A unifying framework for modelling non-negative bi-linear, tri-linear and “in-between” data in chemometrics

The study introduces a new modelling approach that bridges bi-linear and tri-linear factor decompositions for analyzing multi-way chemical data. Using (1, Lr, Lr) block term decompositions within the MCR-tri-linearity framework, the method adaptively balances uniqueness and flexibility by selecting the number of principal components required for each factor matrix, based on a user-defined reconstruction error tolerance.

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If you use the functions, please refer to the original paper

Paul-Albert Schneide, Neal Gallagher, Jesper Løve Hinrich, Rasmus Bro, Romà Tauler, A unifying framework for modelling non-negative bi-linear, tri-linear and “in-between” data in chemometrics. Part I: Theoretical framework and concepts, Chemometrics and Intelligent Laboratory Systems, Volume 265, 2025, 105492, https://doi.org/10.1016/j.chemolab.2025.105492.

Files:

MCRBTD.m – Core algorithm for computing (1, Lr, Lr) block term decompositions within the MCR-tri-linearity framework

analysis_script.m – Script for replicating plots shown in the paper.

Data_exmpl.mat – Simulated low rank non-trip-linear data set

results_facpack_all_D_rs_1.mat – Area of feasible solutions of a bi-linear model, determined with the FACPACK software

results_facpack_all_D_rs_2.mat – Area of feasible solutions of a bi-linear model, determined with the FACPACK software

Revision_second_order_calibration.m – Script for running additional data analysis required for revision