Abstract
Multivariate regression analysis is one of the most important tools in metabolomics studies. For regression of high-dimensional data, partial least squares (PLS) has been widely used. Canonical correlation analysis (CCA) is a classic method of multivariate analysis; it has however rarely been applied to multivariate regression. In the present study, we applied PLS and regularized CCA (RCCA) to high-dimensional data where the number of variables ( p) exceeds the number of observations ( N), N ≪ p. Using kernel CCA with linear kernel can drastically reduce the calculation time of RCCA. We applied these methods to gas chromatography–mass spectrometry (GC–MS) data, which were analyzed to resolve the problem of Japanese green tea ranking. To construct a quality-predictive model, the optimal number of latent variables in RCCA determined by leave-one-out cross-validation (LOOCV) was significantly fewer than in PLS. For metabolic fingerprinting, we successfully identified important metabolites for green tea grade classification using PLS and RCCA.
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