(Preliminary reports of the excavation: Müller-Wiener (1977) and Müller-Wiener (1979), finds: (Real 1977, 105))

This github repository provides all the original data used in said paper. This document contains all the code used to generate the relevant graphs and findings. It is not intended as an explanation of methodology – as this is already provided in the paper itself – but as additional transparency.

The Data

The table provided in the publication (Steinmann 2020, fig. 16) is available as a .csv-file (in the “data-raw” subdirectory) as well as a Data set that is provided in this package:

library(clayringsmiletus)
data("StackRMiletus")

All measurements were gathered by the author during a research stay in Miletus in 2017, funded by the Research School of the Ruhr-University in Bochum. Subsequent work was accomplished during a stipend of the Gerda Henkel Foundation I received for my PhD project “The Sanctuary of Dionysos in the Sacral Landscape of Miletus” at the Ruhr-University Bochum and since 2020 at the University of Hamburg. The table included the following data (sample of inventoried rings):

	Inv	clay	applications	color_appl	slip	markings	markings_type	height	min_DM	max_DM	width	thickness	shape	fragments
59	MK73.C5.3	reddish yellow	none	NA	none	1	tools	1.80	10.0	12.5	1.25	0.39	straight	1
1	MK75.N16.1	pink	stains	red	beige	0	none	1.30	11.6	14.2	1.30	0.51	straight	9
20	MK75.N16.10	pink	none	NA	none	0	none	1.10	6.8	11.8	2.50	0.34	concave	2
66	MK75.N16.11	pink	none	NA	none	1	Theta	1.30	12.2	15.2	1.50	0.49	straight	1
67	MK75.N16.12	pink	stains	NA	none	1	Theta (half), tools	1.48	14.6	18.0	1.70	0.49	concave	1
14	MK75.N16.2	pink	stains	black	beige	1	tools	1.00	10.0	12.2	1.10	0.50	concave	1
65	MK75.N16.3	pink	none	NA	none	0	none	1.17	11.6	12.4	0.40	0.48	convex	1
9	MK75.N16.4	light reddish brown	none	NA	yellowish	0	none	1.50	11.4	14.6	1.60	0.57	concave	3
13	MK75.N16.5	pink	stains	dark red	none	0	none	1.00	10.0	12.4	1.20	0.44	concave	3
6	MK75.N16.6	light reddish brown	streaks	light red	yellowish	0	none	1.20	11.6	14.8	1.60	0.34	straight	4
2	MK75.N16.7	light reddish brown	stains	dark red	none	0	none	1.30	11.4	13.8	1.20	0.50	straight	3
41	MK75.N16.8	pink	none	NA	none	0	none	1.10	7.0	13.0	3.00	0.35	concave	1
18	MK75.N16.9	reddish yellow	streaks	light red	none	0	none	1.70	6.8	13.2	3.20	0.35	concave	3

Classification of the Milesian Clay Rings

The first step in the paper is to look at the distribution of measurements with a density graph of the numeric variables. Thickness and Height are multiplied by 10 to make the outcome more visible. All measurements are originally in cm.

library(reshape2)
library(ggridges)
library(ggplot2)

StackRMiletus %>%
  transmute(
    thickness_mm = thickness * 10,
    height_mm = height * 10, 
    width_cm = width, 
    min_DM_cm = min_DM, 
    max_DM_cm = max_DM) %>%
  melt() %>%
  ggplot(aes(x = value, y = variable, fill = variable)) + 
  geom_density_ridges(scale = 4, bw = "SJ", alpha = 0.8) +
  scale_fill_manual(values = custom_palette(5)) +
  theme(legend.position = "none", 
        panel.background = element_blank(), 
        axis.title = element_blank()) +
  labs(title = "Numerical variables across all rings")

Clustering with hdbscan

As explained in the paper, hdbscan (McInnes, Healy, and Astels 2017) from the dbscan-package (Hahsler, Piekenbrock, and Doran 2017) is used to cluster the rings according to minimum and maximum diameter. First, let hdbscan identify clusters for the original data:

library(dbscan)
#> 
#> Attaching package: 'dbscan'
#> The following object is masked from 'package:stats':
#> 
#>     as.dendrogram
hdbcluster <- StackRMiletus %>%
  select(min_DM, max_DM) %>%
  hdbscan(minPts = 5)

