Tensor decompositions and data fusion in epileptic electroencephalography and functional magnetic resonance imaging data

Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) record a mixture of ongoing neural processes, physiological and nonphysiological noise. The pattern of interest, such as epileptic activity, is often hidden within this noisy mixture. Therefore, blind source separation (BSS) techniques, which can retrieve the activity pattern of each underlying source, are very useful. Tensor decomposition techniques are very well suited to solve the BSS problem, as they provide a unique solution under mild constraints. Uniqueness is crucial for an unambiguous interpretation of the components, matching them to true neural processes and characterizing them using the component signatures. Moreover, tensors provide a natural representation of the inherently multidimensional EEG and fMRI, and preserve the structural information defined by the interdependencies among the various modes such as channels, time, patients, etc. Despite the well‐developed theoretical framework, tensor‐based analysis of real, large‐scale clinical datasets is still scarce. Indeed, the application of tensor methods is not straightforward. Finding an appropriate tensor representation, suitable tensor model, and interpretation are application dependent choices, which require expertise both in neuroscience and in multilinear algebra. The aim of this paper is to provide a general guideline for these choices and illustrate them through successful applications in epilepsy. WIREs Data Mining Knowl Discov 2017, 7:e1197. doi: 10.1002/widm.1197 This article is categorized under: Algorithmic Development > Biological Data Mining Algorithmic Development > Spatial and Temporal Data Mining Algorithmic Development > Structure Discovery Electroencephalography and functional magnetic resonance imaging measure a noisy mixture of brain activity. Tensor‐based blind source separation can estimate and characterize the underlying brain sources and support epilepsy diagnosis.