Multi‐isotope fingerprints in the bioapatite of archaeological skeletons are mostly superior over single isotope analyses for provenance studies. Gaussian mixture model (GMM) clustering is a novel tool for a similarity search among multidimensional data sets and at the same time permits the evaluation of the structural importance of particular isotopic ratios in the data set. We applied three GMM clustering experiments on multi‐isotope fingerprints—stable strontium (Sr), lead (Pb) and oxygen (O) isotopic ratios—established in 217 archaeological animal bones excavated along a specific transect across the European Alps. This reference region had been in use since prehistoric times by humans who crossed the Alps from north to south, andvice versa. The resulting clusters permit a spatial assignment of the specimens with a very high probability, in particular with regard to the geological complexity of the region. A combination of Sr with Pb stable isotopes led to an optimal differentiation between the southern and northern Alpine forelands that cannot be distinguished from each other by87Sr/86Sr ratios alone, while the contribution of δ18O is not particularly high. The isotopic mapping and subsequent cluster analysis is suitable for the analysis of archaeological human finds and the reconstruction of the direction of transalpine mobility and trade.

Around 450 BCE, the Fritzens-Sanzeno culture emerged as a fairly uniform culture to the south of the European Alps and inneralpine regions along the Inn-Eisack-Adige-Brenner passage, a transalpine route that had been in use since the Mesolithic. By the Iron Age, an efficient communication network across the Alps enabling quick culture transfer was established since long. The open question remains as to whether the spread of this culture was due to migration or acculturation processes. 92 human individual skeletons, most of them cremated, were sampled from archaeological sites along the alpine transect. A multi-isotope fingerprint consisting of Sr-87/Sr-86, (208)pb/(204)pb, (207)pb/(204)pb, (206)pb/(204)pb, (208)pb/(207)pb, (206)pb/Pb-207 was established on compact bone samples, and the structure of this multidimensional data-set was evaluated by Gaussian Mixture Model clustering. Resulting clusters firmly reflect the geographical location of the sites of recovery and identified archaeological conspicuous burials as primarily non-local individuals. Strontium stable isotopes were of greatest importance for provenancing migrants. The clusters are also capable of identifying mixed isotopic ratios in early immigrants with a high probability. Lead stable isotopes of all individuals are compatible with the isotopic signatures of the inneralpine copper ores that were heavily exploited that time. This similarity with regard to Pb, and the fact that non-local individuals were only detected at sites that had served as former rest stations along the transect, supports the hypothesis that the spread of the Fritzens-Sanzeno culture resulted from an intensification of contacts rather than migration.

Cremated human remains are a rather neglected research substrate in physical anthropology; its investigation is still mainly restricted to the osteological level. The application of archaeometric methods to cremations is limited because the organic skeletal components are fully combusted at high temperatures. Stable isotope ratios of heavy elements such as strontium and lead, however, are thermally stable and permit research targeting questions of mobility, migration, and trade. In many cremations, neither dental remains nor the petrous bone are preserved. In such case, no skeletal element that retains the isotopic signature of childhood is available and compact bone has to be chosen instead. This raises interpretive problems, since due to its slow remodeling rate, compact bone integrates the element uptake over many years prior to death. This can generate a mixed isotope ratio in migrants. Such mixed ratios are no longer compatible with the place of origin, and not yet with the place of recovery. Provenance analysis with a single isotope ratio (mostly 87Sr/86Sr) therefore has its limits. A combination of strontium and lead stable isotopes in cremations generates a multi-dimensional isotopic fingerprint that is however more difficult to interpret. Data mining methods that permit a similarity search are a promising approach. In this paper, possibilities and limitations of stable isotope analysis of cremated finds are discussed together with the substrate-specific methodological and interpretive problems. The research potential is demonstrated by use of selected examples.

Correlation clustering detects complex and intricate relationships in high-dimensional data by identifying groups of data points, each characterized by differents correlation among a (sub)set of features. Current correlation clustering methods generally limit themselves to linear correlations only. In this paper, we introduce a method for detecting global non-linear correlated clusters focusing on quadratic relations. We introduce a novel Hough transform for the detection of hyperparaboloids and apply it to the detection of hyperparaboloid correlated clusters in arbitrary high-dimensional data spaces. Non-linear correlation clustering like our method can reveal valuable insights which are not covered by current linear versions. Our empirical results on synthetic and real world data reveal that the proposed method is robust against noise, jitter and irregular densities.