The outcome (i.e. cluster membership and membership probability) is then added to the original data.frame:

StackRMiletus$HDBScan_Cluster <- as.factor(hdbcluster$cluster)
StackRMiletus$membership_prob <- hdbcluster$membership_prob

And can be visualized using ggplot2, putting the diameters on the x and y axis, displaying cluster membership as point color, membership probability as opacity and shape of the profile as point shape:

Cluster A: 9 rings
Cluster B: 30 rings
Cluster C: 15 rings
noise: 13 rings

Summary Statistics

To generate samples based on the actual data, we need summary statistics first:

datastructure <- data.frame(matrix(ncol = 5, nrow = 4))
colnames(datastructure) <- c("height", "min_DM", "max_DM", 
                             "width", "thickness") 
rownames(datastructure) <- c("range", "mean", "sd", "cv")

for (col in colnames(datastructure)) {
  range <- range(StackRMiletus[, col])
  sd <- sd(StackRMiletus[, col])
  mean <- mean(StackRMiletus[, col])
  datastructure["range", col] <- range[2] - range[1]
  datastructure["mean", col] <- mean
  datastructure["sd", col] <- sd
  datastructure["cv", col] <- sd / mean * 100
}

Which look like this:

	height	min_DM	max_DM	width	thickness
range	1.200	9.000	6.600	3.100	0.260
mean	1.120	10.103	13.234	1.566	0.441
sd	0.248	1.826	1.511	0.750	0.073
cv	22.120	18.070	11.420	47.878	16.570

Testing for Structure Validity

Setup an empty dataframe to record the results of silhouette-tests:

tests_compare <- data.frame(matrix(ncol = 5, nrow = 1000))
colnames(tests_compare) <- c("N", "n_cluster", "avg_sil_width", 
                             "avg_sil_width_without_0", "n_noise")

Based on the info from the summary statistics, the data.frame created above can be filled with 1000 fictional distributions using the mean of the original data and its standard deviation as a basis. First, 3000 fictional distributions will be generated to randomly sample exactly 1000 of them, as sometimes hdbscan may return no clusters and thus the process would produce NA-values, which can be removed beforehand in this way.

library(cluster)
tests_dummy <- lapply(seq_len(3000), function(x) {
  testsample <- data.frame(matrix(nrow = 67, 
                                  ncol = 2))
  colnames(testsample) <- c("min_DM", "max_DM")
  
  testsample[, "min_DM"] <- rnorm(
    n = 67, 
    mean = datastructure$min_DM[2], 
    sd = datastructure$min_DM[3]
  )
  width <- rnorm(
    n = 67, 
    mean = datastructure$width[2], 
    sd = datastructure$width[3]
  )
  
  testsample[, "max_DM"] <- (width * 2) + testsample[, "min_DM"]
  
  test_dist <- dist(testsample, method = "euclidean")
  test_hdbcluster <- hdbscan(testsample, minPts = 5)
  sil_hdbscan <- silhouette(test_hdbcluster$cluster, 
                            test_dist, 
                            do.clus.stat = T, 
                            do.n.k = T)
  
  x <- list(
    N = nrow(testsample),
    n_cluster = length(unique(test_hdbcluster$cluster)) - 1,
    n_noise = length(which(test_hdbcluster$cluster == 0)),
    avg_sil_width = NA,
    avg_sil_width_without_0 = NA
  )
  
  if (x$n_cluster >= 1) {
    mat <- as.data.frame(sil_hdbscan[1:67, 1:3])
    x$avg_sil_width <- mean(mat$sil_width)
    
    mat <- mat[-which(mat$cluster == 0), ]
    x$avg_sil_width_without_0 <- mean(mat$sil_width)
  } 
  
  if (any(is.na(x))) {
    return(NA)
  } else {
    return(x)
  }
})  

tests_dummy <- tests_dummy[!is.na(tests_dummy)]

tests_compare <- tests_dummy[sample(seq_along(tests_dummy), 
                                    replace = FALSE, 
                                    size = nrow(tests_compare))]
tests_compare <- bind_rows(tests_compare)

