Academia.eduAcademia.edu

Figure 125 – uploaded by Lorenzo Cardarelli

See full PDFdownloadDownload figure
Figure 101. Test set: some examples of reconstruction using BCE.

Figure 101 Test set: some examples of reconstruction using BCE.

Related Figures (130)

Drawing up a synthesis of the historical and archaeological reality of the period analysed in this work is not an easy task. In fact, the chronological range analysed is extremely broad (2300 BC - 480 BC). Nevertheless, it can be divided into three main phases: Bronze Age (2300 BC - 1000/950 BC); Early Iron Age (1000/950 BC - 720 BC); Orientalising/ Archaic period (720 BC - 480 BC) (Fig. 1). Figure 1. A schematic chronological line is presented, highlighting the main archaeological-historical phases (Bronze Age; Iron Age; Historic period). The absolute chronology is also indicated. This division into phases also partly represents different academic domains of study, where different scholars approach the study of material and, above all, archaeological questions differently. In fact, all of the Bronze Age and a portion of the Iron Age (with substantial geographical differences) are usually studied by pre- or protohistoric scholars, whereas part of the Iron Age and most of the Orientalising/ Archaic or preroman petiod are usually dealt with by classical archaeologists, or as far as the Italian academic environment is concerned, those who refer to the world of Etruscology (Bartoloni, 2012, pp. 42-43). Obviously, the contexts, the material is studied and analysed in different ways and for different purposes and, above all, the topics researched are extremely different (§ Challenges and limits in the dataset and approach).
Drawing up a synthesis of the historical and archaeological reality of the period analysed in this work is not an easy task. In fact, the chronological range analysed is extremely broad (2300 BC - 480 BC). Nevertheless, it can be divided into three main phases: Bronze Age (2300 BC - 1000/950 BC); Early Iron Age (1000/950 BC - 720 BC); Orientalising/ Archaic period (720 BC - 480 BC) (Fig. 1). Figure 1. A schematic chronological line is presented, highlighting the main archaeological-historical phases (Bronze Age; Iron Age; Historic period). The absolute chronology is also indicated. This division into phases also partly represents different academic domains of study, where different scholars approach the study of material and, above all, archaeological questions differently. In fact, all of the Bronze Age and a portion of the Iron Age (with substantial geographical differences) are usually studied by pre- or protohistoric scholars, whereas part of the Iron Age and most of the Orientalising/ Archaic or preroman petiod are usually dealt with by classical archaeologists, or as far as the Italian academic environment is concerned, those who refer to the world of Etruscology (Bartoloni, 2012, pp. 42-43). Obviously, the contexts, the material is studied and analysed in different ways and for different purposes and, above all, the topics researched are extremely different (§ Challenges and limits in the dataset and approach).
Table 2. Re-elaboration of the table proposed by Karl et al. (2022). 1: Gilboa et al. (2004); 2: Karasik and Smilansky (2011); 3: Roux and Harush (2022); 4: Van Der Maaten et al. (2009a); 5: Lengauer et al. (2020); 6: Martinez-Carrillo et al. (2012); 7: Wilczek et al. (2014); 8: Wang and Marwick (2020); 9: Lucena et al. (2017); 10: HO6rr et al. (2014); 11: Navarro et al. (2021); 12: Parisotto et al. (2022); 13: Cardarelli (2022).
Table 2. Re-elaboration of the table proposed by Karl et al. (2022). 1: Gilboa et al. (2004); 2: Karasik and Smilansky (2011); 3: Roux and Harush (2022); 4: Van Der Maaten et al. (2009a); 5: Lengauer et al. (2020); 6: Martinez-Carrillo et al. (2012); 7: Wilczek et al. (2014); 8: Wang and Marwick (2020); 9: Lucena et al. (2017); 10: HO6rr et al. (2014); 11: Navarro et al. (2021); 12: Parisotto et al. (2022); 13: Cardarelli (2022).
Figure 2. Outline of the ML and its disciplines. The concept of Learning relates to the tunable parameters of these algorithms, which change according to the input data and the goals we want to make archived to the model. This concept can thus be seen as the ability to arn from the data. The relationship between ML and related disciplines can be seen as hierarchical and is summarised in the Fig. 2: at the top of the hierarchy is computer science, which covers the more general aspects of informatics, such as sorting algorithms and data structure. This is followed by artificial intelligence, an approach that generally attempts to mimic human thinking. But beware, not all AI is ML! There are approaches, such as rule-based systems, that do not learn from data and are therefore not part of ML. The latter includes a number of classic algorithms such as linear regression and random forest. Finally, there is deep learning (DL), which is characterised by deep neural networks.
Figure 2. Outline of the ML and its disciplines. The concept of Learning relates to the tunable parameters of these algorithms, which change according to the input data and the goals we want to make archived to the model. This concept can thus be seen as the ability to arn from the data. The relationship between ML and related disciplines can be seen as hierarchical and is summarised in the Fig. 2: at the top of the hierarchy is computer science, which covers the more general aspects of informatics, such as sorting algorithms and data structure. This is followed by artificial intelligence, an approach that generally attempts to mimic human thinking. But beware, not all AI is ML! There are approaches, such as rule-based systems, that do not learn from data and are therefore not part of ML. The latter includes a number of classic algorithms such as linear regression and random forest. Finally, there is deep learning (DL), which is characterised by deep neural networks.
"Two schematic diagrams are proposed to exemplify the functioning of Swpervised learning (Fig. 3) and Unsupervisea learning algorithms (Fig. 4). Figure 3. Basic example of the operation of a Supervised learning algorithm, in this case a Classifier.
"Two schematic diagrams are proposed to exemplify the functioning of Swpervised learning (Fig. 3) and Unsupervisea learning algorithms (Fig. 4). Figure 3. Basic example of the operation of a Supervised learning algorithm, in this case a Classifier.
Figure 4. Basic example of how an unsupervised learning algorithm works.
Figure 4. Basic example of how an unsupervised learning algorithm works.
Figure 5. Classical Programming and ML approach.
Figure 5. Classical Programming and ML approach.
Figure 7. The AIPPD logo: this represents a Villanovan biconical urn that assumes the shape of overlappin, cylinders, which is typical of schematic database representations.
Figure 7. The AIPPD logo: this represents a Villanovan biconical urn that assumes the shape of overlappin, cylinders, which is typical of schematic database representations.
Figure 8. Example of reasonably reconstructible vessels. The reconstruction and integration were done manually
Figure 8. Example of reasonably reconstructible vessels. The reconstruction and integration were done manually
Figure 9. Manual preprocessing example: The images on the left depict the archaeological drawings as typically presented in publications. On the right, we have only the profile, obtained through manual pre-processing. Adapted from Cardarelli (2022).
Figure 9. Manual preprocessing example: The images on the left depict the archaeological drawings as typically presented in publications. On the right, we have only the profile, obtained through manual pre-processing. Adapted from Cardarelli (2022).
Figure 10. Diagram of the SQL database used. Within each box, you will find the primary components of the AIPPD dataset: Tabular data, Image data, and Geographic data. The geographic and images data are always linked one-to-one with specific elements of the tabular data, which, in contrast, possess a more structured format. The schema not only provides an overview of the specific structure of the relational dataset but also illustrates the relationships between the various tables comprising the tabular information.
Figure 10. Diagram of the SQL database used. Within each box, you will find the primary components of the AIPPD dataset: Tabular data, Image data, and Geographic data. The geographic and images data are always linked one-to-one with specific elements of the tabular data, which, in contrast, possess a more structured format. The schema not only provides an overview of the specific structure of the relational dataset but also illustrates the relationships between the various tables comprising the tabular information.
Figure 11. Morphological zone nomenclature. The image schematically and succinctly represents the various forms of relative nomenclature that can be encountered and used within the text.
Figure 11. Morphological zone nomenclature. The image schematically and succinctly represents the various forms of relative nomenclature that can be encountered and used within the text.
