latin Roma Italy
#6 HD000006 epitaph 0071 0150 limestone: rocks - clastic sediments Latin Sabora, bei Spain
#7 HD000007 epitaph -0100 -0051 travertine: rocks - chemische Sedimente Latin Roma Italy
#8 HD000008 epitaph 0101 0200 marble: rocks - metamorphic rocks Latin Roma Italy
The countries in epinet2 are:
# need first to unlist the component object
R> unique(unlist(epinet2$country))
# [1] "Italy" "Spain" "United Kingdom" "Portugal"
# [5] "France" "Libyan Arab Jamahiriya" "Germany" "Hungary"
# [9] "Austria" "Bulgaria" "Bosnia and Herzegovina" "Montenegro"
#[13] "Netherlands" "Tunisia" "Romania" "Algeria"
#[17] "Jordan" NA "Croatia" "Switzerland"
#[21] "Belgium" "Albania" "Serbia" "Egypt"
#[25] "Syrian Arab Republic" "Morocco" "Turkey" "Lebanon"
#[29] "Kosovo" "Macedonia" "Slovakia" "Greece"
#[33] "Slovenia" "Iraq" "Israel" "unknown"
#[37] "Vatican City State" "Ukraine" "Cyprus" "Yemen"
#[41] "Sudan" "Luxembourg" "Czech Republic" "Malta"
#[45] "Poland" "Armenia" "Monaco" "Azerbaijan"
#[49] "Sweden" "Denmark" "Moldova" "Saudi Arabia"
#[53] "Uzbekistan" "Liechtenstein" "Georgia"
Subsetting the data¶
For example, we use the base [R] function subset() to substract epigraphic material in “Greek-Latin” from Egypt.
# a subset of a subset
R> subset(subset(epinet2, country=="Egypt"), language=="Greek-Latin")
# id type_of_inscription not_before not_after material language findspot_ancient country
#2003 HD002003 identification inscription -0116 NA NA Greek-Latin Philae Egypt
#23091 HD023091 NA 0145 NA Holz, Wachs Greek-Latin NA Egypt
#23138 HD023138 votive inscription -0029 NA NA Greek-Latin Syene Egypt
#27345 HD023091 NA 0145 NA Holz, Wachs Greek-Latin NA Egypt
#27351 HD023138 votive inscription -0029 NA NA Greek-Latin Syene Egypt
#32500 HD030147 NA 0010 0011 NA Greek-Latin Alexandria Egypt
#34436 HD032079 NA NA NA NA Greek-Latin Schedia Egypt
#51198 HD048625 identification inscription 0006 NA NA Greek-Latin Berenice Egypt
#54194 HD051485 NA 0155 0225 NA Greek-Latin Alexandria Egypt
#58318 HD055974 NA 0001 0200 NA Greek-Latin Berenice Egypt
#70110 HD067781 public legal inscription -0037 -0030 NA Greek-Latin Leontopolis Egypt
Ranked frequency¶
A ranked frequency of different kinds of inscriptions including missing information is computed as follows:
R> as.data.frame(sort(table(unlist(epinet2$type_of_inscription), useNA="ifany"), decreasing=TRUE))
# Var1 Freq
#1 epitaph 28522
#2 <NA> 22222
#3 votive inscription 14683
#4 owner/artist inscription 5164
#5 honorific inscription 4338
#6 building/dedicatory inscription 3450
#7 mile-/leaguestone 1766
#8 identification inscription 1600
#9 acclamation 525
#10 military diploma 507
#11 list 363
#12 defixio 311
#13 label 287
#14 boundary inscription 258
#15 public legal inscription 256
#16 elogium 154
#17 seat inscription 88
#18 letter 81
#19 prayer 57
#20 private legal inscription 37
#21 assignation inscription 15
#22 calendar 14
#23 adnuntiatio 3
That is, a decreasing sorted table given as data frame of the type_of_inscription
component of epinet2. Since epinet2 is a list object, it is required to “unlist” the
data object to produce a table with the frequencies.
Example: Similarity among Egyptian epigraphs¶
We can compute similarity among Egyptian epigraphs with function simil().
For this, we look at the attribute types stored in different columns.
R> as.data.frame(colnames(epinet2))
# colnames(epinet2)
#1 id
#2 type_of_inscription
#3 not_before
#4 not_after
#5 material
#6 language
#7 findspot_ancient
#8 country
For instance, in case we want to choose "type_of_inscription", "material", and "findspot_ancient",
these correspond to columns 8, 5, and 3.
Similarities among Egyptian epigraphs by simple matching or default type "sm" with the above attribute variables are recorded in
a matrix object named epEgs where the ID in epinet2 corresponds to the dimensions labels.
# similarity function on the subset for the three variables
R> epEgs <- simil(subset(epinet2, country=="Egypt"), vars=c(8,5,6))
# number of rows in this square matrix
R> nrow(epEgs)
#[1] 170
And then we look at some cell entries
# similarity between the first six inscriptions in 'epEgs'
R> epEgs[1:6, 1:6]
# HD000744 HD002009 HD003137 HD006817 HD006820 HD008184
#HD000744 0 1 1 0 0 0
#HD002009 1 0 0 0 0 0
#HD003137 1 0 0 0 0 0
#HD006817 0 0 0 0 1 0
#HD006820 0 0 0 1 0 0
#HD008184 0 0 0 0 0 0
where we observe six records of a single similarity.
Plot similarities¶
To produce a graph for the similarity among Egyptian epigraphs, we employ the [R] package multigraph that
depends on multiplex.
# define scope for the graph
R> scp <- list(directed=FALSE, valued=TRUE, ecol=8, pos=0)
# load "multigraph" where "multiplex" gets invoked
R> library(multigraph)
# plot similarity graph of 'epEgs' for the chosen variables
R> multigraph(epEgs, scope=scp, layout="force", maxiter=70, main="Similarity among Egyptian epigraphs")
