Dimensionality reduction for metabolome data using PCA, PLS, OPLS, and RFDA with differential penalties to latent variables

Dimensionality reduction is an important technique for preprocessing of high-dimensional data. Because only one side of the original data is represented in a low-dimensional subspace, useful information may be lost. In the present study, novel dimensionality reduction methods were developed that are suitable for metabolome data, where observation varies with time. Metabolomics deal with this type of data, which are often obtained in microorganism fermentation processes. However, no dimensionality reduction method that utilizes information from the original data in a positive manner has been reported to date. The ordinary dimensionality reduction methods of principal component analysis (PCA), partial least squares (PLS), orthonormalized PLS (OPLS), and regularized Fisher discriminant analysis (RFDA) were extended by introducing differential penalties to the latent variables in each class. A nonlinear extension of this approach, using kernel methods, was also proposed in the form of kernel-smoothed PCA, PLS, OPLS, and FDA. Since all of these methods are formulated as generalized eigenvalue problems, the solutions can be computed easily. These methods were then applied to intracellular metabolite data of a xylose-fermenting yeast in ethanol fermentation. Visualization in the low-dimensional subspace suggests that smoothed PCA successfully preserves the information about the time course of observations during fermentation, and that RFDA can produce high separation among different strains.