Figure 12. Dataset creation: vessels recording. Both daily values (blue) and a weekly average (orange) are shown. See See ee ee ee ee In general, the filing period lasted 263 days and is usually not extended over the weekend. Graphs showing the progress of the filing of records (Fig. 12) and contexts (Fig. 3) are proposed. With regard to the scheduling of finds, we see that the trend tends to be linear, towards the end of the period there is an increase in the number of records scheduled on average each day. Considering the whole period and eliminating the non-working weekend, an average of about 115 records archived each day is obtained. A table with the number of records entered the dataset at the end of each month is also proposed (Tab. 3): an average of 2500-3000 records are added each month.
Figure 12. Dataset creation: vessels recording. Both daily values (blue) and a weekly average (orange) are shown. See See ee ee ee ee In general, the filing period lasted 263 days and is usually not extended over the weekend. Graphs showing the progress of the filing of records (Fig. 12) and contexts (Fig. 3) are proposed. With regard to the scheduling of finds, we see that the trend tends to be linear, towards the end of the period there is an increase in the number of records scheduled on average each day. Considering the whole period and eliminating the non-working weekend, an average of about 115 records archived each day is obtained. A table with the number of records entered the dataset at the end of each month is also proposed (Tab. 3): an average of 2500-3000 records are added each month.
Figure 13. Dataset creation: contexts recording. Both daily values (blue) and a weekly average (orange) are shown.
Figure 13. Dataset creation: contexts recording. Both daily values (blue) and a weekly average (orange) are shown.
Table 3. Vessels recorded at the end of the month.
Table 3. Vessels recorded at the end of the month.
Figure 14. The Python logo, which simply and in line with the name of the programming language, represents two snakes. Up to version 3.12.2 (February 2024), Python (McKinney, 2018, pp. 2—3) was born in 1991, created by Guido van Rossum, and is a ‘high-level’, object-oriented, and extremely flexible programming language (Fig. 14). It is known for its simplicity, readability, and versatility, making it one of the most popular programming languages in use today.
Figure 14. The Python logo, which simply and in line with the name of the programming language, represents two snakes. Up to version 3.12.2 (February 2024), Python (McKinney, 2018, pp. 2—3) was born in 1991, created by Guido van Rossum, and is a ‘high-level’, object-oriented, and extremely flexible programming language (Fig. 14). It is known for its simplicity, readability, and versatility, making it one of the most popular programming languages in use today.
Figure 15. The AIPPA logo. The logo’s concept is based on the transformation of a vessel into a binary code, symbolising the connection between the archaeological object and the digital computer system.
Figure 15. The AIPPA logo. The logo’s concept is based on the transformation of a vessel into a binary code, symbolising the connection between the archaeological object and the digital computer system.
The modules and the package are well-documented and include descriptions of parameters, source code, and examples to assist users in getting started and performs some basic analysis without any knowledge of Python.
The modules and the package are well-documented and include descriptions of parameters, source code, and examples to assist users in getting started and performs some basic analysis without any knowledge of Python.
Figure 17. The image shows the same Binary Matrix with pad_to_fit=True (left) and pad_to_fit=False (right).
Figure 17. The image shows the same Binary Matrix with pad_to_fit=True (left) and pad_to_fit=False (right).
Figure 18. Calculating Metric Measurements. For the meaning of », 4, d, v, s please refer to the text. a How the metrics are calculated, as formalised within AIPPA, is now described. During the creation of potds, a bounding box is calculated for each pot ( width (#7dth). To calculate t Fig. 18): the / measure is the height (Aeigh/), and the w measure is the maximum he volume v (volume), the method of stacked-cylinders is basically used (Senior and Birnie, 1995, pp. 322-323). For each line of pixels within the bounding box, the distance between the axis of rotation of the drawing (the / segment) and the interna profile of the vessel is calculated: this measurement will act as the radius of the stacked-cylinder. The process is repeated for each pixel within the bounding box. The process stops when the distance between the bound inner diameter at the rim (dameter). For t the volume: in this case, the inner profile of the vessel is not used, but the outer profile. Furthermore, the outer surface of the stacked-cylinder is calcu ling box and the contour of the vessel equals 0. The ‘first’ radius d corresponds to the he calculation of the surface area (surface), a similar method is proposed as for ated instead of the volume. Finally, for the calculation of the surface area, the process is not stopped in the case of the presence of foot (Fig. 18).
Figure 18. Calculating Metric Measurements. For the meaning of », 4, d, v, s please refer to the text. a How the metrics are calculated, as formalised within AIPPA, is now described. During the creation of potds, a bounding box is calculated for each pot ( width (#7dth). To calculate t Fig. 18): the / measure is the height (Aeigh/), and the w measure is the maximum he volume v (volume), the method of stacked-cylinders is basically used (Senior and Birnie, 1995, pp. 322-323). For each line of pixels within the bounding box, the distance between the axis of rotation of the drawing (the / segment) and the interna profile of the vessel is calculated: this measurement will act as the radius of the stacked-cylinder. The process is repeated for each pixel within the bounding box. The process stops when the distance between the bound inner diameter at the rim (dameter). For t the volume: in this case, the inner profile of the vessel is not used, but the outer profile. Furthermore, the outer surface of the stacked-cylinder is calcu ling box and the contour of the vessel equals 0. The ‘first’ radius d corresponds to the he calculation of the surface area (surface), a similar method is proposed as for ated instead of the volume. Finally, for the calculation of the surface area, the process is not stopped in the case of the presence of foot (Fig. 18).
Figure 19. Boxplots showing the Height distribution. From the analysis of the boxplots, it can be concluded that there is a significant similarity between the two distributions.
Figure 19. Boxplots showing the Height distribution. From the analysis of the boxplots, it can be concluded that there is a significant similarity between the two distributions.
Figure 20. Boxplot showing the distribution of the difference between Height calculated by AIPPA and Paltinier: (2010). do 11U Udla LU lila aA amin aie aaialinin It is important to note that these results assume that the measurements provided in the publication are correct and that the error calculated is a measure of the uncertainty of the AIPPA method. A certain degree of discrepancy is expected. Indeed, the measures are usually obtained from handmade measurements on the original pot. Instead, the measurements in AIPPA were calculated from the drawings, and it is possible that errors may have accumulated during the process of creating the tables, generating the PDF, and printing. However, despite these potential sources of error, the distribution of the data indicates that it represents the same phenomenon, with no significant differences.
Figure 20. Boxplot showing the distribution of the difference between Height calculated by AIPPA and Paltinier: (2010). do 11U Udla LU lila aA amin aie aaialinin It is important to note that these results assume that the measurements provided in the publication are correct and that the error calculated is a measure of the uncertainty of the AIPPA method. A certain degree of discrepancy is expected. Indeed, the measures are usually obtained from handmade measurements on the original pot. Instead, the measurements in AIPPA were calculated from the drawings, and it is possible that errors may have accumulated during the process of creating the tables, generating the PDF, and printing. However, despite these potential sources of error, the distribution of the data indicates that it represents the same phenomenon, with no significant differences.
Figure 22. Example of contour extraction through the ContourDescriptor class. Analyses within AIPPA ate performed using the PyEFD library, a Python implementation of the techniques described in Kuhl and Giardina (1982) (https://pyefd.readthedocs.io/en/latest/#pyefd). The functions of PyYEFD have been adapted for faster and easier use on profiles. PVYEFD works on image contours that need to be defined in advance. The contours are calculated by using a class, called ContourDescriptor, which provides a list of two-dimensional points using the algorithm Marching squares (https://en.wikipedia.org/wiki/Marching squares) represent the outline of the profile (Fig. 22).
