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P. Filzmoser:
"Outlier detection in compositional data: from row-wise to cell-wise";
Talk: ISI 2019, Kuala Lumpur, Malaysia (invited); 2019-08-18 - 2019-08-23.

Compositional data analysis focuses on the (log-) ratios between the
variable values rather than directly on the reported data values. This information contained in all pair-wise log ratios can be aggregated and presented in the realEuclidean space, where standard outlier detection methods, e.g. such which are based on robust Mahalanobis distances, are appropriate. Mahalanobis distances indicate if an observation is flagged as a multivariate outlier or not.
Particularly for high-dimensional data it may become more and more
likely that observations are considered as outliers just because some of their variable values are different. In this case it is more useful to directly flag these cells (variables) of the observations as outliers, rather than the whole observation. Cell-wise outlier detection for compositional data considers the information of the log-ratios between all pairs of variables, and aggregates this information properly. The outlyingness can then be visualized in a color-coding displayed by heat maps. It is shown that this
approach is very useful for the analysis of metabolomic data, not only for cell-wise outlier detection but also for biomarker identification.

https://publik.tuwien.ac.at/files/publik_282823.pdf