Improved one-class modeling of high-dimensional metabolomics data via eigenvalue-shrinkage

Alberto Brini (Corresponding author), Vahe Avagyan, Ric C.H. de Vos, Jack H. Vossen, Edwin R. van den Heuvel, Jasper Engel

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One-class modelling is a useful approach in metabolomics for the untargeted detection of abnormal metabolite profiles, when information from a set of reference observations is available to model “normal” or baseline metabolite profiles. Such outlying profiles are typically identified by comparing the distance between an observation and the reference class to a critical limit. Often, multivariate distance measures such as the Mahalanobis distance (MD) or principal component-based measures are used. These approaches, however, are either not applicable to untargeted metabolomics data, or their results are unreliable. In this paper, five distance measures for one-class modeling in untargeted metabolites are proposed. They are based on a combination of the MD and five so-called eigenvalue-shrinkage estimators of the covariance matrix of the reference class. A simple cross-validation procedure is proposed to set the critical limit for outlier detection. Simulation studies are used to identify which distance measure provides the best performance for one-class modeling, in terms of type I error and power to identify abnormal metabolite profiles. Empirical evidence demonstrates that this method has better type I error (false positive rate) and improved outlier detection power than the standard (principal component-based) one-class models. The method is illustrated by its application to liquid chromatography coupled to mass spectrometry (LC-MS) and nuclear magnetic response spectroscopy (NMR) untargeted metabolomics data from two studies on food safety assessment and diagnosis of rare diseases, respectively.

Original languageEnglish
Article number237
Number of pages20
Issue number4
Publication statusPublished - 13 Apr 2021

Bibliographical note

Funding Information:
Funding: This work was funded by NWO-PTA-COAST3 through the Outfitting the Factory of the Future with Online analysis (OFF/On) consortium.

Funding Information:
Acknowledgments: We would like to thank Gijs Kleter (Wageningen Food Safety Research, Wa-geningen) and Hilko van der Voet (Biometris, Wageningen) for their insightful comments at different stages of this research. Udo Engelke and R. Wevers are gratefully acknowledged for sharing NMR medical data, and Henriëtte van Eekelen and Bert Schipper (Plant Metabolomics group. WUR-Bioscience) are gratefully acknowledged for their help with the potato LCMS measurements. The potato data set was acquired within the context of the Biotechnology and Safety program (Proj. No. 15815) of the Netherlands Organization for Scientific Research and the Ministry of Infrastructure and Water Management.



  • Critical value
  • Eigenvalue-shrinkage
  • High-dimensional data
  • Mahalonobis distance
  • One-class model
  • Scaled Chi-square distribution
  • Untargeted metabolomics


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