Figure 22. Example of contour extraction through the ContourDescriptor class. Analyses within AIPPA ate performed using the PyEFD library, a Python implementation of the techniques described in Kuhl and Giardina (1982) (https://pyefd.readthedocs.io/en/latest/#pyefd). The functions of PyYEFD have been adapted for faster and easier use on profiles. PVYEFD works on image contours that need to be defined in advance. The contours are calculated by using a class, called ContourDescriptor, which provides a list of two-dimensional points using the algorithm Marching squares (https://en.wikipedia.org/wiki/Marching squares) represent the outline of the profile (Fig. 22).
A further application of EFA analysis will concern the definition of complexity of the vessel’s shape (§ Complexity i funeral urns and vascular production between EBA and AP). Figure 23. Profile reconstruction using different harmonics.
A further application of EFA analysis will concern the definition of complexity of the vessel’s shape (§ Complexity i funeral urns and vascular production between EBA and AP). Figure 23. Profile reconstruction using different harmonics.
Figure 24. Schematic diagram of the functioning of an Autoencoder (above) and a Variational Autoencoder (below). Cardarelli (2022). Each block represents a fundamental component of the architecture. In this section, a Convolutional Variational Autoencoder (VAE) (Kingma and Welling, 2013) will be used. In the case of a VAE, the bottleneck-space is a Gaussian distribution, and the decoding process starts from a Sampled vector within this distribution (Kingma and Welling, 2013, pp. 4-5) (Fig. 24).
Figure 24. Schematic diagram of the functioning of an Autoencoder (above) and a Variational Autoencoder (below). Cardarelli (2022). Each block represents a fundamental component of the architecture. In this section, a Convolutional Variational Autoencoder (VAE) (Kingma and Welling, 2013) will be used. In the case of a VAE, the bottleneck-space is a Gaussian distribution, and the decoding process starts from a Sampled vector within this distribution (Kingma and Welling, 2013, pp. 4-5) (Fig. 24).
Figure 25. Architecture of the network used. Cardarelli (2022). The red layers represent the convolutional layers, the green represents the normalisation and activation layers, and the blue represents the linear layer. The image is constructed in such a way as to simulate the process of reducing the size of the image by increasing the number of channels. The architecture of the network is based on Sebastian Raschka’s MNIST Convolutional VAE® and includes 5 Convolutional layers (Krizhevsky et al., 2012), Batch Normalization (Goodfellow et al., 2016, pp. 318-319), Fully Connected /ayers (Caspari and Crespo, 2019, p. 6) and activation functions Rectified Linear Unit (ReLu) (Nair and Hinton, 2010), for a total of 2,300,000 trainable parameters (Fig. 25).
Figure 25. Architecture of the network used. Cardarelli (2022). The red layers represent the convolutional layers, the green represents the normalisation and activation layers, and the blue represents the linear layer. The image is constructed in such a way as to simulate the process of reducing the size of the image by increasing the number of channels. The architecture of the network is based on Sebastian Raschka’s MNIST Convolutional VAE® and includes 5 Convolutional layers (Krizhevsky et al., 2012), Batch Normalization (Goodfellow et al., 2016, pp. 318-319), Fully Connected /ayers (Caspari and Crespo, 2019, p. 6) and activation functions Rectified Linear Unit (ReLu) (Nair and Hinton, 2010), for a total of 2,300,000 trainable parameters (Fig. 25).
Figure 26. Training set: reconstructions epochs 1, 5, 10 using MSE. These problems are resolved by the reconstructions of epochs 25 and 45 (Fig. 27, a, b): the prxelation effect has completely disappeared and local morphological details are also correctly reconstructed, such as the swelling on the neck of the biconical vessel number 2 (Fig. 27, b). being characterised by a phenomenon of pixe/ation it is possible to appreciate the correct reconstruction of the overall shape of the vessel and secondly of some local morphological features such as rims or shoulders. With the conclusion of the tenth epoch (Fig. 26, c), the reconstructions improve mainly in their overall appearance, while some local features are still not correctly reconstructed and oversimplified.
Figure 26. Training set: reconstructions epochs 1, 5, 10 using MSE. These problems are resolved by the reconstructions of epochs 25 and 45 (Fig. 27, a, b): the prxelation effect has completely disappeared and local morphological details are also correctly reconstructed, such as the swelling on the neck of the biconical vessel number 2 (Fig. 27, b). being characterised by a phenomenon of pixe/ation it is possible to appreciate the correct reconstruction of the overall shape of the vessel and secondly of some local morphological features such as rims or shoulders. With the conclusion of the tenth epoch (Fig. 26, c), the reconstructions improve mainly in their overall appearance, while some local features are still not correctly reconstructed and oversimplified.
a) Training set: reconstructions at the end of epoch 0
a) Training set: reconstructions at the end of epoch 0
Figure 27. Training set: reconstructions epochs 25, 45 using MSE. It is then time to evaluate the performance of the model on the Test Set. A graph showing the trend of the Training Loss and Test Loss during the training of the model is proposed. The analysis of Fig. 28 does not indicate any overfitting phenomenon, as the Loss take on almost identical values. Moe ee a SE NS Se LN eA SMR | IER NEN TIES Stn noe pete s: NOSIS TiS EA USTs Seer igien in tees Be Finally, let’s display the reconstructions s of the Test Set t (Fig, 29): the reconstructions are very good. From a global point of view, the shape is reconstructed perfectly, from a local point of view there are some small errors, but these do not seem to compromise the interpretation of the shape: in the case of the biconical vase number 0 in Fig. 29, b we can see that the reconstruction creates a slight bulge in the neck not present in the original vase. An incorrectly reconstructed vessel is number 7 in Fig. 29, c.
Figure 27. Training set: reconstructions epochs 25, 45 using MSE. It is then time to evaluate the performance of the model on the Test Set. A graph showing the trend of the Training Loss and Test Loss during the training of the model is proposed. The analysis of Fig. 28 does not indicate any overfitting phenomenon, as the Loss take on almost identical values. Moe ee a SE NS Se LN eA SMR | IER NEN TIES Stn noe pete s: NOSIS TiS EA USTs Seer igien in tees Be Finally, let’s display the reconstructions s of the Test Set t (Fig, 29): the reconstructions are very good. From a global point of view, the shape is reconstructed perfectly, from a local point of view there are some small errors, but these do not seem to compromise the interpretation of the shape: in the case of the biconical vase number 0 in Fig. 29, b we can see that the reconstruction creates a slight bulge in the neck not present in the original vase. An incorrectly reconstructed vessel is number 7 in Fig. 29, c.
Figure 28. Training Loss and Test Loss using MSE.
Figure 28. Training Loss and Test Loss using MSE.
Figure 29. Test set: some examples of reconstruction using MSE.
Figure 29. Test set: some examples of reconstruction using MSE.
Figure 30. Test set: comparison of the reconstructions obtained through the two cost functions (BCE and MSE). comparison with those obtained by using the MSE (Fig. 30). The reconstructions are good, so it is possible to use the BCE as a cost function within the proposed VAE.
Figure 30. Test set: comparison of the reconstructions obtained through the two cost functions (BCE and MSE). comparison with those obtained by using the MSE (Fig. 30). The reconstructions are good, so it is possible to use the BCE as a cost function within the proposed VAE.
Figure 31: MNIST dataset example The dataset includes 70,000 handwritten digits (training set of 60,000 examples, and a test set of 10,000 examples). ‘They are black-and-white labelled images 28 - 28 pixels and are widely used in the ML as toy-datasets and examples fot educational purposes (http://yann.lecun.com/exdb/mnist/).
Figure 31: MNIST dataset example The dataset includes 70,000 handwritten digits (training set of 60,000 examples, and a test set of 10,000 examples). ‘They are black-and-white labelled images 28 - 28 pixels and are widely used in the ML as toy-datasets and examples fot educational purposes (http://yann.lecun.com/exdb/mnist/).
Figure 33. Features maps, relating to the convolutional layers of the proposed VAE.
Figure 33. Features maps, relating to the convolutional layers of the proposed VAE.
