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Subspace clustering refers to the task of identifying clusters of similar objects or data records (vectors) where the similarity is defined with respect to a subset of the attributes (i.e., a subspace of the data space). The subspace is not necessarily (and actually is usually not) the same for different clusters within one clustering solution. In this article, the problems motivating subspace clustering are sketched, different definitions and usages of subspaces for clustering are described, and exemplary algorithmic solutions are discussed. Finally, we sketch current research directions. © 2012 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Clustering refers to the task of identifying groups or clusters in a data set. In density‐based clustering, a cluster is a set of data objects spread in the data space over a contiguous region of high density of objects. Density‐based clusters are separated from each other by contiguous regions of low density of objects. Data objects located in low‐density regions are typically considered noise or outliers. In this review article we discuss the statistical notion of density‐based clusters, classic algorithms for deriving a flat partitioning of density‐based clusters, methods for hierarchical density‐based clustering, and methods for semi‐supervised clustering. We conclude with some open challenges related to density‐based clustering. This article is categorized under:Technologies > Data PreprocessingEnsemble Methods > Structure DiscoveryAlgorithmic Development > Hierarchies and Trees [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

RATIONALE: Modern 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. METHODS: Gaussian 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). RESULTS: Restriction 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. CONCLUSIONS: The 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. [ABSTRACT FROM AUTHOR]

A reverse k-nearest neighbour (R kNN) query determines the objects from a database that have the query as one of their k-nearest neighbors. Processing such a query has received plenty of attention in research. However, the effect of running multiple R kNN queries at once (join) or within a short time interval (bulk/group query) has only received little attention so far. In this paper, we analyze different types of R kNN joins and provide a classification of existing R kNN join algorithms. We discuss possible solutions for solving the non-trivial variants of the problem in vector spaces, including self and mutual pruning strategies. Further, we generalize the developed algorithms to general metric spaces. During an extensive performance analysis we provide evaluation results showing the IO and CPU performance of the compared algorithms for a wide range of different setups and suggest appropriate query algorithms for specific scenarios. [ABSTRACT FROM AUTHOR]

Rationale: Due 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. Methods: Gaussian 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 87Sr/86Sr, 208Pb/204Pb, 207Pb/204Pb, 206Pb/204Pb, 208Pb/207Pb, and 206Pb/207Pb ratios, and δ18Ophosphate values in uncremated bone apatite, while the thermally unstable δ18O values of human cremations from this region were discarded. Results: The 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 δ18Ophosphate 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. Conclusions: Gaussian mixture clustering is a promising method for the interpretation of multi‐isotopic fingerprints aiming at detecting and quantifying migration and trade. [ABSTRACT FROM AUTHOR]

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 δ 13 C carb and δ 18 O carb , respectively, it was not possible to validate or approximate this effect in δ 13 C coll and δ 15 N coll . Indeed, detection of the sea spray effect not only in δ 34 S coll , but also in δ 13 C carb and δ 18 O 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 (δ 13 C carb , δ 18 O carb , δ 34 S coll ) and the correction for the limnic influence on δ 15 N 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. [ABSTRACT FROM AUTHOR]