A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings

In many areas of science, various sensing technologies are used to obtain information about a single system of interest. Often, none of the datasets alone contains a complete view of the system, but the data measured from different modalities can complement each other. For instance, brain activity patterns can be captured using both electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) signals, which have complementary temporal and spatial resolutions. Similarly, in metabolomics, multiple analytical techniques such as LCMS (Liquid Chromatography - Mass Spectrometry) and NMR (Nuclear Magnetic Resonance) spectroscopy are used to measure chemical compounds in biological samples, providing a more complete picture of underlying biological processes. Joint analysis of datasets from multiple sources, also referred to as data fusion (or multi-modal data mining), exploits these complementary measurements, and allows for better interpretability and, potentially, more accurate recovery of patterns characterizing the underlying phenomena. Nevertheless, data fusion poses many challenges, and there is an emerging need for data fusion methods that can take into account different characteristics of data from multiple sources in many disciplines [1-4]. Data from multiple sources can often be represented in the form of matrices and higher-order tensors. Coupled matrix and tensor factorizations (CMTF) are an effective approach for joint analysis of such datasets in many domains including social network analysis [5-8], neuroscience [9-13], and chemometrics [2, 14]. In such coupled factorizations, each dataset is modelled by a low-rank approximation.