Automated multigroup outlier identification in molecular high-throughput data using bagplots and gemplots

Jochen Kruppa, Klaus Jung

Analyses of molecular high-throughput data often lack in robustness, i.e. results are very sensitive to the addition or removal of a single observation. Therefore, the identification of extreme observations is an important step of quality control before doing further data analysis. Standard outlier detection methods for univariate data are however not applicable, since the considered data are high-dimensional, i.e. multiple hundreds or thousands of features are observed in small samples. Usually, outliers in high-dimensional data are solely detected by visual inspection of a graphical representation of the data by the analyst. Typical graphical representation for high-dimensional data are hierarchical cluster tree or principal component plots. Pure visual approaches depend, however, on the individual judgement of the analyst and are hard to automate. Existing methods for automated outlier detection are only dedicated to data of a single experimental groups. In this work we propose to use bagplots, the 2-dimensional extension of the boxplot, to automatically identify outliers in the subspace of the first two principal components of the data. Furthermore, we present for the first time the gemplot, the 3-dimensional extension of boxplot and bagplot, which can be used in the subspace of the first three principal components. Bagplot and gemplot surround the regular observations with convex hulls and observations outside these hulls are regarded as outliers. The convex hulls are determined separately for the observations of each experimental group while the observations of all groups can be displayed in the same subspace of principal components. We demonstrate the usefulness of this approach on multiple sets of artificial data as well as one set of gene expression data from a next-generation sequencing experiment, and compare the new method to other common approaches. Furthermore, we provide an implementation of the gemplot in the package 'gemPlot' for the R programming environment. Bagplots and gemplots in subspaces of principal components are useful for automated and objective outlier identification in high-dimensional data from molecular high-throughput experiments. A clear advantage over other methods is that multiple experimental groups can be displayed in the same figure although outlier detection is performed for each individual group.