A multi‐isotope fingerprint consisting of δ 18 O phosphate , 87 Sr/ 86 Sr, 208 Pb/ 204 Pb, 207 Pb/ 204 Pb, 206 Pb/ 204 Pb, 208 Pb/ 207 Pb and 206 Pb/ 207 Pb was established in the bioapatite of 219 individual archaeofaunal remains (cattle, pig, red deer) excavated from sites located along a specific transect of the European Alps, namely the Inn–Eisack–Adige–Brenner Passage, that has been of eminent importance since European prehistory. This reference area is vertically stratified, and since δ 18 O in the skeleton is influenced by climate, water source, physiology and even culture, we tested the relative contribution and importance of δ 18 O as a component of the multi‐isotope fingerprint for provenance analysis in this alpine region by a novel mathematical approach. In particular, we adapted a supervised learning approach through expectation–maximization (EM) clustering for fingerprint extraction and evaluated the contribution of each isotopic ratio to the data structure. While an altitude effect was evident in δ 18 O, its overall structural importance in the complete isotopic fingerprint was rather low. Therefore, provenance analysis of bioarchaeological finds in this region is possible by measuring stable Sr and Pb ratios alone, which is of considerable importance when δ 18 O values are not available, e.g., in cremated finds, although some information is lost. Whether this is tolerable depends on the scientific question to be solved.

Palaeobiodiversity research based on stable isotope analysis in coastal environments can be severely hampered by the so-called "sea spray" effect. This effect shifts the isotopic signal of terrestrial individuals towards too marine values. It is commonly agreed upon that sea spray influences sulphur stable isotopes. However, we were able to approximate a remarkable sea spray effect also in carbon and oxygen stable isotopes of bone carbonate previously. In the present study we could approximate a minimum sea spray effect of about 13.9% even present in oxygen isotope values of bone phosphate, which was validated by Gaussian Mixture Model (GMM) clustering. This approximated value is by some magnitudes smaller than the minimum sea spray effect approximated for both δ13Ccarb and δ18Ocarb, and quite close to the sea spray detected for δ34Scoll in a previous study. It may therefore be interpreted as purer minimum sea spray signal compared to the approximation in bone carbonate. Furthermore, detection of sea spray in δ18Ophos can serve as additional validation of the effect present in bone carbonate, which is more prone to diagenetic alteration compared to bone phosphate. Moreover, the presence of the sea spray effect in both δ18Ocarb and δ18Ophos demonstrates that sea spray can be taken up by terrestrial mammals not only via food (δ18Ocarb) but also via drinking water (δ18Ophos). Finally, this study once more confirmed that calculation of δ18Ophos from δ18Ocarb values using a fixed oxygen isotope spacing (Δδ18O) can be highly misleading, especially in coastal environments affected by sea spray.

Rationale Methods for multi-isotope analyses are gaining in importance in anthropological, archaeological, and ecological studies. However, when material is limited (i.e., archaeological remains), it is obligatory to decide a priori which isotopic system(s) could be omitted without losing information. Methods We introduce a method that enables feature ranking of isotopic systems on the basis of distance-based entropy. The feature ranking method is evaluated using Gaussian Mixture Model (GMM) clustering as well as a cluster validation index ("trace index"). Results Combinations of features resulting in high entropy values are less important than those resulting in low entropy values structuring the dataset into more distinct clusters. Therefore, this method allows us to rank isotopic systems. The isotope ranking depends on the analyzed dataset, for example, consisting of terrestrial mammals or fish. The feature ranking results were verified by cluster analysis. Conclusions Entropy-based feature ranking can be used to a priori select the isotopic systems that should be analyzed. Consequently, we strongly suggest that this method should be applied if only limited material is available.

