Augmenting interictal mapping with neurovascular coupling biomarkers by structured factorization of epileptic EEG and fMRI data.

EEG-correlated fMRI analysis is widely used to detect regional BOLD fluctuations that are synchronized to interictal epileptic discharges, which can provide evidence for localizing the ictal onset zone. However, the typical, asymmetrical and mass-univariate approach cannot capture the inherent, higher order structure in the EEG data, nor multivariate relations in the fMRI data, and it is nontrivial to accurately handle varying neurovascular coupling over patients and brain regions. We aim to overcome these drawbacks in a data-driven manner by means of a novel structured matrix-tensor factorization: the single-subject EEG data (represented as a third-order spectrogram tensor) and fMRI data (represented as a spatiotemporal BOLD signal matrix) are jointly decomposed into a superposition of several sources, characterized by space-time-frequency profiles. In the shared temporal mode, Toeplitz-structured factors account for a spatially specific, neurovascular 'bridge' between the EEG and fMRI temporal fluctuations, capturing the hemodynamic response's variability over brain regions. By analyzing interictal data from twelve patients, we show that the extracted source signatures provide a sensitive localization of the ictal onset zone (10/12). Moreover, complementary parts of the IOZ can be uncovered by inspecting those regions with the most deviant neurovascular coupling, as quantified by two entropy-like metrics of the hemodynamic response function waveforms (9/12). Hence, this multivariate, multimodal factorization provides two useful sets of EEG-fMRI biomarkers, which can assist the presurgical evaluation of epilepsy. We make all code required to perform the computations available at https://github.com/svaneynd/structured-cmtf.

Regression and Classification With Spline-Based Separable Expansions.

We introduce a supervised learning framework for target functions that are well approximated by a sum of (few) separable terms. The framework proposes to approximate each component function by a B-spline, resulting in an approximant where the underlying coefficient tensor of the tensor product expansion has a low-rank polyadic decomposition parametrization. By exploiting the multilinear structure, as well as the sparsity pattern of the compactly supported B-spline basis terms, we demonstrate how such an approximant is well-suited for regression and classification tasks by using the Gauss-Newton algorithm to train the parameters. Various numerical examples are provided analyzing the effectiveness of the approach.

Irregular heartbeat classification using Kronecker Product Equations.

Cardiac arrhythmia or irregular heartbeats are an important feature to assess the risk on sudden cardiac death and other cardiac disorders. Automatic classification of irregular heartbeats is therefore an important part of ECG analysis. We propose a tensor-based method for single- and multi-channel irregular heartbeat classification. The method tensorizes the ECG data matrix by segmenting each signal beat-by-beat and then stacking the result into a third-order tensor with dimensions channel × time × heartbeat. We use the multilinear singular value decomposition to model the obtained tensor. Next, we formulate the classification task as the computation of a Kronecker Product Equation. We apply our method on the INCART dataset, illustrating promising results.