Dynamic brain effective connectivity analysis based on low-rank canonical polyadic decomposition: application to epilepsy

Abstract

In this paper, a new method to track brain effective connectivity networks in the context of epilepsy is proposed. It relies on the combination of partial directed coherence with a constrained low-rank canonical polyadic tensor decomposition. With such combination being established, the most dominating directed graph structures underlying each time window of intracerebral electroencephalographic signals are optimally inferred. Obtained time and frequency signatures of inferred brain networks allow respectively to track the time evolution of these networks and to define frequency bands on which they are operating. Besides, the proposed method allows also to track brain connectivity networks through several epileptic seizures of the same patient. Understanding the most dominating directed graph structures over epileptic seizures and investigating their behavior over time and frequency plans are henceforth possible. Since only few but the the most important directed connections in the graph structure are of interest and also for a meaningful interpretation of obtained signatures to be guaranteed, the low-rank canonical polyadic tensor decomposition is prompted respectively by the sparsity and the non-negativity constraints on the tensor loading matrices. The main objective of this contribution is to propose a new way of tracking brain networks in the context of epileptic iEEG data by identifying the most dominant effective connectivity patterns underlying the observed iEEG signals at each time window. The performance of the proposed method is firstly evaluated on simulated data imitating brain activities and secondly on real intracerebral electroencephalographic signals obtained from an epileptic patient. The partial directed coherence based tensor has been decomposed into space, time and frequency signatures in accordance with the expected ground truth for each consecutive sequence of the simulated data. The method is also in accordance with the clinical expertise for iEEG epileptic signals, where the signatures were investigated through a simultaneous multi-seizure analysis.

Multiplex dynamic networks in the newborn brain disclose latent links with neurobehavioral phenotypes

“…Our work extends prior knowledge by showing that intrinsic multiplex network characteristics are indeed latent properties in the high‐level noise, and they can be uncovered by the developed framework in a robust manner. Specifically, prior studies in infants have only examined temporally and/or spectrally static networks (Omidvarnia et al, 2015 ; Tokariev et al, 2019 ; Westende et al, 2020 ; Yrjölä et al, 2022 ), whereas some studies in adults have explored the combination of spectrally distributed networks (Buldú & Porter, 2018 ; Vaiana & Muldoon, 2020 ; Zhu, Liu, Ye, et al, 2020 ) and their dynamic changes (Chantal et al, 2021 ; Esfahlani et al, 2020 ; Mahyari et al, 2017 ; Mehrkanoon et al, 2014 ; Tewarie et al, 2019 ; Zhu, Liu, Mathiak, et al, 2020 ; Zhu, Liu, Ye, et al, 2020 ). In contrast, the proposed mdFCN analysis pipeline fully exploits the network dynamic multiplexity and introduces significant improvements.…”

“…The CPD defines the latent mdFCNs as a sum of tensors with each being the outer product of three non‐negative vectors describing pairwise connections, time/subject, and spectral factors (see Supplementary Section 3 ). In brief, it is mainly intended to break the latent mdFCNs into subnetworks (Chantal et al, 2021 ) to reveal patterns in the complex network feature space that could be linked to neurobehavioral phenotypes (Dron et al, 2021 ). Moreover, the CPD number of components was automatically selected using the introduced entropy‐based technique to suppress any remaining intersubject variability and noise (see Supplementary Section 4.2 ).…”

Enabling All In-Edge Deep Learning: A Literature Review

“…This approach, when applied over the CIFAR-10 dataset with VGG-16 architecture, achieved 3.6× times smaller compression ratio to the SVD. Other commonly used methods for low-rank factorization are tucker decomposition (TD) [155,156,157] and canonical polyadic decomposition (CPD) [158,159]. The main idea behind the early exit approach is to find the best tradeoff between the deep DNN structure of a DL model and the latency requirements for inference.…”

Enabling Deep Learning for All-in EDGE paradigm

“…This approach, when applied over the CIFAR-10 dataset with VGG-16 architecture, achieved 3.6× times smaller compression ratio to the SVD. Other most commonly used methods for Low rank factorization are Tucker Decomposition (TD) [62,155,222] and canonical polyadic decomposition (CPD) [25,197].…”