Unsupervised Classification of Neolithic Pottery From the Northern Alpine Space Using t-SNE and HDBSCAN

1.1 Overall Research Topic and Objectives of the MET Project

Throughout the research history, the understanding of the Neolithic in the Northern Alpine Foreland – as in the entire Central European Neolithic research – was characterized by concepts of “archaeological cultures” defined based on pottery. The epistemological consequences associated with this will be outlined very briefly below – since a more in-depth discussion is not possible here for reasons of space and, beyond that, has already taken place elsewhere (Furholt, 2008; Hafner & Suter, 2003; Heitz, 2017, pp. 258–262; 2018, pp. 15–19). As common in the cultural-historical research paradigm, pottery was first and foremost used to establish typo-chronologies before scientific dating techniques like dendrochronological and radiocarbon dating were available. Based on certain vessel types or the quantitatively predominant main characteristics of pottery, newly excavated sites could be assigned to the respective cultures (Hafner & Suter, 2003, pp. 2–4; Hafner et al., 2016). Hence, the Neolithic was structures in spatial-temporal “cultural blocks”, most obvious in typo-chronological schemes and maps of cultures (Figure 1).

Figure 1

Vogt’s (1964) Chronology Scheme of Neolithic Cultures in Switzerland.

These typo-chronological units were subsequently equated with ethnic groups at that time, as was the case everywhere in Europe. Over time this led to a problematic research practice in which Neolithic cultures were defined exclusively by using pottery and conceptualized as homogeneous, spatially clearly definable units. In consequence, the farming communities assigned to these to these Neolithic cultures were imagined as sedentary, spatially barely mobile groups (Heitz, 2018, pp. 20–52; there further literature). The premises were that one settlement equates with one pottery style and one ethnic group and that Neolithic societies were living rather autarkic, subsistent-based, and predominantly sedentary lives where “cultural contacts” happen rather sporadically, mainly in onetime events of migration (Heitz, 2017, p. 259; Heitz & Stapfer, 2021).

One way to test and question this premise about ‘Neolithic cultures’ is to examine spatial mobility and accompanying cultural relations in depth by drawing on ceramic finds and analysing spatial and temporal similarities and differences. One way to test and challenge this premise about ‘Neolithic cultures’ is to examine spatial mobility and the associated cultural relationships in depth using ceramic finds by highlighting similarities and differences in pottery practices across space and time. For understanding spatial mobility based on pottery, it is decisive that regional stylistic differences can be separated from chronological ones. However, this circumstance is not given if pottery itself is used to establish typo-chronologies in different regions as only means of dating. In such cases, no degrees of freedom are left for further social-archaeological analyses. Morphological differences and similarities can no longer be used as chronology-independent source of cultural and social information. In this respect, working with pottery assemblages deriving from prehistoric wetland sites in the circum-alpine region offers a research potential of enormous value (Hafner, 2014). Due to the anaerobic preservation conditions of the waterlogged remains of settlements, thousands of organic artefacts are preserved. Among them are the wooden remains of houses that – in the optimal cases – allow us to date the settlement histories to the exact year by means of dendrochronology. Hence, combined with stratigraphic information and radiocarbon dates, an absolute chronological grid can be established for Neolithic wetland sites in the Northern Alpine Foreland.

The wide application of dendrochronological dating in Switzerland and adjacent countries makes chronologies independent from pottery typologies today. With the discovery of culturally “foreign pots” in dendrochronologically dated settlements, e.g., Arbon-Bleiche 3 (3384–3370 BCE), at Lake Constance, the premises-loaded notion of “Neolithic cultures” was challenged (De Capitani, Deschler-Erb, Leuzinger, Marti-Grädel, & Schibler, 2002, pp. 209–26, 220–221, 223; Freudiger-Bonzon, 2005; in general see also Burri-Wyser, 2007; Matuschik, 2010, 2011; Matuschik & Müller, 2016; Schlichtherle, 1998). During our project, an initial review of already published catalogues of pottery deriving from wetland sites in the Northern Alpine Foreland dated to the first half of the 4th millennium BCE quickly revealed that stylistic plurality in the pottery deriving from these sites was rather the norm than the exception (Heitz & Stapfer, 2016, pp. 150–151; 2021).

Pottery assemblages that derive from these settlement phases offer a rare possibility to separate temporal from spatial cultural differences. Furthermore, thanks to the favourable preservation conditions, an abundance of pottery per site can be analysed whose low fragmentation allows to reconstruct the full profile shapes. Accordingly, the methodology elaborated here based on such high-quality data promises to be ground-breaking and applicable to other projects.

To gain a deeper understanding of this phenomenon related to spatial mobility and social configurations, we developed two classification methods to approach stylistic and morphological similarities and dissimilarities between the pottery of different sites:

1. a qualitative impressionistic classification of the vessels’ designs that allows to understand social practices of pottery production from the actors’ perspective and

2. a quantitative computational unsupervised classification using t-SNE and HDBSCAN for cluster analyses based on the pottery vessels’ profile shape and further variables that allows to explore those social practises connected to the pottery consumption practice across several settlements.

