Dealing with missing data blocks in Multivariate Curve Resolution. Towards a general framework based on a single factorization model.

Abstract

Multivariate Curve Resolution (MCR) deals with the mixture analysis problem by decomposing a data set with mixed information into a bilinear model of pure component contributions. Multiset analysis deals with fused data blocks linked to related experiments and/or techniques. Nevertheless, experiments and techniques often show differences that lead, when concatenated, to incomplete multisets with missing blocks of information. Incomplete multisets aim at incorporating all available information in the initial blocks of measurements but require adapted algorithms to be properly handled. This work presents the evolution of the different perspectives adopted to analyze incomplete multisets with advantages and drawbacks. Finally, a new methodology is proposed that adapts to any data configuration with missing entries without the need to perform data imputation or multiple factorizations. The new method adapts very well to analytical applications where the blocks of information to be fused are not acquired in equivalent experimental conditions.