Bayesian Topological Learning for Brain State Classification

Nasrin, Farzana; Oballe, Christopher; Boothe, David L.; Maroulas, Vasileios

doi:10.1109/icmla.2019.00205

Cited by 11 publications

(10 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, when the amount of data allows, deep learning methods show promising performance (Bischof and Bunch, 2021 ). TDA can also be combined with other frameworks such as Bayesian networks (Nasrin et al, 2019 ).…”

Section: Tda Applied On Eeg Datamentioning

confidence: 99%

Topological Data Analysis as a New Tool for EEG Processing

Drougard

Roy

2021

Front. Neurosci.

View full text Add to dashboard Cite

Electroencephalography (EEG) is a widely used cerebral activity measuring device for both clinical and everyday life applications. In addition to denoising and potential classification, a crucial step in EEG processing is to extract relevant features. Topological data analysis (TDA) as an emerging tool enables to analyse and understand data from a different angle than traditionally used methods. As a higher dimensional analogy of graph analysis, TDA can model rich interactions beyond pairwise relations. It also distinguishes different dynamics of EEG time series. TDA remains largely unknown to the EEG processing community while it fits well the heterogeneous nature of EEG signals. This short review aims to give a quick introduction to TDA and how it can be applied to EEG analysis in various applications including brain-computer interfaces (BCIs). After introducing the objective of the article, the main concepts and ideas of TDA are explained. Next, how to implement it for EEG processing is detailed, and lastly the article discusses the benefits and limitations of the method.

show abstract

Section: Tda Applied On Eeg Datamentioning

confidence: 99%

Topological Data Analysis as a New Tool for EEG Processing

Drougard

Roy

2021

Front. Neurosci.

View full text Add to dashboard Cite

show abstract

“…These diagrams are multisets of points in the plane, each point representing a homological feature whose time of appearance and disappearance is contained in the coordinates of that point (Edelsbrunner and Harer (2010)). Persistent homology has proven to be promising in a variety of applications such as shape analysis Patrangenaru et al (2018), image analysis Guo et al (2018), neuroscience Sizemore et al (2018); Biscio and Møller (2019); Nasrin et al (2019Nasrin et al ( ), sensor networks D lotko et al (2012; Carlsson and de Silva (2010), biology Sgouralis et al (2017); Maroulas and Nebenführ (2015); Mike et al (2016); Nicolau et al (2011), dynamical systems Khasawneh and Munch (2016), action recognition Venkataraman et al (2016), signal analysis Maroulas (2018, 2016), chemistry and material science, Kimura et al (2018); Maroulas et al (2020); Townsend et al (2020), and genetics Humphreys et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Topological Learning for Classifying the Structure of Biological Networks

2022

Self Cite

View full text Add to dashboard Cite

“…Intuitively, the homological features represented in a PD measure the connectedness of data as their resolution changes. PH has proven to be promising in a variety of applications such as shape analysis [2], image analysis [3,4], neuroscience [5][6][7], dynamical systems [8], signal analysis [9], chemistry and material science [10,11], and genetics [12].…”

Section: Introductionmentioning

confidence: 99%

A Random Persistence Diagram Generator

Papamarkou¹,

Nasrin²,

Lawson³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology (PH) is a widely used method in TDA that summarizes homological features of data at multiple scales and stores this in persistence diagrams (PDs). As TDA is commonly used in the analysis of high dimensional data sets, a sufficiently large amount of PDs that allow performing statistical analysis is typically unavailable or requires inordinate computational resources. In this paper, we propose random persistence diagram generation (RPDG), a method that generates a sequence of random PDs from the ones produced by the data. RPDG is underpinned (i) by a parametric model based on pairwise interacting point processes for inference of persistence diagrams and (ii) by a reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm for generating samples of PDs. The parametric model combines a Dirichlet partition to capture spatial homogeneity of the location of points in a PD and a step function to capture the pairwise interaction between them. The RJ-MCMC algorithm incorporates trans-dimensional addition and removal of points and same-dimensional relocation of points across samples of PDs. The efficacy of RPDG is demonstrated via an example and a detailed comparison with other existing methods is presented.

show abstract

Bayesian Topological Learning for Brain State Classification

Cited by 11 publications

References 41 publications

Topological Data Analysis as a New Tool for EEG Processing

Topological Data Analysis as a New Tool for EEG Processing

Bayesian Topological Learning for Classifying the Structure of Biological Networks

A Random Persistence Diagram Generator

Contact Info

Product

Resources

About