With accurate data, governments can make the most informed decisions to keep people safer through pandemics such as the COVID-19 coronavirus. In such events, data reliability is crucial and therefore outlier detection is an important and even unavoidable issue. Outliers are often considered as the most interesting observations, because the fact that they differ from the data majority may lead to relevant findings in the subject area. Outlier detection has also been addressed in the context of multivariate functional data, thus smooth functions of several characteristics, often derived from measurements at different time points (Hubert et al. in Stat Methods Appl 24(2):177–202, 2015b). Here the underlying data are regarded as compositions, with the compositional parts forming the multivariate information, and thus only relative information in terms of log-ratios between these parts is considered as relevant for the analysis. The multivariate functional data thus have to be derived as smooth functions by utilising this relative information. Subsequently, already established multivariate functional outlier detection procedures can be used, but for interpretation purposes, the functional data need to be presented in an appropriate space. The methodology is illustrated with publicly available data around the COVID-19 pandemic to find countries displaying outlying trends.
Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is known that a relationship only exists between very specific variables (e.g. for metabolomic pathways), while for other pairs a relationship does not exist. Modeling absence or presence of relationships is done in graph theory, where the vertices represent the variables, and the connections refer to relations. This paper links compositional data analysis with graph signal processing, and it extends the Aitchison geometry to a setting where only selected log-ratios can be considered. The presented framework retains the desirable properties of scale invariance and compositional coherence. An additional extension to include absolute information is readily made. Examples from bioinformatics and geochemistry underline the usefulness of this approach in comparison to standard methods for compositional data analysis.
Detecting subcropping mineralizations but also deeply buried mineralizations is one important goal in geochemical exploration. The identification of useful indicators for mineralization is a difficult task as mineralization might be influenced by many factors, such as location, investigated media, depth, etc. We propose a statistical method which indicates chemical elements related to mineralization along a transect. Moreover, the method determines along a transect the potential area of the deposit. The identification is based on General Additive Models (GAMs) for the element concentrations across the spatial coordinate(s). The log-ratios of the GAM fits are taken to compute the curvature, where high and narrow curvature is supposed to indicate the mineralization area. By defining a measure for the quantification of high curvature, the log-ratios can be ranked, and elements can be identified that are indicative of the anomaly patterns.
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