Exploring the effects of sparsity constraint on the ranges of feasible solutions for resolution of GC-MS data

摘要

AbstractMany practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations are non-negative. Sparse non-negative matrix factorizations (SNMFs) are useful when some degrees of sparseness exist in original data, intrinsically. The present contribution is about the implementation of sparsity constraint in multivariate curve resolution-alternating least square (MCR-ALS) technique for analysis of GC-MS/LC-MS data. The GC-MS and LC-MS data are sparse in mass dimension, and implementation of SNMF techniques would be useful for analyzing such two-way chromatographic data. In this work, L1-regularization paradigm has been implemented in each iteration of the MCR-ALS algorithm in order to force the algorithm to return more sparse mass spectra. L1-regularization has been applied by using the least absolute shrinkage and selection operator (Lasso) instead of the ordinary least square. A comprehensive comparison has been made between MCR-ALS and Lasso-MCR-ALS algorithms for resolution of the simulated and real GC-MS data. The comparison has been made by calculation of the values of sum of square errors (SSE) for 5000 times repetition of both algorithms using the random mass spectra and concentration profiles as initial estimates. The results revealed that regularization of L1-norm in mass dimension prevents occurrence of overfitting in ALS algorithm and this increases the probability of finding “true solution” after the resolution procedure. Moreover, the effect of this “sparsity constraint” has been explored on the area of feasible solutions in MCR methods. The results in this work revealed that implementation of this constraint reduces the extent of rotational ambiguity in MCR solutions and can be helpful for resolution of GC-MS data with high degrees of overlapping in mass spectra and concentration profiles.Highlights?L1-norm regularization has been implemented in MCR-ALS algorithm.?This modification confines the L1-norm of estimated mass spectra using Lasso approach.?The sparsity constraint reduces the extent of rotational ambiguity in MCR solutions.]]>