Three-way data reduction based on essential information

In this article, the idea of essential information-based compression is extended to trilinear datasets. This basically boils down to identifying and labelling the essential rows (ERs), columns (ECs) and tubes (ETs) of such three-dimensional datasets that allow by themselves to reconstruct in a linear way the entire space of the original measurements. ERs, ECs and ETs can be determined by exploiting convex geometry computational approaches such as convex hull or convex polytope estimations and can be used to generate a reduced version of the data at hand. These compressed data and their uncompressed counterpart share the same multilinear properties and their factorisation (carried out by means of, e.g., Parallel Factor Analysis-Alternating Least Squares - PARAFAC-ALS) yield, in principle, indistinguishable results. More in detail, an algorithm for the assessment and extraction of the essential information encoded in trilinear data structures is here proposed. Its performance was evaluated in both real-world and simulated scenarios which permitted to highlight the benefits that this novel data reduction strategy can bring in domains like multiway fluorescence spectroscopy and imaging.