Using both combined, the problematic models of Neolithic societies following the cultural-historical paradigm can be deconstructed by inquiring directions and rhythms of spatial mobility based on material entanglements in pottery that are indicative for social configurations.

1.2 Computer-Assisted and Visual Classification

In archaeology, classification is one of the recurring basic problems. The purpose of classification in general is to enable statements about a specific set of objects and thus to go beyond the description of individual items (Nakoinz & Hinz, 2015, p. 226). Classification is the process of gathering similar entities into groups called classes. The entities of a group should be more similar (“high within-group homogeneity”) than two entities from different groups (“low between-group homogeneity”) (Rice, 2015, pp. 220–221). Classification is based on a selection of features (variables), which are usually examined for their different characteristics in all entities to be classified. In principle, the entities to be classified, such as ceramic vessels, have an endless number of possible features that can be investigated (Rice, 2015, pp. 221, 224). Ceramic vessels, or rather ceramic fragments, can be classified in a variety of different ways and with a variety of different objectives. The assessment of which of these are relevant and thus to be selected is one of the most subjective moments in the entire investigation process, which cannot be avoided also by computer-assisted methods (for an overview of different classification methods, see Heitz, 2018, pp. 185–194).

The process of classification can be done impressionistically intuitively by eye/brain – what we refer to as qualitative classification – or by means of a quantitative computer-aided procedures, referred to as quantitative classification (Heitz, 2018, pp. 199–203). A classification based on a visual approach in the framework of subjective decisions does have various advantages (Heitz, 2018, pp. 190, 200–201): first, it certainly comes closest to the methodology in which the contemporaries of the production of the vessels would have classified them. Practically, it is usually quicker to carry out; moreover, humans can concentrate each time on different dimensions of similarity but combine these again in an overall view and distinguish situationally important from unimportant criteria. Furthermore, visual classification built on the extraordinary capacity of the human brain to find pattern but is also dependent on the researcher’s experience and knowledge. It is therefore subjective and the ability to verify the results of such classifications relies on intersubjectivity. Implementing this for computer-aided procedures is not trivial (Read, 2016, p. 27).

Quantitative computer-assisted classification is based on a statistical model (variables and their characteristics, distance measure, algorithm, etc.) created by humans (Rice, 2015, pp. 231–232). Similarities between the entities are calculated with the help of a mathematical distance measure and based on this, classes (clusters) are formed with the help of an algorithm. Two basic directions can be used: the so-called “supervised” and “unsupervised” approaches. In the first case (“machine learning”), the computer is taught in a learning phase to classify according to a predefined classification system. In the second case, the aim is to find unknown groups in a dataset based on certain characteristics (“automatic classification”).

When such quantitative, inductive bottom-up approaches of computer-assisted classification emerged in archaeology at the end of the 1950s, the classification results were initially considered essentially objective and the classes discovered and types derived from them were considered real, i.e., relevant for past societies (Hutson & Markens, 2002, pp. 9–14). However, it soon became apparent that subjective moments also exist in such classifications, where decisions must be made by humans: (1) in the selection of the variables to be considered at all, (2) in the weighting of the same, (3) in the choice of the algorithm, (4) in the assessment of the calculated classes and possible outliers, etc. (Hutson & Markens, 2002, pp. 9–14). The same selection of ceramic vessels can thus be classified very differently using different statistical models.

Nevertheless, computer-based classifications also have decisive advantages: With the appropriate programming skills and computing power, an large number of variables can be processed for an equally large number of entities or datasets, which makes these methods particularly interesting for comparative studies of larger space/time windows. Furthermore, the methodological procedure can be documented step by step, so that a cluster solution becomes comprehensible and reproducible for third parties if the code, the software used, and the corresponding datasets are disclosed. Although these methods are not objective, they achieve a higher degree of intersubjectivity than intuitive classifications (see Heitz, 2018, pp. 178–179).

Because the pottery of the first half of the 4th millennium BCE is barely decorated, the vessels’ shapes were an important feature for morphological and stylistic differentiation in the case study presented here. Therefore, the morphometrics of the half-profiles of pottery vessels – as represented by pottery drawings in general – were of central importance (Heitz, 2018, pp. 202–208). A classification of vessels based on profile images or profile curves has already been suggested several times in archaeology (Jammet-Reynal, 2006; Lăzărescu & Mom, 2016; Mom, 2007; Saev, 2015; van der Maaten, Lange, & Boon, 2010; Karasik & Smilansky, 2011). The computer-assisted classification method proposed in this article provides solutions to two sets of problems that occur in archaeological pottery classification and haven’t been solved yet:

1. It combines the profile images with other variables and makes them evaluable for cluster analysis. So far, no other procedure in archaeology makes this possible. Thus, a completely new explorative clustering procedure is tested here, which enables automatic and thus comparatively unsupervised classification of the vessels, including their metrics and nominal variables.