Figure 34. pairplot showing differences and relationship within the LS.
Figure 34. pairplot showing differences and relationship within the LS.
Figure 36. Scatterplot with the interpolated space of PC1 and PC2. The markers represent the actual vessels. Please refer to the chapter § Principal Component Analysis (PCA) for further details on the technique used. In the proposed graph, the two primary components (PC1 and PC2) and their loadings are depicted. The divisior between the two epochs and the values assumed within the loadings are clearly discernible in this example.
Figure 36. Scatterplot with the interpolated space of PC1 and PC2. The markers represent the actual vessels. Please refer to the chapter § Principal Component Analysis (PCA) for further details on the technique used. In the proposed graph, the two primary components (PC1 and PC2) and their loadings are depicted. The divisior between the two epochs and the values assumed within the loadings are clearly discernible in this example.
Figure 38. Scatterplot of the first two components. The creation of two groups corresponding to closed shape: (Functional class 3 and Functional class 4) and open shapes (Functional class 1 and Functional class 2) can be appreciated.
Figure 38. Scatterplot of the first two components. The creation of two groups corresponding to closed shape: (Functional class 3 and Functional class 4) and open shapes (Functional class 1 and Functional class 2) can be appreciated.
Figure 39. Result of Component Loadings calculation for each component. The first two components offer better and easily interpretable results.
Figure 39. Result of Component Loadings calculation for each component. The first two components offer better and easily interpretable results.
As an example of application, EIA1 urns from 6 ‘Villanovan’ (Bartoloni, 2012) necropolises were selected: Quattro Fontanili, Valle la Fata, Le Rose (Southern Etruria); Sant’Antonio, Pagliarone, Picentino (Campanian Etruria) (Tab. 6). As in the previous example (§ Principal Component Analysis (PCA)), the Vectorization is used as the method of features extraction. The LDA will therefore attempt to separate the vessels according to their context: the first component absorbs 67% of the variance, the second 15%. Figure 40. Scatterplot of the first two components of the LDA. The creation of three clusters is appreciated.
As an example of application, EIA1 urns from 6 ‘Villanovan’ (Bartoloni, 2012) necropolises were selected: Quattro Fontanili, Valle la Fata, Le Rose (Southern Etruria); Sant’Antonio, Pagliarone, Picentino (Campanian Etruria) (Tab. 6). As in the previous example (§ Principal Component Analysis (PCA)), the Vectorization is used as the method of features extraction. The LDA will therefore attempt to separate the vessels according to their context: the first component absorbs 67% of the variance, the second 15%. Figure 40. Scatterplot of the first two components of the LDA. The creation of three clusters is appreciated.
Let us analyse the projection of these coordinates on the scatterplot (Fig. 40): the LDA discriminates 3 main eroups. One group (cluster 1) is composed exclusively by Le Rose’s records; this is also the most isolated. A second eroup (cluster 2) is formed by the records of Quattro Fontanili and Valle la Fata. Finally, we have a grouping (cluster 3) containing the Picentino, Pagliarone and Sant’Antonio records. Within these groupings, the individual contexts are almost indiscriminate, especially with regard to cluster 3. Looking at this graph, some important considerations can be made: the highlighted clusters refer to geographical groupings: cluster 2 identifies two necropolis (Valle la Fata, Quattro Fontanili) that refer to the same settlement, namely Veii Cluster 3 instead contains contexts from Etruria Campana. Cluster 1 instead exclusively identifies the proto-urban centre of Tarquinia. Especially looking at the amount of variance expressed by the first component (67 %), the analysis shows that the difference between Tarquinia and Veii is much higher than the difference between the contexts from Etruria Campana. Moreover, Veii would be more similar to the contexts of Etruria Campana than to Tarquinia, a context that - like Veli - is part of the same geographical area (Southern Etruria). Table 6. Number of records for each context. We should note that Pagliarone, Picentino, and Sant’ Antonio pertain to Campanian Etruria, whereas Le Rose, Quattro Fontanili, and Valle la Fata relate to Southern Etruria. For references, refer to the Supplementary Materials.
Let us analyse the projection of these coordinates on the scatterplot (Fig. 40): the LDA discriminates 3 main eroups. One group (cluster 1) is composed exclusively by Le Rose’s records; this is also the most isolated. A second eroup (cluster 2) is formed by the records of Quattro Fontanili and Valle la Fata. Finally, we have a grouping (cluster 3) containing the Picentino, Pagliarone and Sant’Antonio records. Within these groupings, the individual contexts are almost indiscriminate, especially with regard to cluster 3. Looking at this graph, some important considerations can be made: the highlighted clusters refer to geographical groupings: cluster 2 identifies two necropolis (Valle la Fata, Quattro Fontanili) that refer to the same settlement, namely Veii Cluster 3 instead contains contexts from Etruria Campana. Cluster 1 instead exclusively identifies the proto-urban centre of Tarquinia. Especially looking at the amount of variance expressed by the first component (67 %), the analysis shows that the difference between Tarquinia and Veii is much higher than the difference between the contexts from Etruria Campana. Moreover, Veii would be more similar to the contexts of Etruria Campana than to Tarquinia, a context that - like Veli - is part of the same geographical area (Southern Etruria). Table 6. Number of records for each context. We should note that Pagliarone, Picentino, and Sant’ Antonio pertain to Campanian Etruria, whereas Le Rose, Quattro Fontanili, and Valle la Fata relate to Southern Etruria. For references, refer to the Supplementary Materials.
Figure 41. Scatterplot of the first two components of the NCA.
Figure 41. Scatterplot of the first two components of the NCA.
Visualising the dendrogram (Fig. 44, b), the difference between open and closed shapes is clearly visible, occupying a large part of the distance. A good way to define clusters would be to cut the dendrogram around 15, thus obtaining 4 clusters (Fig. 45, b). Obviously, the way in which the dendrogram is cut, responds to the specific requirements of the analysis. 1) Pianello di Genga embedding. Markers are coloured based on their membership in a specific Functional_class.
Visualising the dendrogram (Fig. 44, b), the difference between open and closed shapes is clearly visible, occupying a large part of the distance. A good way to define clusters would be to cut the dendrogram around 15, thus obtaining 4 clusters (Fig. 45, b). Obviously, the way in which the dendrogram is cut, responds to the specific requirements of the analysis. 1) Pianello di Genga embedding. Markers are coloured based on their membership in a specific Functional_class.
9) Pianello di Genga Dendrogram. The dendrogram identifies two large, well-divided clusters.
9) Pianello di Genga Dendrogram. The dendrogram identifies two large, well-divided clusters.
a) Pianello di Genga embedding. Markers are coloured based on their cluster attribution.
a) Pianello di Genga embedding. Markers are coloured based on their cluster attribution.
a) K-means elbow plot. The so-called elbow method can be used to identify an optimal number of 3 clusters.
a) K-means elbow plot. The so-called elbow method can be used to identify an optimal number of 3 clusters.
») LDA scatterplot, markers are coloured in accordance with the cluster assignment. In addition, the centroid of each cluster is also plotted.
») LDA scatterplot, markers are coloured in accordance with the cluster assignment. In addition, the centroid of each cluster is also plotted.
Figure 47. Correspondence Analysis between cluster and context. we can see, in this basic example, a perfect correspondence between contexts and clusters.
Figure 47. Correspondence Analysis between cluster and context. we can see, in this basic example, a perfect correspondence between contexts and clusters.
Figure 48. BIC and AIC scores for GMM density estimation. AIC does not show evidence of reaching a minimum, while BIC shows a minimum at around 9-10 Gaussian components. The funerary urn dataset is used as an example (§ Amtoencoder (AE)). We apply the GMM directly to the Laten Space and test through BIC and AIC the number of Gaussian components that best fit the data within the LS (Fig 48).
