Spatially Informed Nonnegative Matrix Trifactorization for Coclustering Mass Spectrometry Data

Mass spectrometry imaging techniques measure molecular abundance in a tissue sample at a cellular resolution, all while preserving the spatial structure of the tissue. This kind of technology offers a detailed understanding of the role of several molecular factors in biological systems. For this reason, the development of fast and efficient computational methods that can extract relevant signals from massive experiments has become necessary. A key goal in mass spectrometry data analysis is the identification of molecules with similar functions in the analyzed biological system. This result can be achieved by studying the spatial distribution of the molecules' abundance patterns. To do so, one can perform coclustering, that is, dividing the molecules into groups according to their expression patterns over the tissue and segmenting the tissue according to the molecules' abundance levels. We present TRIFASE, a semi-nonnegative matrix trifactorization technique that performs coclustering while accounting for the spatial correlation of the data. We propose an estimation algorithm that solves the proposed matrix trifactorization problem. Moreover, to improve scalability, we also propose two heuristic approximations of the most expensive steps, which help the algorithm converge while significantly streamlining the computational cost. We validated our method on a series of simulation experiments, comparing the different estimating strategies discussed in the article. Last, we analyzed a mouse brain tissue sample processed with MALDI-MSI technology, showing how TRIFASE extracts specific expression patterns of molecule abundance in localized tissue areas and discovers blocks of proteins whose activation is directly linked to specific biological mechanisms.