Multivariate Curve Resolution with Elastic Net Regularization

Abstract

The purpose of Multivariate Curve Resolution (MCR) is to recover the concentration profile and the source spectra without any prior knowledge. We hypothesis that each source is characterized by a linear superposition of Gaussian peaks of fixed spread. Multivariate curve resolution–alternating least squares (MCR-ALS) is a Conventional MCR method. MCR-ALS has some disadvantages. We proposed a solver with L1 regularizer and L2 regularizer to obtain a sparse solution within MCR-ALS. L1-norm involves a sparse but non-smooth solution, L2-norm will keep all the information and bring the smoothness, but it will lead non-sparse solutions. So we combined the L1-norm and the squared L2-norm to seek the optimal solutions. This is accomplished via Elastic Net Regularization algorithem which is LARS (least-angle regression). We named this method MCR-LARS. This paper applies MCR-LARS to resolve the hard overlapped spectroscopic signals belonging to the three aromatic amino acids (phenylalanine, tyrosine and tryptophan) in their mixtures. MCR–LARS was compared with MCR-ALS. The results show the effectiveness and efficiency of MCR–LARS and the results show that MCR-LARS provides more nicely resolved concentration profiles and spectra than pure MCR-ALS solution.