Topological Learning for Brain Networks

Songdechakraiwut, Tananun; Chung, Moo K.

doi:10.48550/arxiv.2012.00675

Cited by 5 publications

(24 citation statements)

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“…We considered a resting-state fMRI dataset collected as part of the Human Connectome Project (HCP) [44,45]. The dataset consisted of the subset of fMRI scans of 400 subjects (168 males and 232 females) over approximately 14.5 minutes using a gradient-echoplanar imaging sequence with 1200 time points [24,32]. Informed consent was obtained from all participants by the Washington University in St. Louis institutional review board [46].…”

Section: Datamentioning

confidence: 99%

“…The number of connected components and the number of independent cycles in a graph are referred to as the 0th Betti number (β 0 ) and 1st Betti number (β 1 ), respectively. For 1-skeletons, there is an efficient 1D filtration method called the graph filtration, which filters at the edge weights from −∞ to ∞ in a sequentially increasing manner [6,32]. The graph filtration of G is defined as a collection of nested binary networks…”

Section: Simplicial Complexmentioning

confidence: 99%

“…Since the real brain networks are often affected by heterogeneity and intrinsic randomness [30,31], it is challenging to build a coherent statistical framework to transform these topological features as quantitative measures to compare across different brain networks by averaging or matching [32]. The brain networks are inherently noisy which makes it even harder to establish similarity across networks.…”

Section: Introductionmentioning

confidence: 99%

“…We consider a random complete graph, where all the nodes are connected with its edge weights randomly drawn from a continuous distribution. The consideration of a complete graph model simplifies building graph filtration straightforward [22,32]. We then compute the expected 0D and 1D barcodes through the order statistics [38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

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Topological Data Analysis of Human Brain Networks Through Order Statistics

Das

Anand

Chung

2022

Preprint

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Understanding the topological characteristics of the brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological features of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using the order statistics for analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We conclude a statistically significant topological difference between the male and female brain networks.

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Section: Datamentioning

confidence: 99%

Section: Simplicial Complexmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topological Data Analysis of Human Brain Networks Through Order Statistics

Das

Anand

Chung

2022

Preprint

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“…The complete proof is given in the supplementary material. The results in [Songdechakraiwut and Chung, 2020] may be used to find the centroid of different size networks.…”

Section: Topological Clusteringmentioning

confidence: 99%

Fast Topological Clustering with Wasserstein Distance

Songdechakraiwut¹,

Krause²,

Banks³

et al. 2021

Preprint

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The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and dense networks whose node degrees range over multiple orders of magnitude. In this paper, we propose a novel and computationally practical topological clustering method that clusters complex networks with intricate topology using principled theory from persistent homology and optimal transport. Such networks are aggregated into clusters through a centroid-based clustering strategy based on both their topological and geometric structure, preserving correspondence between nodes in different networks. The notions of topological proximity and centroid are characterized using a novel and efficient approach to computation of the Wasserstein distance and barycenter for persistence barcodes associated with connected components and cycles. The proposed method is demonstrated to be effective using both simulated networks and measured functional brain networks.

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Topological data analysis of human brain networks through order statistics

Das

Anand²,

Chung³

2023

PLoS ONE

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Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological properties of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using the order statistics for analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We found a statistically significant topological difference between the male and female brain networks.

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Topological Learning for Brain Networks

Cited by 5 publications

References 0 publications

Topological Data Analysis of Human Brain Networks Through Order Statistics

Topological Data Analysis of Human Brain Networks Through Order Statistics

Fast Topological Clustering with Wasserstein Distance

Topological data analysis of human brain networks through order statistics

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