2. It considers that morphological standardization is limited in handmade Neolithic pottery and that the metrics of individual vessels of the same design can vary considerably. Style – understood here as material style associated with particular pottery production practices (see Section 2) – is not a rigid category but a fluent phenomenon. Since styles emerge in a correspondence of the material, the individual and the social, they include standardization but also variations. In consequence – and when taking mobility into account too – it is to be expected that the standardization of pottery found in Neolithic settlements is limited and tends to include marked deviation and outliers. This calls on the one hand for a targeted selection of variables that consider the intentional and unintentional/random emergence of pottery features. On the other hand, statistical techniques are needed that deal with the high-dimensional structure and the noisiness of such data.

Both issues were addressed in the classification method propose here. The concrete procedure of our method and the results achieved are directly reproducible through the disclosure of the data and R scripts. We also hope that the statistical model itself will be useful for other research projects. Therefore, in the following, after explaining our theoretical approach, we will briefly present the ceramic objects analysed in the classification and then explain the methods used for the computer-assisted classification. We will then outline and discuss the results of our analysis.

3.1 Selected Sites and Pottery Vessels

We applied our new methodological approach to assemblages of pottery dating to the period of 4000–3750 BC, accuracy depending on the dating method.^[3] Taking an actor’s perspective, we can expect this span of 250 years to cover up to 8–10 generations. This is a long time relative to a potter’s life, the making of pottery in communities of practice and thus shared forms of habitus. Hence, within this time span, we must take transformations in pottery production practices into account. Therefore, we established a spatial–temporal model that separates phenomena of regional stylistic differences from local transformations (Heitz, 2018, pp. 145–153, Figure 5.7). The model founded on stratified pottery assemblages that can be reliably attributed to absolutely dated structures. Furthermore, sites encompassing as many as possible complete semi-profiles of pottery vessels were given priority, since our aim was to compare the vessels’ shapes and designs based on their silhouettes.

The different kinds of archaeological structures from which the chosen pottery assemblages derive have a considerable impact on the nature of the data that we generated out of them. Except from one case, the burial pits of Didenheim-Lerchenberg (Alsace, F) (Schweitzer, 1987), the chosen pottery originates from different kinds of settlement structures: cultural layers of lakeshore, bog, river, and cave sites as well as pits and trenches from hilltop sites and earthworks. These different find contexts affect the number and preservation of pottery vessels and the accuracy of dating: while wetland sites might be dated to the exact years by means of dendrochronology and thus show the different length of time in which the pottery accumulated, trenches tend to have several cultural layers and thus fillings while pits might represent short-lived closed finds. The latter two, however, can only be dated by ¹⁴C into a probability range of several decades.^[4] In cases where no absolute pottery-independent dating of the structures was available, the pottery assemblages could be matched with absolute dated ones based on typo-chronological arguments (Heitz, 2018, pp. 154–182). The resulting chronological framework that considers the differences between wetland and dryland site conditions, can be seen in Figure 2, which also indicates the different dating methods.

Figure 2

Temporal model of considered settlements and assemblages of pottery (figure: after Heitz, 2018, Figure 5.7). MK = Michelsberg.

Within the core region of the MET project, the Northern Alpine Foreland, the settlement phases of dendro-dated wetland sites were assigned to an absolute chronology based on the oldest and youngest known felling dates per site. In the case of wetland sites with several stratigraphically separable settlements or settlement phases, cultural layers lacking scientific dating could be relatively dated within these stratigraphic sequences. Thus, it was possible to allocate their pottery assemblages to a certain absolute time span in a second step. In case of existing ¹⁴C-dates they sometime could be modelled using the Bayesian “sequence-models.” Thanks to the high density of precisely dendro-dated wetland sites of the Swiss Plateau the typo-chronological transformation of pottery can be closely traced. This allowed us also to include only typologically datable pottery assemblages into the absolute time model too. Most of the sites in Southern Germany and Eastern France cannot be dated more precisely then to the overall time span of the 250 years. However, since typical pottery-designs from these regional styles, early NMB (Néolithique Moyen Bourguignon, Petrequin & Pétrequin, 2015), Michelsberg (primarily the periods MK III and IV, after Lüning, 1968; Seidel, 2017), and Munzingen (Jammet-Reynal, 2017) occur in the dendro-dates wetland sites, the relative dating of the chosen pottery assemblages could be verified.

While the time model is basically based on dendrochronologically dated settlement phases and stratigraphy, the grey and black bars in Figure 2 indicated approximate timespans and in the case of ¹⁴C dates the probability intervals (95% likelihood) within these settlements existed and the pottery assemblages formed, respectively. The longer time spans thus are only a result of lesser accurate dating methods, not necessarily a result of long-duration settlement occupations.

