Feasible band boundaries computation in bilinear matrix decomposition using essential data

Multivariate curve resolution methods are usually confronted with non-unique pure component factors. This rotational ambiguity can be represented by ranges of feasible profiles, which are equally compatible with the imposed constraints. Sensor-wise N-BANDS is an effective algorithm for the calculation of the bounds of feasible profiles in the presence of noise, but suffers from high computational cost.

Sensor-wise N-BANDS has been combined with the concept of essential data points to speed up the computation. The combined algorithm provides full curve resolution independent of the number of chemical species. The effectiveness of the proposed algorithm is demonstrated for simulated chromatographic data and experimental spectro-electrochemical data.

With the new proposal, the boundaries of the set of feasible profiles in bilinear matrix decomposition can be estimated in a reasonable time, for any number of components, and in the presence of instrumental noise. For the simulated data, the reduction in computation time was more than 95 %. Similarly, for the relatively large experimental spectro-electrochemical data, the reduction in computation time was over 85 %.