Table 1
Summary of sampled modern and archaeological species.
| SPECIES | VARIETY | CURATOR | NUMBER |
|---|---|---|---|
| Alpine ibex (Capra ibex) | Archaeological from Southern Alps (Liguro-Provençal Bassin) | Museum of Prehistoric Anthropology of Monaco – Archeological site of “Grotte de l’Observatoire” | 29 |
| Modern from Alps | Osteological collection from Thierry Argant (Éveha Lyon, ArAr UMR 5138) | 1 | |
| Goat (Capra sp.) | Modern Capra nubiana (zoological specimen) | National Museum of Natural History Paris’ Mammalian and Birds collection | 2 |
| Modern domestic goat from France | Osteological collections from Archéorient UMR 5133; National Museum of Natural History Paris’ Mammalian and Birds collection | 5 | |
| Modern domestic goat from Iran | Osteological collections from Bioarchaeology Laboratory, University of Tehran, Iran | 20 | |
| Modern domestic goat from Egypt (zoological specimen) | National Museum of Natural History Paris’ Mammalian and Birds collection | 2 | |
| Modern feral goat from Crete (Capra aegagrus cretica) | Osteological collections from Archéorient UMR 5133 | 1 | |
| Roe deer (Capreolus capreolus) | Modern from France | National Museum of Natural History Paris’ Mammalian and Birds collection | 30 |
| Gazelle (Gazella sp.) | Modern Gazella cuvieri | National Museum of Natural History Paris’ Mammalian and Birds collection | 2 |
| Modern Gazella dorcas | National Museum of Natural History Paris’ Mammalian and Birds collection | 5 | |
| Modern Gazella spekei | National Museum of Natural History Paris’ Mammalian and Birds collection | 1 | |
| Modern Gazella sp. | National Museum of Natural History Paris’ Mammalian and Birds collection; Osteological collections from Archéorient UMR 5133 | 7 | |
| Archaeological from Syria (Gazella cf. subgutturosa?) | Daniel Helmer – Emmanuelle Vila (UMR 5133 Archéorient) | 15 | |
| Sheep (Ovis aries) | Modern sheep from France | Osteological collections from CEPAM UMR 7264, AASPE UMR 7209 & Archéorient UMR 5133 | 7 |
| Modern sheep from Ethiopia | ILRI – Agraw Amane – Emmanuelle Vila – EvoSheep projet (ANR ANR-17-CE27-0004) | 23 | |
| Total of 3D astragali | 150 |
Figure 1
3D astragalus presented in dorsal view of (a) Alpine ibex (Capra ibex), (b) sheep (Ovis aries), (c) goat (Capra hircus), (d) roe deer (Capreolus capreolus) and (e) gazelle (Gazella sp.). Alpine ibex astragalus is untextured.
Figure 2
Evolution of the simplicial complex of a 3D astragalus (reference name Obs_1997_187) during the Alpha filtration process, highlighting the impact of varying radius thresholds r. (Left) At this stage, the bone’s structure is partially reconstructed, with multiple connected components and some topological cycles, 1-dimensional features, visible. (Center) The Alpha complex has merged into a single connected component, capturing the overall structure of the bone. The cycles from the previous step have been filled (died), and the complex closely approximates the 3D shape of the bone. (Right) At this advanced stage, most topological cycles have disappeared, and the complex over-reconstructs the bone’s shape. The filtration process concludes once all topological voids, 2-dimensional features, are filled.
Figure 3
Wasserstein kernel matrices without bone’s normalisation. Up: topological dimension 1; Down: topological dimension 2. For both the matrices the color code, indicated by the colour bar on the right of the matrix, represents pairwise similarity within the range [0, 1]. Yellow cells (similarity equals to 1), such as those along the diagonal, signify that the x and y bones are identical. As the color shifts towards blue, the bones exhibit increasing dissimilarity (similarity approaching 0).
Figure 4
Illustration of topological dissimilarities observed in sheep in the Wasserstein kernel matrices without bone’s normalisation (dimension 1). Picture of sheep breed “Bonga” (a) and “Menz” (b) from Ethiopia © A. Amane / E. Vila. c) Picture of sheep breed “Landes de Bretagne” from France ©H. Ronné https://www.ecomusee-rennes-metropole.fr/le-mouton-des-landes/.
Figure 5
Wasserstein kernel matrices with bone’s normalisation. Up: topological dimension 1; Down: topological dimension 2. For both the matrices the color code, indicated by the colour bar on the right of the matrix, represents pairwise similarity within the range [0, 1]. Yellow cells (similarity equals to 1), such as those along the diagonal, signify that the x and y bones are identical. As the color shifts towards blue, the bones exhibit increasing dissimilarity (similarity approaching 0).
Table 2
Average test classification accuracy.
| ACC. std.dv. | ALPINE IBEX | GOAT | ROE DEER | GAZELLE | SHEEP | |
|---|---|---|---|---|---|---|
| Multiple KLR | 0.8110.064 | 0.9730.061 | 0.6230.218 | 0.9270.101 | 0.8970.124 | 0.6370.228 |
Figure 6a
Boxplot average test classification accuracies. The first column (leftmost) represents the average performance over the five classes, while the others show the average accuracy for each specie. The central line (orange) within each box represents the median accuracy, while the lower and upper edges of the box correspond to the first (Q1) and third quartiles (Q3), respectively, indicating the interquartile range (IQR). The whiskers extend to the minimum and maximum values within (1.5*IQR) from Q1 and Q3. Beyond this range are considered outliers and are shown as individual markers.
Table 3
Kernel weight’s estimates.
| KERNEL WEIGHTS (POSTERIOR MEAN) | ||||
|---|---|---|---|---|
| β1 | β2 | β3 | β4 | |
| IW-SWI | 0.2310.007 | 0.2330.006 | 0.2750.010 | 0.4810.020 |
Figure 6b
Kernel densities estimates. Different colors correspond to the weights of the four Wasserstein kernel matrices obtained via TDA. The X axis corresponds to weights values, while the y axis indicates the estimated density, reflecting the relative frequency of occurrence. Peaks in the density curves show the most probable values of the weights, while the spread of each distribution provides insight into the variability and uncertainty of the estimates.
Figure 7
Learned kernel matrix for a single data split. It represents the optimal linear combination, where each input kernel matrix is weighted by its corresponding estimated weight value. The color code follows the same interpretation as in Figures 3 and 5.