For the quantitative analysis, 1,046 vessels were used, which are distributed over 14 microregions (Figure 3) and 44 strata or diagnostic feature units of sites from the time between 4000 and 3750 BC. The dataset with a basic description of the metadata can be found here: doi: 10.5281/zenodo.7258694.

Figure 3

Selection of sites dating approx. 4000–3750 BCE and their geographical location in the northern Alpine Foreland and adjacent regions, highlighted in black: sites with pottery assemblages used in this paper for the unsupervised classification approach (figure: C. Heitz., map base according to Jammet-Reynal, 2017).

The vessels were selected according to the principle of weighted random sampling. The aim was to record the range of forms and decoration of the pottery of the respective site feature unit based on the already published catalogues of pottery drawings. In the case of the wetland sites, it was also possible to sift through the original material in the archaeological collections. For each site and ceramic assemblage, all vessels with reconstructed semi-profiles as presented in the respective catalogues were selected. This ensured that a maximum of morphological features could be recorded. In the case of very large ceramic assemblages, a representative selection was made (Heitz, 2018; Stapfer, 2019). The drawings were scanned and kept as separate “png” files per individual ceramic vessel (see Section 3.2.3).

3.2 Methodology

3.2.4 Implemented Workflow

These mentioned considerations led to a specific selection of data and methods. The largest amount of the data represents 400 individual values which describe the shape of each vessel. For this purpose, the drawings of the vessels were aligned perpendicularly (as good as possible) and the vessel shape was filled in black. This was done by hand using standard graphics processing software (GIMP). The resulting representation of the vessel profiles was halved (centreline of the vessel on the right of the resulting image) because the vessel body could be understood as a rotational body for analytical simplification. In this context, the handles and other three-dimensional decorative elements were also removed from the drawing and their presence was later reintegrated into the dataset by adding nominal variables. The resulting pure black and white images were then scaled to 400 px to ensure uniform data recording. This of course also removed any reference to the absolute vessel height or true-to-scale image. Therefore, information on absolute measures was included as separate parameters in the dataset. The resulting pictures were saved as PNG graphics and served as a basis for further analysis, which was carried out by means of R. An automation of this process was developed in the course of the analysis (https://github.com/ISAAKiel/shapAAR), but it was not yet used in the study presented here.

In R, the individual images were loaded using the command readPNG (package png) and converted into a matrix consisting of 0 and 1. In this matrix, the last occurrence of a white pixel was detected in each row from the left (i.e., from the outside of the vessel, represented by 1 in the matrix) and this was subtracted from the total width of the image. Thus, the distance of the profile line to the centreline of the vessel can be obtained for each of the 400 sampling lines. This information represents the complete information available about the vessel profile, as it (for the comparatively rather simply shaped vessels of our case study) can be reconstructed unambiguously from these values.

The database thus obtained regarding the vessel shape was enriched by further information, as can be seen in figure (Figure 4). Without going into detail here (see Heitz, 2018, pp. 195–197), nominal classifications were compiled on three-dimensional applications (position, shape, and series, if applicable), handles (position, shape, and series, if applicable), decorative elements, as well as aspects of the shaping of design elements that are difficult to grasp with the scanning of the overall shape (bottom shape, break). Furthermore, the absolute height of the vessel (bottom to rim) as well as two diameters (minimum and maximum diameter excluding the bottom, in the case of bowls minimum and maximum diameter including the bottom) given as landmarks were added as metric values to provide a closeness attribute.

Figure 4

Full workflow of the computer-aided classification (figure: M. Hinz).

The weighting is chosen in such a way that all variable groups from Figure 4 each have a total weight of 1, so that each variable within a group receives a weight of 1/n__variable__per__group. Thus, for example, the total height of the vessel has the same weighting as the total shape, as well as the bottom shape. This setting may seem arbitrary, but due to the clearly different quality of the variables in each group, on the one hand, and the most neutral possible parameterization, on the other hand (all definitely different qualities are weighted equally), this setting seemed to us to be the model with the lowest amount of assumptions. The PCA command (Package FactoMineR; Husson, Josse, Le, & Mazet, 2017) was used to achieve a weighted principal component analysis.

The results of the principal component analysis are used as input values for the t-SNE in the next step using the Rtsne command. One of the few and perhaps the only relevant parameter for t-SNE is perplexity, a parameter that balances how much the local neighbourhood is weighted against the global neighbourhood for ordination. A perplexity of 30 was selected as the default value, but this was reduced if necessary for small datasets (in the following subclustering process), so that it always corresponded to a maximum of 1/3 of the number of data – 1. This dynamization was necessary because a large perplexity value resulted in an error in such cases where there were few vessels within a cluster. At the same time, a PCA was skipped during t-SNE (pca = false) since it had already been performed. The parameter theta, which determines the compromise between speed and accuracy, was set to 0 to obtain an exact ordination. An output dimensionality of 2 dimensions was chosen.

