Constrained principal component analysis with stochastically ordered scores for high-dimensional mass spectrometry data

In this paper, we consider a constrained principal component analysis (PCA) for the projection of high-dimensional samples from different groups to a lower-dimensional space for which the principal scores are stochastically ordered over the groups. We express the problem as the minimization of a constrained biconvex problem and develop an iterative algorithm to solve it. We numerically show that the solution to our constrained PCA problem approximately rotates the principal coordinates of the ordinary PCA to achieve ordered scores. Consequently, our approach significantly improves the scores and the corresponding loading matrix compared to the original PCA if their true values are ordered over groups. We finally apply our method to two data examples: (i) the direct infusion multiple reaction monitoring mass spectrometry (DI-MRM-MS) data of white rice to verify the authenticity of adulterated Japonica rice and (ii) high-dimensional lipidomics data from ultra-performance liquid chromatography-mass spectrometry/mass spectrometry (UPLC-MS/MS) analysis of patients with liver diseases.restrictio