Topological Distances Between Brain Networks

Chung, Moo K.; Lee, Hyekyoung; Solo, Victor; Davidson, Richard J.; Pollak, Seth D.

doi:10.1007/978-3-319-67159-8_19

Cited by 39 publications

(30 citation statements)

References 184 publications

(351 reference statements)

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“…Although we did not provide a comparison against baseline approaches, KS-distance was compared against other topological distances and matrix norms before [14]. Schematic of how Betti numbers change over graph filtration.…”

Section: Discussionmentioning

confidence: 99%

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Statistical Inference on the Number of Cycles in Brain Networks

Chung

Huang

Gritsenko

et al. 2019

2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019)

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A cycle in a graph is a subset of a connected component with redundant additional connections. If there are many cycles in a connected component, the connected component is more densely connected. While the number of connected components represents the integration of the brain network, the number of cycles represents how strong the integration is. However, enumerating cycles in the network is not easy and often requires brute force enumerations. In this study, we present a new scalable algorithm for enumerating the number of cycles in the network. We show that the number of cycles is monotonically decreasing with respect to the filtration values during graph filtration. We further develop a new statistical inference framework for determining the significance of the number of cycles. The methods are applied in determining if the number of cycles is a statistically significant heritable network feature in the functional human brain network.

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Section: Discussionmentioning

confidence: 99%

“…Given network = (V, w) with node set V and edge weight w = (w ij ) between nodes i and j, define binary network ϵ = V, w ϵ , where any edge weight of w less than or equal to ϵ is made into zero while edge weight larger than ϵ is made into one. Then we have graph filtration [5,14] ϵ 0…”

Section: Monotonicity Of Number Of Cyclesmentioning

confidence: 99%

Statistical Inference on the Number of Cycles in Brain Networks

Chung

Huang

Gritsenko

et al. 2019

2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019)

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“…Naturally, we are interested in using correlations or their simple functions such asρij=boldxi⊤boldxj1emor1emρij=1−boldxi⊤boldxjas edge weights. Among possible functions of correlations,wij=false(1−ρijfalse)1/2satisfies triangle inequality w ij ≤ w ik + w kj and other metric properties (Chung, Lee, Solo, Davidson, & Pollak, 2017a). Having metric distances facilitates more mathematically coherent interpretation of brain networks and offers many nice mathematical properties.…”

Section: Correlation Brain Networkmentioning

confidence: 99%

Exact topological inference of the resting-state brain networks in twins

Chung

Lee

DiChristofano

et al. 2019

Network Neuroscience

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A cycle in a brain network is a subset of a connected component with redundant additional connections. If there are many cycles in a connected component, the connected component is more densely connected. Whereas the number of connected components represents the integration of the brain network, the number of cycles represents how strong the integration is. However, it is unclear how to perform statistical inference on the number of cycles in the brain network. In this study, we present a new statistical inference framework for determining the significance of the number of cycles through the Kolmogorov-Smirnov (KS) distance, which was recently introduced to measure the similarity between networks across different filtration values by using the zeroth Betti number. In this paper, we show how to extend the method to the first Betti number, which measures the number of cycles. The performance analysis was conducted using the random network simulations with ground truths. By using a twin imaging study, which provides biological ground truth, the methods are applied in determining if the number of cycles is a statistically significant heritable network feature in the resting-state functional connectivity in 217 twins obtained from the Human Connectome Project. The MATLAB codes as well as the connectivity matrices used in generating results are provided at http://www.stat.wisc.edu/∼mchung/TDA .

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“…The above simulation produces modular structures in the network (Chung et al, 2017a). Let Y 1 be the 20 × 5 data matrix…”

Section: Validationmentioning

confidence: 99%

Statistical model for dynamically-changing correlation matrices with application to brain connectivity

Huang

Samdin

Ting

et al. 2020

Journal of Neuroscience Methods

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Background: Recent studies have indicated that functional connectivity is dynamic even during rest. A common approach to modeling the dynamic functional connectivity in whole-brain resting-state fMRI is to compute the correlation between anatomical regions via sliding time windows. However, the direct use of the sample correlation matrices is not reliable due to the image acquisition and processing noises in resting-sate fMRI.New method: To overcome these limitations, we propose a new statistical model that smooths out the noise by exploiting the geometric structure of correlation matrices. The dynamic correlation matrix is modeled as a linear combination of symmetric positive-definite matrices combined with cosine series representation. The resulting smoothed dynamic correlation matrices are clustered into disjoint brain connectivity states using the k-means clustering algorithm.Results: The proposed model preserves the geometric structure of underlying physiological dynamic correlation, eliminates unwanted noise in connectivity and obtains more accurate state spaces. The difference in the estimated dynamic connectivity states between males and females is identified. statistical model has less rapid state changes caused by noise and improves the accuracy in identifying and discriminating different states.Conclusions: We propose a new regression model on dynamically changing correlation matrices that provides better performance over existing windowed correlation and is more reliable for the modeling of dynamic connectivity.

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Topological Distances Between Brain Networks

Cited by 39 publications

References 184 publications

Statistical Inference on the Number of Cycles in Brain Networks

Statistical Inference on the Number of Cycles in Brain Networks

Exact topological inference of the resting-state brain networks in twins

Statistical model for dynamically-changing correlation matrices with application to brain connectivity

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