Tracing Evolving Networks Using Tensor Factorizations vs. ICA-Based Approaches

Abstract

Analysis of time-evolving data is crucial to understand the functioning of dynamic systems such as the brain. For instance, analysis of functional magnetic resonance imaging (fMRI) data collected during a task may reveal spatial regions of interest, and how they evolve during the task. However, capturing underlying spatial patterns as well as their change in time is challenging. The traditional approach in fMRI data analysis is to assume that underlying spatial regions of interest are static. In this article, using fractional amplitude of low-frequency fluctuations (fALFF) as an effective way to summarize the variability in fMRI data collected during a task, we arrange time-evolving fMRI data as a subjects by voxels by time windows tensor, and analyze the tensor using a tensor factorization-based approach called a PARAFAC2 model to reveal spatial dynamics. The PARAFAC2 model jointly analyzes data from multiple time windows revealing subject-mode patterns, evolving spatial regions (also referred to as networks) and temporal patterns. We compare the PARAFAC2 model with matrix factorization-based approaches relying on independent components, namely, joint independent component analysis (ICA) and independent vector analysis (IVA), commonly used in neuroimaging data analysis. We assess the performance of the methods in terms of capturing evolving networks through extensive numerical experiments demonstrating their modeling assumptions. In particular, we show that (i) PARAFAC2 provides a compact representation in all modes, i.e., subjects, time, and voxels, revealing temporal patterns as well as evolving spatial networks, (ii) joint ICA is as effective as PARAFAC2 in terms of revealing evolving networks but does not reveal temporal patterns, (iii) IVA's performance depends on sample size, data distribution and covariance structure of underlying networks. When these assumptions are satisfied, IVA is as accurate as the other methods, (iv) when subject-mode patterns differ from one time window to another, IVA is the most accurate. Furthermore, we analyze real fMRI data collected during a sensory motor task, and demonstrate that a component indicating statistically significant group difference between patients with schizophrenia and healthy controls is captured, which includes primary and secondary motor regions, cerebellum, and temporal lobe, revealing a meaningful spatial map and its temporal change.

Analyzing postprandial metabolomics data using multiway models: A simulation study

“…However, those factor matrices may change over time. To account for such subject-specific temporal profiles or time-evolving factors in the metabolites mode, alternative multiway methods such as the PARAFAC2 model [52] may prove useful as already shown for the analysis of neuroimaging signals [53][54][55] and in chemometrics [56].…”

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

“…Particularly, they first detect change points at which the functional connectivity across subjects presents abrupt changes and then summarize DFCNs between successive change points. Recently, Acar et al in [134] proposed to use the Parafac2 model for tracking the evolution of connectivity networks and compared its performance with ICA and IVA. For the problem of localizing dynamic brain sources over time, Ardeshir et al in [135] utilized the boundary element method (BEM) [136] and the adaptive PARAFAC-RLST tracker [46] with two operational windowing schemes.…”

Status of deep learning for EEG-based brain–computer interface applications

“…In that case, the non-invasive method is preferred due to its flexibility and reduced risk. There are many techniques (Lotte et al, 2018 ) by which the neural activity is recorded, such as magnetoencephalography (MEG), functional magnetic resonance imaging (fMRI) (Acar et al, 2022 ; Hossain et al, 2022 ), and electroencephalography (EEG), and fully functioning near-infrared spectroscopy (fNIRS). The EEG method is preferred due to its robustness and user-friendly approach (Bi et al, 2013 ).…”