Dynamic Topological Data Analysis for Functional Brain Signals

Discussion of ‘Event history and topological data analysis’

“…In Biscio & Møller (2019) , the accumulated persistence function, which simply sums the length of barcodes, is proposed for brain artery trees. In Songdechakraiwut & Chung (2020a) , barcodes are also accumulated for time series data. In graph filtration, the accumulating barcode is equivalent to computing the area under the Betti curves.…”

Topological Learning for Brain Networks

“…Topological Data Analysis (TDA) (Edelsbrunner et al, 2000;Wasserman, 2018), a general framework based on algebraic topology, can provide such novel solution to the long-standing multimodal brain network analysis challenge. Numerous TDA studies have been applied to increasingly diverse problems such as genetics (Chung et al, 2017b(Chung et al, , 2019b, epileptic seizure detection (Wang et al, 2018), sexual dimorphism in the human brain (Songdechakraiwut and Chung, 2020), analysis of brain arteries (Bendich et al, 2016), image segmentation (Clough et al, 2019), classification (Singh et al, 2014;Reininghaus et al, 2015;Chen et al, 2019), clinical predictive model (Crawford et al, 2020) and persistencebased clustering (Chazal et al, 2013). Persistent homology begins to emerge as a powerful mathematical representation to understand, characterize and quantify topology of brain networks (Lee et al, 2012;Chung et al, 2019b).…”

Topological Data Analysis for Functional Brain Networks

“…Recently popular Topological data analysis (TDA) can fill this gap providing a topologically consistent solution across varying thresholds [25,81,56,32,15,75]. Within TDA, persistent homology based approaches have become increasingly popular as a tool for analyzing different brain imaging data because they can capture the persistences [48,57] of different topological features that are robust under different scales [10,32,41,19]. The persistences are usually summarized and expressed using barcodes [58].…”

“…Although such approaches have been applied to increasingly diverse biomedical problems, they are mostly limited to investigating the static summary of dynamically changing data such as functional magnetic resonance images (fMRI) and electroencephalography [18,3,74]. However, a few recent studies applied TDA to capture dynamic patterns of data including the applications to financial data [33] and gene expression data [50,57].…”

“…Motivated by these studies, we develop a novel dynamic-TDA based approach that can statistically discriminate two groups of brain networks. This dynamic-TDA framework builds persistent homology over a multivariate time series [57] and constructs a test statistic using the Wasserstein distance between barcodes. The proposed Dynamic-TDA is applied on the resting-state fMRI (rs-fMRI) human and uncovers interesting topological differences in the temporal dynamics between males and females.…”