Transport of sea spray aerosol in coastal areas ("sea spray" effect) can have a marked influence on isotopic ratios of terrestrial ecosystems shifting terrestrial isotopic ratios towards unusual high values masking the original terrestrial signature. It is unclear so far if and to what extend sea spray influences other stable isotopes besides sulphur. In this study, we examined if the effect was also detectable in carbon, nitrogen, and oxygen stable isotopes of bone collagen and carbonate, respectively. Multi-isotope data of mammals sampled from the Viking Haithabu and medieval Schleswig sites in Northern Germany were analysed according to a previously developed approximation procedure and Gaussian Mixture Model (GMM) clustering in order to quantify the sea spray effect in the isotopes under study. While we were able to approximate an influence of the sea spray effect of at least 32.8% and 62.8% in delta C-13(carb) and delta C-13(carb), respectively, it was not possible to validate or approximate this effect in delta C-13(coll) and delta N-15(coll). Indeed, detection of the sea spray effect not only in delta S-34(coll), but also in delta C-13(carb) and delta O-18(carb) is of particular importance for studies on both prehistoric and recent material. GMM clustering on terrestrial herbivorous and marine piscivorous mammals was used to confirm the existing influence and to validate the approximated correction for the sea spray effect in the respective isotopic ratios (delta C-13(carb), delta C-13(carb), delta C-13(coll)) and the correction for the limnic influence on delta N-15(coll) approximated in a previous study. After correction, the clustering results markedly changed corresponding to the actual diet and habitat preference of the examined species. Although our study focused on palaeoecology, we suggest that GMM clustering also constitutes a very useful tool for modern landscape ecology based on stable isotope analyses.

RationaleDue to the spatial heterogeneity of stable isotope ratios of single elements measured in attempts to georeference bioarchaeological finds, multi-isotope fingerprints are frequently employed under the assumption that similar isotopic signatures are indicative of similar shared environments by the individuals studied. The extraction of the spatial information from multi-isotope datasets, however, is challenging. MethodsGaussian mixture clustering of six- to seven-dimensional isotopic fingerprints measured in archaeological animal and human bones was performed. Uncremated animal bones served for an isotopic mapping of a specific reference area of eminent archaeological importance, namely the Inn-Eisack-Adige passage across the European Alps. The fingerprints consist of Sr-87/Sr-86, Pb-208/Pb-204, Pb-207/Pb-204, Pb-206/Pb-204, Pb-208/Pb-207, and Pb-206/Pb-207 ratios, and O-18(phosphate) values in uncremated bone apatite, while the thermally unstable O-18 values of human cremations from this region were discarded. ResultsThe bone finds were successfully decontaminated. Animal and human isotope clusters not only reflect individual similarities in the multi-isotopic fingerprints, but also permit a spatial allocation of the finds. This holds also for cremated finds where the O-18(phosphate) value is no longer informative. To our knowledge, for the first time Pb stable isotopes have been systematically studied in cremated skeletal remains and proved significant in a region that was sought after for its ore deposits in prehistory. ConclusionsGaussian mixture clustering is a promising method for the interpretation of multi-isotopic fingerprints aiming at detecting and quantifying migration and trade.

Data science methods have the potential to benefit other scientific fields by shedding new light on common questions. One such task is choosing good features for analysis. In this paper, we introduce a data science framework that was designed to allow domain experts to consider their domain knowledge in assembling suitable data sources for complex analyses. The structure of experimental data as represented by a clustering is used to measure the relevance as well as the redundancy of each feature. We present an application of this technique to bioarchaelogical data from a region in the European Alps, a transalpine passage of eminent archaeological importance in European prehistory, the Inn-Eisack-Adige passage, spanning Italy, Austria, and Germany. These results are applied to the task of provenance analysis. The application of the presented data mining technique leads to new insights which were not found using standard bioarchaeological approaches.

We present GMMbuilder, a tool that allows domain scientists to build Gaussian Mixture Models (GMM) that adhere to domain specific constraints like spatial coherence. Domain experts use this tool to generate different models, extract stable object communities across these models, and use these communities to interactively design a final clustering model that explains the data but also considers prior beliefs and expectations of the domain experts.