In the third step, the ordination thus obtained was clustered using hdbscan. The parameter minPts, which acts as a minimum cluster size to detect and as a ‘smoothing’ factor of the density estimates, was set to 5 under the assumption that less than five vessels cannot reasonably represent an ideal type.

The fact that t-SNE is a stochastic algorithm results in each run producing a slightly different configuration of the ordination. Consequently, the result of the subsequent clustering becomes stochastic, so that in each run slightly different assignments of particularly ambiguous objects can occur. To stabilize the result, the procedure of majority-based consensus clustering was chosen, in which 101 ordination/classification runs were generated, and then, the objects, which occurred together in the majority of cases, were mapped into new, stabilized clusters.

This workflow (Figure 5) was first applied to the entire dataset. After this run, the same routine was applied recursively to the objects within these clusters until either a hierarchy depth of 3 was reached or the cluster in question contained less than five vessels (with the same reasoning as for the setting of the minPts parameter in HDBSCAN).

Figure 5

Attributes or states of attributes and their weighting (figure: C. Heitz, for an English translation of all variables, see doi: 10.5281/zenodo.7258694).

The resulting clusters were stored as folder structures in the file system, and the resulting data of the cluster-internal objects and the images of the vessels were saved here. In a further step, descriptive statistics and diagrams could be generated for each cluster.

It was also helpful for the evaluation that a “typical” vessel in the sense of a centroid could be determined for the respective cluster, on the one hand, as a virtual, ideal vessel and, on the other hand, by identifying the vessel, which could be regarded as the most typical real vessel. The centroid was calculated and then, the vessel was selected that was closest to the centroid. This vessel then served as a typical example for the hierarchy graph, which was generated by the program Graphviz.

Finally, all statistics and diagrams as well as the images of the vessels included in each cluster were converted into a PDF using an R Markdown script, and the PDF then provided the basis for the evaluation and interpretation of the results.

4.1 Description of the Cluster Solution

The unsupervised classification procedure separated the pottery vessels into 90 clusters on three different hierarchical levels. On the first hierarchical level, the vessels were grouped into 27 clusters, while some vessels, the black dots (marked as cluster 0) in Figure 6, were excluded as noise. In the ordination by t-SNE as discussed above, the local similarity of the data is taken more into account than the global one. Consequently, only the relative position of clusters connected by a point cloud of noise objects is meaningful. This applies to the centrally mapped group of clusters, but not to the position of the isolated individual clusters. The latter, clusters 6, 19, 14, and 23, are not surrounded by noise and are clearly separated from the more central group of other clusters. The number of data points (ceramic vessels) per main cluster varies considerably, from n = 6 to n = 209. Especially the large main clusters can be subdivided into subclusters or sub-subclusters on the second and third hierarchical levels.

Figure 6

Representation of the 1st hierarchy level (main cluster) of the HDBSCAN cluster analysis on the two-dimensional t-SNE visualization; data points identified as noise are indicated in black (cluster 0) (figure: M. Hinz).

Following the implemented iterative procedure, similarity groups were again formed within all of the 27 main clusters – omitting the noise – and again data points were marked as noise. On the second hierarchical level, again excluding the noise, a total of 32 clusters were formed, whereby not every main cluster has subclusters. In the same way, similarity groups were also calculated on a third hierarchy level and a total of 29 clusters were formed anew, whereby again not every second level cluster could be further subdivided. Since the minimum number of vessels was limited to n = 5, the third hierarchy level could not be calculated in any case. The entire representation of the cluster hierarchy is seen in Figure 7, whereby the individual groups are represented by the “most typical” vessel (objects nearest to the centroids).

Figure 7

The clusters and their subcluster on three hierarchical levels, represented by the centroid vessels, displayed as hierarchical network (figure: M. Hinz and C. Heitz, Copyright of pottery drawings: doi: 10.5281/zenodo.7258694.).

Within the (sub)clusters of each hierarchical level, various uni- and bivariate statistics and graphical representations were automatized based on the variables recorded in the projects database. The following turned out to be particularly suitable for characterizing the (sub)clusters:

1. box plots for data scattering of vessel heights;

2. histograms and kernel densities for frequency distribution of vessel heights;

3. plots of superimposed curves of the profile shapes (400 points);

4. mean values and standard deviation respectively 1 and 2 σ-intervals for the profile shapes; and

5. bar charts of the absolute frequencies of the bottom shapes.

In addition, the individual statistics and drawings of the vessels per (sub)cluster are compiled automatically, the centroid vessel is indicated, and any noise and further subclusters are shown on the t-SNE visualizations.

As an example, the results regarding cluster 14, respectively, subclusters 14.1 and 14.2, as well as the clusters on the third hierarchical level, clusters 14.1.2, 14.1.6, and 14.1.8 are shown (Figures 8 and 9).

