Glycan mixture analysis by kernel component composition for matrix factorization

A major challenge in structural glycomics is the presence of isomeric glycan structures, which may not be fully resolved by separation techniques such as liquid chromatography (LC) and ion mobility spectrometry (IMS). Tandem mass spectrometry (MS/MS) can be employed following on-line separation to distinguish unresolved features, as the temporal profiles of various fragment ions reflect different combinations of those from their respective precursor ions. However, traditional principal component analysis can produce negative signals that are unrealistic for real data, and classic non-negative matrix factorization (NMF) methods may result in factors that include contributions from multiple components. This paper introduces a new variation of NMF, termed kernel component composition (KCC), which enables users to impose domain-specific prior knowledge about the components as parametric kernels. These kernel parameters are then learned directly from the data. We developed a theoretically guaranteed algorithm based on proximal gradient descent to solve the optimization problem posed by KCC and derived detailed parameter update rules when using Gaussian kernels. The effectiveness of the KCC algorithm is demonstrated through simulation tests and its application to deconvoluting chemical datasets, including LC- and IM-MS/MS analysis of isomeric glycan mixtures.