RationaleModern methods in mass spectrometry permit fast accumulation of a huge amount of data. The analysis of multi‐isotope data sets of archaeological remains is of increasing importance for the study of palaeobiodiversity. However, common bivariate isotopic data analysis fails to detect certain patterns in a multi‐dimensional data set. This problem can be solved by cluster analysis.MethodsGaussian Mixture Model (GMM) clustering was applied to a multi‐isotope data set including 184 individual mass spectrometric measurements (δ13Ccollagen, δ15Ncollagen, δ13Ccarbonate, and δ18Ocarbonate values) of archaeological fish bones (n = 46) from the Viking Haithabu and medieval Schleswig sites in northern Germany. The number of components was first restricted to the expected number of three (freshwater, brackish, and marine environment). Subsequently, classification was conducted with respect to an optimal Bayesian Information Criterion (BIC).ResultsRestriction of the number of components to three clusters leads to the expected clustering results according to the gross ecological niches (freshwater, brackish, marine). The isotopic data of fish bone were, however, optimally clustered into four clearly separated, reasonable groups, namely a freshwater, a brackish, and two marine groups. The two marine clusters differ in their oxygen isotope ratios, indicating different water temperature and therefore probably imported fish. Restriction of the number of clusters resulted in better training and test results.ConclusionsThe GMM clustering method is applicable to complex multi‐dimensional stable isotope data sets established by isotope ratio mass spectrometry (IRMS). This exemplary application resulted in an identification of habitat preferences and non‐local individuals. Depending on the scientific question to be solved, restriction of the cluster size could lead to a better reproducibility; however, with loss of dissolution. Copyright © 2016 John Wiley & Sons, Ltd.

Isotopic mapping has become an indispensable tool for the assessment of mobility and trade of the past. However, modeling and understanding spatio-temporal isotopic variation is complicated by the small number of available samples, potential mobility of the investigated samples, sample preservation quality, uncertainty of measurements, and so forth. In this work, we use data mining techniques to build an isotopic map (descriptive modeling) and to determine the spatial origin of new samples (predictive modeling). In particular, we propose a clustering-based isotope ratio model and a scoring function for the origin prediction of new samples. Our data was extracted from real animal finds from an Alpine passage that spans three countries (Germany, Austria, and Italy) and comprises a high variety of isotopes and geological characteristics. Our results and evaluation by domain experts show that it is possible to derive a model of the area for both descriptive and predictive purposes.

This work tackles the management of novel types of inconsistencies in Spatio-Temporal Databases, different from traditional database settings where integrity constraints pertain to the explicitly stored (or, defined via views and aggregates) values. We observe that spatio-temporal data has its specific types of ßemanticconstraints and we aim at minimization of the changes needed for repairing their violations.

Isotopic fingerprinting is a task of paramount importance for region description and origin prediction. In this work, we use isotopic data, namely oxygen, strontium and lead, from animal remains in the Alps region. Our current samples are not cremated, however the majority of the data to be analysed in the project would be cremated. It is known that oxygen isotopes are not stable under high temperatures, making their application in the analysis of cremated material problematic. We study through Data Mining techniques the effect of oxygen on isotopic fingerprinting (treated as a supervised learning task) and on origin prediction (treated as a supervised task) and explore whether including oxygen in these analyses makes a significant difference to the results.

We present an idea of a novel similarity model for objects represented by 3D point clouds that were generated by scans of real-world objects. Various existing approaches find descriptive points on the object surface or extract features of groups of points. However, 3D object scans when conducted outside a lab environment often suffer from imprecisions and noise artifacts, which many existing approaches do not handle well. To better tolerate these imperfections, our model extracts stable sub-clouds from the input point cloud, which represent classes of adjacent sub-clouds sharing similar features. We demonstrate experimentally that features generated from these sub-clouds can be used to establish a measure of similarity between objects. We show preliminary results of an application of this technique to point clouds of models scanned from real-world objects and demonstrate that this technique has good potential to deal with imperfect data by showing how the computed distance relates to degrees of modification of the data. Our technique extracts features from particularly resilient portions of the object and is thus better able to accommodate deficiencies in the input data.