Figure 8

Cluster 14 and subclusters 14.1 and 14.2 (figure: M. Hinz and C. Heitz, for the picture credits of the pottery drawings, see doi: 10.5281/zenodo.7258694).

Figure 9

Subcluster 14.1, 14.1.8, 14.1.2, and 14.1.6 on the third hierarchical level (figure: M. Hinz and C. Heitz, for the picture credits of the pottery drawings, see doi: 10.5281/zenodo.7258694).

Overall, this results in a classification that primarily groups according to vessel size, compactness (height-width proportions) and closure (Dm 1 to Dm 2, see Figure 4). On the first hierarchical level, the height tends to be more dominant and on the second, the profile shape. Characteristics, such as bottom and break shapes, handles, and ornamental elements, play a subordinate role but are nevertheless incorporated. In some (sub)clusters, the nominal variables occur in different degrees. This is less due to the chosen statistical model itself than to the dataset as such: The total variance in the data is relatively large. If the number of similar vessels was larger with respect to the variables, clusters with lower dispersion would result. The relatively small number of sufficiently preserved vessels, the large vessel spectrum of the various Late Neolithic ceramics, and the rather low standardization of ceramic production all contribute to this.

The existing or lacking seriality (Heitz, 2017; 2018, pp. 119–126, 300) of the vessels produced also plays a role. Cluster 14, vessels with handles, was produced in relatively large numbers in a relatively standardized manner, i.e., clearly in series. Not only does cluster 14 separate itself from the rest of the vessels without noise points, but subclusters 14.1 and 14.2 also have a finer subdivision into jar-shaped and cup-shaped handle vessels, i.e., taller and more closed, contrasting with wider and more open forms. Here, therefore, a very clear separation is achieved by computer-based classification.

A further example are subclusters 2.1, 2.2, and 2.4 of cluster 2, in which the Michelsberg bag and tulip beakers (‘Tulpen- und Beutelbecher’ according Lüning, 1968), which are also produced in a highly standardized way, are grouped and separated from other bulbous tulip-shaped vessels (Figure 10). Subcluster 2.1 (n = 26) groups bag and tulip Beakers together, although these are even more strongly subdivided into subclusters 2.1.2, 2.1.3, and 2.1.6 based on their profile shape. Subcluster 2.2 (n = 72) collects much more bulbous vessels compared to subcluster 2.1, but they are also strongly open and tend to be tulip-shaped. The group is relatively heterogeneous. Flat and raised bases also occur, as well as applications of all kinds. The distinction into further three sub-subclusters, 2.2.2, 2.2.3, and 2.1.6, allows an even finer subdivision according to the profile shape and thus the squatness and closedness of the vessels. Subcluster 2.4 (n = 10) classifies compared to 2.1 more slender vessels together, which are called slender tulip beakers (‘schlanke Tulpenbecher’) according to Lüning’s typology (Figure 10).

Figure 10

Cluster 2 and subclusters 2.1, 2.2, and 2.3 (figure: M. Hinz and C. Heitz, for the picture credits of the pottery drawings, see doi: 10.5281/zenodo.7258694).

Figure 11

Cluster 6 and subclusters 6.1, 6.3, and 6.5 (figure: M. Hinz and C. Heitz, for the picture credits of the pottery drawings, see doi: 10.5281/zenodo.7258694).

Figure 12

Subclusters 6.6, 6.17, and 6.22 (figure: M. Hinz and C. Heitz, for the picture credits of the pottery drawings, see doi: 10.5281/zenodo.7258694).

Other clusters, such as cluster 6, unite morphologically very different vessels, which, however, still show comprehensible similarities: prominent rims and spherical vessel bodies. On the second hierarchical level, these are then subdivided according to their different profile forms, closeness, and compactness (Figures 11 and Figures 12). Especially in the case of the deep and shallow bowl-shaped vessels, it is noticeable that the dominance of the variable height on the first hierarchical level provides for separation. Since with such forms, the height seems less relevant from an archaeological point of view than, for example, the width or the closeness, there is rather a too fine subdivision here. In addition to sorting out noise points using HDBSCAN, the integrative procedure implemented is particularly helpful here, as clusters at different hierarchical levels can be used for further investigations.

The division of the vessels into clusters makes it obvious that the classification neither follows qualitatively defined typo-chronological units such as so-called “archaeological cultures” nor spatial units such as settlements or regions (Figure 13). The distribution of the settlements (diagnostic units) among the main clusters is very heterogeneous: none of the clusters consists solely of vessels of one settlement. This shows that the unsupervised classification detects similarity groups that basically connect the vessel spectra of the different settlements. A second look at the distribution of the traditional typo-chronological ceramic groups also shows that similarity structures are found with this method that cross, so to speak, the common “cultures” or potentially combine different ceramic practices.