Figure 48. BIC and AIC scores for GMM density estimation. AIC does not show evidence of reaching a minimum, while BIC shows a minimum at around 9-10 Gaussian components. The funerary urn dataset is used as an example (§ Amtoencoder (AE)). We apply the GMM directly to the Laten Space and test through BIC and AIC the number of Gaussian components that best fit the data within the LS (Fig 48).
Figure 49. Generated pots using GMM. Most of the images are plausible, while there are a few examples of vessels that are either not plausible or contain reconstruction errors.
Figure 49. Generated pots using GMM. Most of the images are plausible, while there are a few examples of vessels that are either not plausible or contain reconstruction errors.
Figure 50. Comparison between Rea/and Fake pots UMAP embedding. The data structure is well respected. 4.2.4 Density-based methods: DBSCAN, HDBSCAN As Fig. 50 shows, the structure of the data is almost identical.
Figure 50. Comparison between Rea/and Fake pots UMAP embedding. The data structure is well respected. 4.2.4 Density-based methods: DBSCAN, HDBSCAN As Fig. 50 shows, the structure of the data is almost identical.
Figure 51. Example of how DBSCAN works: the red dots are the core-points, the yellow dots the density-reachable. The black point is a noise-point. Let us consider the example in Fig. 51: a eps of value d, and a min_samples of 3 have been chosen. This means that points within distance d are required for a point to be considered a core-point (the red points). The yellow points fail o fulfil the min_samples assumption, as there is only one point in their eps. However, they are still part of the cluster as ensity-reachable. If a new point is only connected to the latter, it will not be part of the cluster (Ester et al., 1996, p. 28). The black point, on the other hand, is separated from the high-density zone and can therefore be regarded as uther or notse-point.
Figure 51. Example of how DBSCAN works: the red dots are the core-points, the yellow dots the density-reachable. The black point is a noise-point. Let us consider the example in Fig. 51: a eps of value d, and a min_samples of 3 have been chosen. This means that points within distance d are required for a point to be considered a core-point (the red points). The yellow points fail o fulfil the min_samples assumption, as there is only one point in their eps. However, they are still part of the cluster as ensity-reachable. If a new point is only connected to the latter, it will not be part of the cluster (Ester et al., 1996, p. 28). The black point, on the other hand, is separated from the high-density zone and can therefore be regarded as uther or notse-point.
Figure 52. Quattro Fontanili UMAP embedding. Markers are coloured based on their membership in Functional_class. As can be seen from the example on the relationship between typology and non-linear dimensionality reduction (§ UMAP and other non-linear dimensionality reduction methods), the embedding of the Quattro Fontanili necropolis was rather complex: there were in fact non-linear clusters or clusters that were often interconnected. The situation differs markedly from the necropolis of Pianello di Genga where it is possible to identify 3 more or less circular clusters, which are extremely simple to identify. The scenario with features extracted with Vectorization, and reduction with UMAP using #_neighbors = 10 (Fig. 52) is repeated.
Figure 52. Quattro Fontanili UMAP embedding. Markers are coloured based on their membership in Functional_class. As can be seen from the example on the relationship between typology and non-linear dimensionality reduction (§ UMAP and other non-linear dimensionality reduction methods), the embedding of the Quattro Fontanili necropolis was rather complex: there were in fact non-linear clusters or clusters that were often interconnected. The situation differs markedly from the necropolis of Pianello di Genga where it is possible to identify 3 more or less circular clusters, which are extremely simple to identify. The scenario with features extracted with Vectorization, and reduction with UMAP using #_neighbors = 10 (Fig. 52) is repeated.
a) Quattro Fontanili UMAP embedding with cluster. The grey markers represent the noise-points.
a) Quattro Fontanili UMAP embedding with cluster. The grey markers represent the noise-points.
9) Hierarchical condensed tree using eom as cluster_selection_method.
9) Hierarchical condensed tree using eom as cluster_selection_method.
Table 7. The table offers the median results of the clustering metrics calculation as described in the text. In bold style are the best results, which are attributable to the HDBSCAN method. In terms of formulation, these types of algorithms can fail when analysing a large number of clusters, so it is decided to use an equal number of clusters '° (3) for each algorithm to calculate the correspondence between cluster: and functional groups and within these. Thus, 3 clusters are randomly selected for each algorithm and within thes¢ the calculation of the metrics is performed. The process was carried out 100 times to sample different clusters. A median table of results is then proposed (Tab. 7).
Table 7. The table offers the median results of the clustering metrics calculation as described in the text. In bold style are the best results, which are attributable to the HDBSCAN method. In terms of formulation, these types of algorithms can fail when analysing a large number of clusters, so it is decided to use an equal number of clusters '° (3) for each algorithm to calculate the correspondence between cluster: and functional groups and within these. Thus, 3 clusters are randomly selected for each algorithm and within thes¢ the calculation of the metrics is performed. The process was carried out 100 times to sample different clusters. A median table of results is then proposed (Tab. 7).
a) Dendrogram showing the number of clusters identified.
a) Dendrogram showing the number of clusters identified.
Figure 55. Comparison of clustering algorithms diagnostic plots.
Figure 55. Comparison of clustering algorithms diagnostic plots.
Figure 56. Quattro Fontanili embeddings according to each clustering algorithm.
Figure 56. Quattro Fontanili embeddings according to each clustering algorithm.
Figure 58. Imaginary taxonomic scale and relative position of each typology in Cardarelli (2023). The necessity for a reference and classification system in ceramics is particularly evident in the study conducted by Cardarelli (2023). The study compares the results of typological classifications performed on protohistoric materials using traditional methods with those obtained using the proposed pipeline (vectorisation + UMAP + HDBSCAN). The results highlight the capability of the proposed digital typology to generate digital types with minimal morphological variability, consisting of a similar number of specimens on average. The varying levels of morphological variability observed among the different traditional types suggest that a type proposed by one author does not correspond to a type proposed by another author, as they exhibit taxonomic differences in terms of variability. Consequently, the types identified by different methods exist at different levels, and their relationship can be better understood and contextualised by considering this ‘objective’ support (Fig. 58).
Figure 58. Imaginary taxonomic scale and relative position of each typology in Cardarelli (2023). The necessity for a reference and classification system in ceramics is particularly evident in the study conducted by Cardarelli (2023). The study compares the results of typological classifications performed on protohistoric materials using traditional methods with those obtained using the proposed pipeline (vectorisation + UMAP + HDBSCAN). The results highlight the capability of the proposed digital typology to generate digital types with minimal morphological variability, consisting of a similar number of specimens on average. The varying levels of morphological variability observed among the different traditional types suggest that a type proposed by one author does not correspond to a type proposed by another author, as they exhibit taxonomic differences in terms of variability. Consequently, the types identified by different methods exist at different levels, and their relationship can be better understood and contextualised by considering this ‘objective’ support (Fig. 58).
Figure 59. Three different embeddings represent information on the absolutely qualitative dimension, morphology, dimension, and their union in the fourth and overall embedding.
