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Temporal associations in longitudinal nontargeted metabolomics data are generally ignored by common pattern recognition methods such as partial least squares discriminant analysis (PLS-DA) and orthogonal partial least squares discriminant analysis (OPLS-DA). To discover temporal patterns in longitudinal metabolomics, a multitask learning (MTL) method employing structural regularization was proposed. The group regularization term of the proposed MTL method enables the selection of a small number of tentative biomarkers while maintaining high prediction accuracy. Meanwhile, the nuclear norm imposed into the regression coefficient accounts for the interrelationship of the metabolomics data obtained on consecutive time points. The effectiveness of the proposed method was demonstrated by comparison study performed on a metabolomics dataset and a simulating dataset. The results showed that a compact set of tentative biomarkers charactering the whole antipyretic process of Qingkailing injection were selected with the proposed method. In addition, the nuclear norm introduced in the new method could help the group norm to improve the method's recovery ability.

Discovering Temporal Patterns in Longitudinal Nontargeted Metabolomics Data via Group and Nuclear Norm Regularized Multivariate Regression