Figure 13

Result of the unsupervised classification regarding temporal and spatial attribution of the potter, (a) proportions (relative frequency) of sites (pottery assemblages of feature units) per cluster of the first hierarchy level and (b) of the typo-chronological ceramic groups per cluster on the first hierarchy level (figure: M. Hinz).

4.2 Interpretation of the Cluster Solution

In view of the Late Neolithic, morphologically highly variable pottery, however, the statistical model chosen succeeds in creating a surprisingly stringent, archaeologically meaningful, unsupervised classification: at different hierarchical levels, the vessels are roughly separated into similarity groups regarding morphologically fundamental properties. These were composed of the absolute size, the degree of closeness and compactness, and the profile curve. Variables such as break (shoulder rsp. belly) or bottom shapes and attachments are of secondary importance. This fails in separating types or designs in the way one would do impressionistically. However, computer-aided classification provides something else which the human eye and memory can hardly achieve – especially not for more than 1,000 vessels: a separation into different morphological similarities, including size, on which the ceramic dataset is based. Thus, the cluster solution shows primarily a grouping according to “basic forms” in different degrees of refinement. Interestingly, these now lead the perspective from production to the consumption level, since basic forms are associated with “functions” or rather “latent potentials of vessel use” (Heitz, 2018, pp. 289, 300; 2022, pp. 390–392): The basic morphology of the vessels, the basic form, has an influence on phenomena of affordance: on what the vessels are considered suitable and useful for and the different actions in which they can be integrated, in short: the practices of vessel use.

In this respect, an article by Wotzka (1997) is instructive, in which he examines the connections between metric ceramic features and the orally stated functions of vessels from ethnological investigations using multivariate statistics (main component and discriminant analyses). According to Gallay, Huysecom, and Honegger (1991), he distinguishes three different functional concepts – and thus emic categorization types:

1. Primary function: the intended use in the production of vessels by the producers.

2. Secondary function: This is to be understood as what the consumers indicate in the survey as the intended use of the vessels, essentially these are ethnotaxonomies.

3. Tertiary function: actually, observable numerous functions, i.e., the uses of the vessels in practice.

On the one hand, this shows that there is a fundamental relationship between the size, proportions and closeness of vessels and their functionality – or rather, their potential uses. In the sense of affordance, however, a whole spectrum of actual uses per basic form is to be expected. In short (Heitz, 2022, pp. 390–392): the basic forms of the vessels refer to groups of possible, similar utilizations. Therefore, we define basic, latent groups of use potentials by means of unsupervised classification. The clusters can be described as latent groups because they do not necessarily catch the eye from a typological point of view when looking at the vessel drawings. Furthermore, the groups of use potentials are also latent because the vessels elude any fixed functional attribution in the sense of affordance. The relationship between form and function is thus not stable and rigid but involves a certain unsteadiness that results from the dynamics of the mutual, situationally varying human-object relationships. The benefit of the computer-aided procedure in general lies furthermore in the reproducibility of its results, but also in the fact that it reduces subjectivity – to at least partly – for the classification result. This opens new perspectives on the finds, which complement those of conventional classification.

4.3 Regional Similarities and Differences as Indication for Spatial Mobility

As mentioned above, the unsupervised classification provides us with a hierarchical cluster solution, which allows to work with differentiations on several scales. From an archaeological point of view, not all clusters or subclusters are equally useful. As explained above, cluster 6 in itself is too heterogeneous, however, its subclusters, 6.1, 6.3, and 6.5 are more homogeneous and thus useful. Thus, it is necessary to validate the quantitative classification result critically to select the informative (sub)clusters for further archaeological analyses. Accordingly, to examine the distribution of latent groups of use potentials in settlements and time periods, one can select the most informative clusters or subclusters of the second or third hierarchical level, depending on the research question. The latter can be grouped visually into cluster groups, which has the advantage of yielding larger numbers of units per spatial or temporal unit for the comparison of functional spectra, as it was done for the MET project (Figure 14; Heitz, 2018, pp. 303–305). The results in Figures 15 and 16, which are described below, show that the analyses based on the combined cluster groups lead to the same results as the calculations based on individual clusters and subclusters. The only difference lies in the greater or lesser variability considered in each case.

Figure 14

Choosen clusters and subclusters from different hierarchical level for further research question-dependent analyses within the MET project (after: C. Heitz, for the picture credits of the pottery drawings see doi: 10.5281/zenodo.7258694).

Figure 15

Relative frequencies of represented cluster groups per region (figure: C. Heitz).

Figure 16

Relative frequencies of represented clusters per region (figure: C. Heitz).

Since the MET project aimed at a better understanding of spatial mobility between settlement communities based on material interconnections in pottery practices, the first question was to what extent similarities and differences exist between the small regions (Heitz, 2018, pp. 305–309). For this purpose, the spectra were compared based on the absolute or relative frequency (shares in %) of the formed cluster groups and the cultures as such per region (cf. Figure 3). When examining the spectra, we compared their basic patterns with each other, whereby the values of the frequencies were understood as tendencies depending on the number of cases.