Figure 59. Three different embeddings represent information on the absolutely qualitative dimension, morphology, dimension, and their union in the fourth and overall embedding.
n [he purpose of this chapter is to compare the various methods of feature extraction. Basically, for each feature extraction method, the pipe/ine consisting of UMAP and HDBSCAN is proposed (§ Proposal of a pipeline for the study and analysis of vessels’ profile), the embedding and clustering results are analysed. To this will be added a performance check, where the time required for feature extraction and the dimensionality reduction process with UMAP will be measured. The dataset analysed will be that of funeral urns in the MBA — AP period (§ The dataset). All function arguments have been left by default. The experiments were carried out on both available devices during the PhD!8 (§ Hardware used). The results are always expressed in seconds. Once the main methodologies used in this study have been outlined, this chapter will move on to the actual analysis of the dataset. The approach is to carry out several case studies with the dual aim of showing both the potential of the applied method and answering some archaeological questions, as well as raising some methodological issues or considerations. The applications will start with a comparison between proposed Features extraction methods (§ Comparison between Features extraction methods: a benchmark). Then, I will proceed to define the complexity of a ceramic shape and its diachronic implications (§ Complexity in funeral urns and vascular production between EBA and AP). After that, the standardisation analysis will be applied to the entire dataset (§ Standardisation analysis: a proposal of a method and its application: EBA - AP). The analysis will then shift to the global analysis of a ceramic assemblage using the non-linear dimensionality reduction techniques proposed in this work (§ Pottery assemblages maps) and to more experimental techniques, such as an ML application to reconstruct entire vascular forms from fragments (§ Reconstructing entire vessels from fragments: an ML approach). Each chapter will be accompanied by a supplementary notebook in the Supplementary Materials, providing a detailed description and justification for each analvsis choice made.
n [he purpose of this chapter is to compare the various methods of feature extraction. Basically, for each feature extraction method, the pipe/ine consisting of UMAP and HDBSCAN is proposed (§ Proposal of a pipeline for the study and analysis of vessels’ profile), the embedding and clustering results are analysed. To this will be added a performance check, where the time required for feature extraction and the dimensionality reduction process with UMAP will be measured. The dataset analysed will be that of funeral urns in the MBA — AP period (§ The dataset). All function arguments have been left by default. The experiments were carried out on both available devices during the PhD!8 (§ Hardware used). The results are always expressed in seconds. Once the main methodologies used in this study have been outlined, this chapter will move on to the actual analysis of the dataset. The approach is to carry out several case studies with the dual aim of showing both the potential of the applied method and answering some archaeological questions, as well as raising some methodological issues or considerations. The applications will start with a comparison between proposed Features extraction methods (§ Comparison between Features extraction methods: a benchmark). Then, I will proceed to define the complexity of a ceramic shape and its diachronic implications (§ Complexity in funeral urns and vascular production between EBA and AP). After that, the standardisation analysis will be applied to the entire dataset (§ Standardisation analysis: a proposal of a method and its application: EBA - AP). The analysis will then shift to the global analysis of a ceramic assemblage using the non-linear dimensionality reduction techniques proposed in this work (§ Pottery assemblages maps) and to more experimental techniques, such as an ML application to reconstruct entire vascular forms from fragments (§ Reconstructing entire vessels from fragments: an ML approach). Each chapter will be accompanied by a supplementary notebook in the Supplementary Materials, providing a detailed description and justification for each analvsis choice made.
Table 8. Features extraction benchmark. The table shows the timing of dimensionality reduction with UMAP (Tab. 9). In this case, Vectorization took the longest, followed by HOGs and finally EFA and VAE. Embeddings are normalised (they are forcibly scaled between 0 and 1 a#as min-max normalisation).
Table 8. Features extraction benchmark. The table shows the timing of dimensionality reduction with UMAP (Tab. 9). In this case, Vectorization took the longest, followed by HOGs and finally EFA and VAE. Embeddings are normalised (they are forcibly scaled between 0 and 1 a#as min-max normalisation).
Table 10. Pairwise UMAP embedding procrusted analysis. Pairwise means that all data points are compared with each other, including comparisons with themselves. In fact, on the diagonal of the matrix, the distance is always 0.
Table 10. Pairwise UMAP embedding procrusted analysis. Pairwise means that all data points are compared with each other, including comparisons with themselves. In fact, on the diagonal of the matrix, the distance is always 0.
Figure 60. Embeddings comparison. Markers are coloured according to Functional Class.
Figure 60. Embeddings comparison. Markers are coloured according to Functional Class.
This result does not mean that EFA produces erroneous results, but that it simply describes the morphology of the vessels differently, whereas Vectorization, HOGs and VAE obtain very similar cluster and noise-point values. It is evident that the vanilla parameters of HDBSCAN cannot be used for EFA, when they offer a tendentially plausible result for the other feature extraction methods. Figure 61. Embedding clustering comparison. The colour of each cluster is assigned randomly, while the grey dots represent the noise points.
This result does not mean that EFA produces erroneous results, but that it simply describes the morphology of the vessels differently, whereas Vectorization, HOGs and VAE obtain very similar cluster and noise-point values. It is evident that the vanilla parameters of HDBSCAN cannot be used for EFA, when they offer a tendentially plausible result for the other feature extraction methods. Figure 61. Embedding clustering comparison. The colour of each cluster is assigned randomly, while the grey dots represent the noise points.
CO Z 4 4 A sufficient number of harmonics is chosen (25 harmonics — Fig. 62) to accurately describe and represent all the morphological characteristics of the vessel. The distance is measured with its increasingly complex representations, starting from low-complexity representations. Figure 62. Binary matrix and its representation by 25 harmonics. It can be observed that in the representation by harmonics, all the characteristics of the original vessel in a binary matrix are accurately depicted.
CO Z 4 4 A sufficient number of harmonics is chosen (25 harmonics — Fig. 62) to accurately describe and represent all the morphological characteristics of the vessel. The distance is measured with its increasingly complex representations, starting from low-complexity representations. Figure 62. Binary matrix and its representation by 25 harmonics. It can be observed that in the representation by harmonics, all the characteristics of the original vessel in a binary matrix are accurately depicted.
Figure 63. Comparison between corrected and simplified versions of the records PDG_0001 (a) and PDG_0081 (b). Below each simplified version are the Procrustes distance and Hausdorff distance.
Figure 63. Comparison between corrected and simplified versions of the records PDG_0001 (a) and PDG_0081 (b). Below each simplified version are the Procrustes distance and Hausdorff distance.
Figure 64. Comparison between corrected and simplified versions of the records PDG_0095 (a) and PDG_0102 (b). Below each simplified version are the Procrustes distance and Hausdorff distance.
Figure 64. Comparison between corrected and simplified versions of the records PDG_0095 (a) and PDG_0102 (b). Below each simplified version are the Procrustes distance and Hausdorff distance.
Higher numbers of harmonics result in profiles that better capture the original characteristics. This is evident not only in the representation itself but also in the values of the distances. Additionally, it can be observed that lower numbers of harmonics (e.g., 3 and 4 harmonics) primarily capture general complexities within the profile, such as prominent keel, or shoulder. In contrast, higher numbers of hanwonics can capture more localised complexities and specific characteristics, such as the shape of the rim, as they provide a more detailed definition of the overall shape. In order to have a relative comparison, the values of the Procrustes distance and Hausdorff distance have been plotted on a eraph (Fig. 65). igure 65. Line plots showing differences between original shape and its simplified versions using Procrustes distance (a) and Hausdorff distance (b).
Higher numbers of harmonics result in profiles that better capture the original characteristics. This is evident not only in the representation itself but also in the values of the distances. Additionally, it can be observed that lower numbers of harmonics (e.g., 3 and 4 harmonics) primarily capture general complexities within the profile, such as prominent keel, or shoulder. In contrast, higher numbers of hanwonics can capture more localised complexities and specific characteristics, such as the shape of the rim, as they provide a more detailed definition of the overall shape. In order to have a relative comparison, the values of the Procrustes distance and Hausdorff distance have been plotted on a eraph (Fig. 65). igure 65. Line plots showing differences between original shape and its simplified versions using Procrustes distance (a) and Hausdorff distance (b).
Figure 66. Image processing for Dimensional correction: 1) Original image 2) Extraction of the bounding box 3) Forced resizing. Before moving on to further analysis, one consideration must be made: during the process of creating pofds, the images are insert into a square box without distorting their aspect-ratio. This means that taller pots will suffer a greater reduction in size than low pots (such as open forms), which instead are better adapted to being inserted and resised within a square. This leads to the reduction in dimensionality of specific morphological features. For this reason, all the vessels are forcibly scaled within a square box, so that the ‘horizontal’ morphological features stand out (Fig. 66). This process is called Dimensional correction.