We might as well take a quick look at the silhouette plot for the clusters found in the original data. The silhouette first needs a distance matrix of the original data as well.

dist <- StackRMiletus %>%
  select(min_DM, max_DM) %>%
  dist(method = "euclidean")
sil_hdbscan <- silhouette(hdbcluster$cluster, 
                          dist, 
                          do.clus.stat = T, 
                          do.n.k = T)

Range of SC	Interpretation
0.71-1.0	A strong structure has been found (min. green line)
0.51-0.70	A reasonable structure has been found (min. blue line)
0.26-0.50	The structure is weak and could be artificial (min. red line)
< 0.25	No substantial structure has been found

(see: Spector (2011))

Results from the Silhouette-Test for the original data will be are compiled in a separate data.frame:

miletus_data_sil <- data.frame(matrix(ncol = 5, nrow = 1))
colnames(miletus_data_sil) <- colnames(tests_compare)
miletus_data_sil$N[1] <- nrow(StackRMiletus)
miletus_data_sil$n_cluster[1] <- length(unique(hdbcluster$cluster)) - 1
miletus_data_sil$n_noise[1] <- length(which(hdbcluster$cluster == 0))
mat <- as.data.frame(sil_hdbscan[1:67, 1:3])
miletus_data_sil$avg_sil_width[1] <- mean(mat$sil_width)
mat <- mat[-which(mat$cluster == 0), ]
miletus_data_sil$avg_sil_width_without_0[1] <- mean(mat$sil_width)

And can then be compared to the distribution of respective values from the generated sample, seen here in density graphs:

Scaled Comparison of Measured Variables

For the plot in Fig. 12 all the numerical variables where scaled using scale() to ease visual comparison:

However, a look at the original boxplot might be interesting as well:

As I am unsure of copyright issues in making the data available online, I did not incorporate the comparisons with rings from Monaco (2000) and Cracolici (2003).

References

Cracolici, Vincenzo. 2003. I Sostegni Di Fornace Dal Kerameikos Di Metaponto. Beni Archeologici–Conoscenza e Tecnologie ; Quaderno 3. Bari: Edipuglia.

Hahsler, Michael, Matthew Piekenbrock, and Derek Doran. 2017. “Dbscan: Fast Density-Based Clustering with r.” CRAN. 2017. https://CRAN.R-project.org/package=dbscan.

McInnes, L., J. Healy, and S. Astels. 2017. “Hdbscan: Hierarchical Density Based Clustering.” Journal of Open Source Software, The Open Journal 2 (11). https://doi.org/10.21105/joss.00205.

Monaco, Maria Chiara. 2000. Ergasteria: Impianti Artigianali Ceramici Ad Atene Ed in Attica Dal Protogeometrico Alle Soglie Dell’ellenismo. Vol. 109. Studia Archaeologica. Rom.

Müller-Wiener, Wolfgang. 1977. “Milet 1973 – 1975. Michaelskirche Und Dionysos-Tempel. Baubefunde Und Phasengliederung.” Istanbuler Mitteilungen 27/28: 94–103.

———. 1979. “Milet 1977. Arbeiten Im Stadtgebiet. Untersuchungen Im Dionysos-Heiligtum.” Istanbuler Mitteilungen 29: 161–69.

Real, Willi. 1977. “Milet 1973 – 1975. Ausgewählte Funde Aus Dem Dionysos Tempel.” Istanbuler Mitteilungen 27/28: 105–16.

Spector, Phil. 2011. “Statistics 133, Spring 2011, Class Homepage. University of California, Berkeley.” https://www.stat.berkeley.edu/~s133/all2011.pdf.

Steinmann, Lisa. 2020. “Finds from Miletus XXXII: Clay Rings from the Sanctuary of Dionysos in Miletus.” Archäologischer Anzeiger 2020/1: 93–119. https://doi.org/10.34780/aa.v0i1.1014.

Clay Rings from the Sanctuary of Dionysos in Miletus: Supplement