If the spectra of cluster groups are grouped based on the relative frequencies, it becomes apparent that there are definitely patterns (Figure 15, see also Figure 3 for the spatial location of the regional groups). The effects of the different numbers of cases become particularly clear with this approach, whereby the spectra of the mineral soil sites are likely to be fundamentally thinned out. A quantitative investigation of the latter with respect to the relative frequencies of individual cluster groups in the spectrum is thus limited.

It is immediately apparent that each small region shows a slightly different spectrum in terms of the presence and frequency of cluster groups. Nevertheless, there are also clear similarities between individual small regions. In part, their spatial proximity to each other plays a role, but not exclusively.

Overall, the following lines of connection between the regions are revealed on a general level by the similarities and differences of the basic form spectra (Heitz, 2018, p. 310): the settlement communities living at the Lakes in Central Switzerland and in the Three Lakes region in western Switzerland used a more similar spectrum of basic vessel shapes as those Lac de Clairvaux or the Sâone region, respectively. This also applies to the settlement communities in the Lake Zurich area, although here there is a commonality with the pottery practice of the settlement communities at Lake Constance and in the Danube area, especially through the use of vessels with handles (jars, mugs). In the latter settlement areas, a similar spectrum of basic vessel shapes was used, whereby a connection to the areas around the Black Forest, the Kaiserstuhl, Kraichgau, and the Neckar area can be determined through individual groups of potential use such as cluster group 3. It is also clearly expressed that two spheres of different pottery practices and habitus groups overlapped in the area between Lake Constance and Lake Zurich during this period. This result corresponds to the insight from a cultural-historical perspective that there are fundamental differences between eastern Switzerland (Hornstaad/Pfyn) and central or western Switzerland (Cortaillod). The result is most satisfying, because it shows two things: with the statistical approach of unsupervised classification of “whole” pottery vessels elaborated here, quite reasonable, and straightforwardly interpretable results can be obtained in relation to settlement areas. On the general level of latent groups of use potentials mentioned so far, these do not contradict the basic findings of the conventional typological approach but confirm or rather refine and complement them.

Particularly meaningful are the spectra of clusters of small regions in which wetland settlements are present, which provide an optimal basis for comparison due to similar preservation conditions and numbers of cases. These include – listed according to their geographical position from west to east – the small regions Lac de Clairvaux, Three Lakes, Central Switzerland, Lake Zurich, Lake Constance, and Danube.

If the spectra of the clusters as such are plotted regarding their relative frequencies (Figure 16), the picture becomes even more clear (Heitz, 2018, pp. 311–312): within the fundamentally large similarities at the cluster group level when comparing adjacent regions, a closer look at the clusters within them reveals slight differences, which, however, speak overall for interconnections between the settlement communities in the small regions of Saône, Lac de Clairvaux, Trois-Lacs, and Lake Zurich. This shows that there was possibly the same need for certain basic functions of the vessels and that they were used in similar quantities – but possibly in slightly different functional variants or designs.

The heterogeneity or homogeneity in the clusters is interesting as far as the nominal variables are concerned (Heitz, 2018, pp. 319–321): shapes of the breaks, bottom shapes, decorations, and handles. However, this subjectively perceived, and to some extent statistically demonstrated, heterogeneity is much more likely to capture what actually takes place at the consumption level of ceramics from the actor’s perspective: the ever-changing affordances that result from the human-thing relationship between ceramic vessels and their users. Vessels can be used in a variety of ways. Their use is rarely reduced to one function, but rather materially similar vessels can be used similarly – or very differently. However, the fact that vessels were produced in certain similar basic shapes at all shows that the latter respond to a need for them on the part of the consumers.

It is significant that especially the clusters that have more than one distribution centre or are rather equally frequent in several regions show a greater inner variability. This can be exemplified by the vessels of cluster 1.1. Basically, these are tall, slender pot- and cup-shaped vessels with a fundamentally similar functional potential. In some of them, encrusted food remains are present, as we observed for example in vessels from Lake Zurich and Lake Constance. Such vessels have thus been used for cooking but are also suitable for storing food or other things. Thus, they occur in all small regions. The detailed profile or rim shapes are unlikely to have played a role in their use. This is probably more an expression of stylistic or practical aspects of production (e.g., ability). More decisive for the habitual use of these are handles, bottom shapes, or slip. These could refer to regionally different social practices of consumption. In their basic functional potential, however, the vessels are very similar.

Such regional differences can be found in almost all clusters. They point to the fact that vessels of the same potential functionality were produced in different designs in the individual small regions, with temporal differences also emerging within them. Thus, it should be emphasized once again that autoclassification provides a complementary perspective to the impressionistic design or style classification of ceramics.