Figure 66. Image processing for Dimensional correction: 1) Original image 2) Extraction of the bounding box 3) Forced resizing. Before moving on to further analysis, one consideration must be made: during the process of creating pofds, the images are insert into a square box without distorting their aspect-ratio. This means that taller pots will suffer a greater reduction in size than low pots (such as open forms), which instead are better adapted to being inserted and resised within a square. This leads to the reduction in dimensionality of specific morphological features. For this reason, all the vessels are forcibly scaled within a square box, so that the ‘horizontal’ morphological features stand out (Fig. 66). This process is called Dimensional correction.
Figure 67. Line plots showing differences between original shape and its simplified versions using Procrustes distance (a) and Hausdorff distance (b) (Weighted Complexity).
Figure 67. Line plots showing differences between original shape and its simplified versions using Procrustes distance (a) and Hausdorff distance (b) (Weighted Complexity).
‘igure 68. Scatterplot showing correlation between Procrustes and Hausdorff distances. The correlation between the two measutes is evident.
‘igure 68. Scatterplot showing correlation between Procrustes and Hausdorff distances. The correlation between the two measutes is evident.
Table 11. Urns number for each wide_chronology. Urns are analysed as a set of objects with similar morphology and, above all, identical function. The number of urns within AIPPD amounts to 2487, divided as follows by wide_chronology (Tab. 11). Regarding results obtained in the previous chapter, an arbitrary choice is made in using the Procustes distance in the calculation of complexity. Furthermore, harmonic @3 is discarded in order to focus the algorithm’s attention on more local characteristics.
Table 11. Urns number for each wide_chronology. Urns are analysed as a set of objects with similar morphology and, above all, identical function. The number of urns within AIPPD amounts to 2487, divided as follows by wide_chronology (Tab. 11). Regarding results obtained in the previous chapter, an arbitrary choice is made in using the Procustes distance in the calculation of complexity. Furthermore, harmonic @3 is discarded in order to focus the algorithm’s attention on more local characteristics.
Figure 70. Complex (a) and simplex (b) urns. ids and Procrustes distance of each record are provided.
Figure 70. Complex (a) and simplex (b) urns. ids and Procrustes distance of each record are provided.
Figure 71. Funerary urns complexity.
Figure 71. Funerary urns complexity.
Figure 72, Example of the selection of the base area of the vessel using Binary Matrices. To do this, it is therefore necessary to first identify and eliminate the vessels with base and then repeat the operation. Within the binary matrices, the area corresponding to the base is selected as in the example (Fig. 72).
Figure 72, Example of the selection of the base area of the vessel using Binary Matrices. To do this, it is therefore necessary to first identify and eliminate the vessels with base and then repeat the operation. Within the binary matrices, the area corresponding to the base is selected as in the example (Fig. 72).
For this subsection of the urns, feature extraction method EFA was applied, followed by UMAP for visualisation using a scatterplot in two dimensions (Fig. 73, a).
For this subsection of the urns, feature extraction method EFA was applied, followed by UMAP for visualisation using a scatterplot in two dimensions (Fig. 73, a).
The result of the embedding reveals a complex structure consisting of two main groups (Fig. 73, a). It is suspected that one of these groups includes vessels with articulated foot, while the other group represents vessels with flat ot unartticulated bases.
The result of the embedding reveals a complex structure consisting of two main groups (Fig. 73, a). It is suspected that one of these groups includes vessels with articulated foot, while the other group represents vessels with flat ot unartticulated bases.
O Lt OI 7 a Cluster 1 (Figure 73, b) is indeed characterised by the presence of a more developed foot, unlike the other clusters Fig. 74). Figure 74, Heatmap of the clusters identified by GaussianMixtureClustering. Warmer colours represent zones with major overlap. The presence of the articulated foot in cluster 1 is clearly visible.
O Lt OI 7 a Cluster 1 (Figure 73, b) is indeed characterised by the presence of a more developed foot, unlike the other clusters Fig. 74). Figure 74, Heatmap of the clusters identified by GaussianMixtureClustering. Warmer colours represent zones with major overlap. The presence of the articulated foot in cluster 1 is clearly visible.
Figure 75. Complexity of urns without an articulated foot. By removing cluster 1, and consequently all shapes characterised by an articulated foot, it is possible to verify whether the increase in complexity in a diachronic sense may depend exclusively on this morphological feature. The result is shown in the boxplot (Fig. 75), where the trend shown in Fig. 71 is even accentuated. It would thus seem that the presence of the articulated foot contributes and does not determine the complexity of a given chronology.
Figure 75. Complexity of urns without an articulated foot. By removing cluster 1, and consequently all shapes characterised by an articulated foot, it is possible to verify whether the increase in complexity in a diachronic sense may depend exclusively on this morphological feature. The result is shown in the boxplot (Fig. 75), where the trend shown in Fig. 71 is even accentuated. It would thus seem that the presence of the articulated foot contributes and does not determine the complexity of a given chronology.
4 7 However, the issue is easy to solve. It would be sufficient to calculate the average Weighted Complexity for each context and then for each chronology. Thus, the context is used as the éaget and no longer the individual record. Furthermore, those contexts with less than 3 records are removed from the analysis to make the result more robust. Visualising Fig. 76, it can be stated that the trend highlighted in the previous analyses is real within all contexts. Figure 76. Boxplot showing the average Complexity scores of each context.
4 7 However, the issue is easy to solve. It would be sufficient to calculate the average Weighted Complexity for each context and then for each chronology. Thus, the context is used as the éaget and no longer the individual record. Furthermore, those contexts with less than 3 records are removed from the analysis to make the result more robust. Visualising Fig. 76, it can be stated that the trend highlighted in the previous analyses is real within all contexts. Figure 76. Boxplot showing the average Complexity scores of each context.
the sample may create peaks or troughs, a trend towards greater complexity for each context type highlighted seems to be evident.
the sample may create peaks or troughs, a trend towards greater complexity for each context type highlighted seems to be evident.
Figure 77. Complex (a) and simplex (b) shapes. ids and Procrustes distance of each record are provided.
Figure 77. Complex (a) and simplex (b) shapes. ids and Procrustes distance of each record are provided.
Figure 79. Boxplot realised through the scores divided by Functional class. In addition, a line representing the median values of open and closed shapes is plotted (Open/Closed shapes).
Figure 79. Boxplot realised through the scores divided by Functional class. In addition, a line representing the median values of open and closed shapes is plotted (Open/Closed shapes).
Figure 80. Average complexity for each type of context
Figure 80. Average complexity for each type of context
Figure 81. Reconstruction from Test set.
Figure 81. Reconstruction from Test set.
Figure 82. Toy-dataset example (see text). It is worth noting that the dataset used in this example is very simple, with only two features and two clear clusters. In the actual data being analysed, the situation is more complex as it is necessary to calculate distances within a high- dimensional dataset. In this case, it was chosen to define the clusters on the UMAP embedding, but to calculate the distance within the original VAE representation, due to the non-linear nature of the dimensionality reduction algorithm, which could lead to the definition of unrepresentative distances.
Figure 82. Toy-dataset example (see text). It is worth noting that the dataset used in this example is very simple, with only two features and two clear clusters. In the actual data being analysed, the situation is more complex as it is necessary to calculate distances within a high- dimensional dataset. In this case, it was chosen to define the clusters on the UMAP embedding, but to calculate the distance within the original VAE representation, due to the non-linear nature of the dimensionality reduction algorithm, which could lead to the definition of unrepresentative distances.
figure 83. Some of the clusters used for the calculation of standardisation metrics are shown below. Each pair of row represents a cluster.
figure 83. Some of the clusters used for the calculation of standardisation metrics are shown below. Each pair of row represents a cluster.
Figure 84. context_score for context_typology. Finally, as far as the dimensional score is concerned, we see that it declines in the middle stages of the period analysed (FBA, EIA1) and then tends to rise again.
Figure 84. context_score for context_typology. Finally, as far as the dimensional score is concerned, we see that it declines in the middle stages of the period analysed (FBA, EIA1) and then tends to rise again.
As far as the extra-cluster distance is concerned, on the other hand, the values of urn and cover tend to decrease while the value of grave goods increases from the EIA1 phase onwards. The Covers do not seem to show a clea: trend. Finally, turning to dimensional analysis, we see that the dimensional_score of Cover and Grave good tends tc increase substantially from the EIA2 stage onwards, while urns tend to behave differently, showing greate! dimensional variability over time. Figure 85. context_score for correspondence_funerary.
As far as the extra-cluster distance is concerned, on the other hand, the values of urn and cover tend to decrease while the value of grave goods increases from the EIA1 phase onwards. The Covers do not seem to show a clea: trend. Finally, turning to dimensional analysis, we see that the dimensional_score of Cover and Grave good tends tc increase substantially from the EIA2 stage onwards, while urns tend to behave differently, showing greate! dimensional variability over time. Figure 85. context_score for correspondence_funerary.
Figure 86. contect_score for manufacture and material.
Figure 86. contect_score for manufacture and material.
EO a ee Se Ne SESW CNIS ENESCO e nS Ne See Sen cew Te RN TORT Te SEES TR WSN NENTS AE Te UERENWA NTS TSN SEA TORENT Nn cee CNW STENT On TEE NCTE s + SWMnnoeW a MenennE nT aveTT ere Let us take the most generic dynamic as an example: only one context score is obtained for each context, as an example (Fig. 84). When we calculate the ratio between the two measures, we obtain the following values shown by boxplots (Fig. 87). Figure 87. Ratio between dntra-cluster and extra-cluster distances.
EO a ee Se Ne SESW CNIS ENESCO e nS Ne See Sen cew Te RN TORT Te SEES TR WSN NENTS AE Te UERENWA NTS TSN SEA TORENT Nn cee CNW STENT On TEE NCTE s + SWMnnoeW a MenennE nT aveTT ere Let us take the most generic dynamic as an example: only one context score is obtained for each context, as an example (Fig. 84). When we calculate the ratio between the two measures, we obtain the following values shown by boxplots (Fig. 87). Figure 87. Ratio between dntra-cluster and extra-cluster distances.
Figure 88. Intra-cluster and extra-cluster distances model. A graphical representation of the phenomenon is proposed: in Fig. 88, a the clusters are characterised by a high intra-cluster distance and a low extra-cluster distance, and this is the feature highlighted by the oldest phases of the period under consideration. On the contrary, in Fig. 88, b the clusters are characterised by a low intra-cluster distance and a high extra-cluster distance, features that are instead found in the most recent phases of the period.
Figure 88. Intra-cluster and extra-cluster distances model. A graphical representation of the phenomenon is proposed: in Fig. 88, a the clusters are characterised by a high intra-cluster distance and a low extra-cluster distance, and this is the feature highlighted by the oldest phases of the period under consideration. On the contrary, in Fig. 88, b the clusters are characterised by a low intra-cluster distance and a high extra-cluster distance, features that are instead found in the most recent phases of the period.
Figure 89. Ratio between sntra-cluster and extra-cluster distances using only context in continuity.
Figure 89. Ratio between sntra-cluster and extra-cluster distances using only context in continuity.
Figure 90. intra-cluster distance between specialised and non-specialised production.
Figure 90. intra-cluster distance between specialised and non-specialised production.
Figure 91. extra-cluster distance between specialised and non-specialised production.
Figure 91. extra-cluster distance between specialised and non-specialised production.
Figure 92. Osteria dell’Osa embedding using PCA (a) and UMAP (b).
Figure 92. Osteria dell’Osa embedding using PCA (a) and UMAP (b).
Figure 93. Quattro Fontanili embedding using UMAP. Upon analysing the embedding of the EIA2 phase of the Quattro Fontanili necropolis, we observe a much more complex situation: the functional classes do not seem to be as clearly divided into distinct groups as they were in the case of Osteria dell’Osa, and the structure of the clusters appears to be significantly more complex and challenging tc analyse. From these graphs, it is immediately apparent that there is a stronger correspondence between morphology (VAE) and functional interpretation at Osteria dell’?Osa compared to Quattro Fontanili. On the other hand, the material culture, and relationships between the ceramics at Quattro Fontanili seem significantly more complex (Fig. 93).
Figure 93. Quattro Fontanili embedding using UMAP. Upon analysing the embedding of the EIA2 phase of the Quattro Fontanili necropolis, we observe a much more complex situation: the functional classes do not seem to be as clearly divided into distinct groups as they were in the case of Osteria dell’Osa, and the structure of the clusters appears to be significantly more complex and challenging tc analyse. From these graphs, it is immediately apparent that there is a stronger correspondence between morphology (VAE) and functional interpretation at Osteria dell’?Osa compared to Quattro Fontanili. On the other hand, the material culture, and relationships between the ceramics at Quattro Fontanili seem significantly more complex (Fig. 93).
Figure 94. Osteria dell’Osa (all chronology) embedding using UMAP.
Figure 94. Osteria dell’Osa (all chronology) embedding using UMAP.
Figure 96. ELA1 clustermap.
Figure 96. ELA1 clustermap.
Figure 98. Entire and fragmented pots. As clarified in the text, the purpose of this action is to simulate the creation of fragments from entire pots.
Figure 98. Entire and fragmented pots. As clarified in the text, the purpose of this action is to simulate the creation of fragments from entire pots.
Figure 100. Training set: some examples of reconstruction using BCE — 2. As we teach epoch 50, the provided examples show no significant problems, and the reconstructions appear to be accurate overall. However, there is still uncertainty regarding certain morphological features, such as in Fig. 100, b, 5, where the rim features cannot be reconstructed correctly due to the poor preservation of the fragment. Again, it is important to note that this behaviour cannot be considered an error, as the limited morphological features preserved in the fragment are insufficient for the complete reconstruction. The introduction of a second neural network in the process will help the model bias towards providing a plausible profile, compensating for these limitations.
Figure 100. Training set: some examples of reconstruction using BCE — 2. As we teach epoch 50, the provided examples show no significant problems, and the reconstructions appear to be accurate overall. However, there is still uncertainty regarding certain morphological features, such as in Fig. 100, b, 5, where the rim features cannot be reconstructed correctly due to the poor preservation of the fragment. Again, it is important to note that this behaviour cannot be considered an error, as the limited morphological features preserved in the fragment are insufficient for the complete reconstruction. The introduction of a second neural network in the process will help the model bias towards providing a plausible profile, compensating for these limitations.
Figure 102. Reconstruction loss.
Figure 102. Reconstruction loss.
Figure 103. Real fragments have been reconstructed. The reconstruction is remarkably faithful, yielding a highly verisimilar result. To demonstrate this application, a sample of 10 fragmented vessels from the Quattro Fontanili necropolis was selected, and cards were generated (see Fig. 103, a). These cards were then processed through the trained model, including both the VAE and the denoiser, resulting in excellent or highly positive outcomes (see Fig. 103, b). Naturally, as these are real fragments, it is not possible to measure their accuracy objectively. However, the overall features appear plausible, and the local morphological details seem well-preserved.
Figure 103. Real fragments have been reconstructed. The reconstruction is remarkably faithful, yielding a highly verisimilar result. To demonstrate this application, a sample of 10 fragmented vessels from the Quattro Fontanili necropolis was selected, and cards were generated (see Fig. 103, a). These cards were then processed through the trained model, including both the VAE and the denoiser, resulting in excellent or highly positive outcomes (see Fig. 103, b). Naturally, as these are real fragments, it is not possible to measure their accuracy objectively. However, the overall features appear plausible, and the local morphological details seem well-preserved.
Related topics:
Pottery (Archaeology)Quantitative methods (Archaeology)
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved