Computing the Shape of Brain Networks Using Graph Filtration and Gromov-Hausdorff Metric

Lee, Hyekyoung; Chung, Moo K.; Kang, Hyejin; Kim, Boong-Nyun; Lee, Dong Hoon

doi:10.1007/978-3-642-23629-7_37

Cited by 80 publications

(117 citation statements)

References 14 publications

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“…Similarly, we also have graph filtration for the case of the sequence of nested binary networks [44] …”

Section: B Multiscale Network As Graph Filtrationmentioning

confidence: 99%

“…In our brain network model, the node sets X and Y is given in the fixed identical locations in the template. Therefore, the node x i ∈ X is simply mapped to y i ∈ Y [44], [57]. Therefore, GH-distance can be trivially discretized as…”

Section: Gromov-hausdorff Distancementioning

confidence: 99%

“…Since the construction of a single linkage dendrogram is equivalent to that of the minimum spanning tree (MST) [44], it is possible to speed up the computation by using either the Prim's or Kruskal's algorithm that are often used in finding MST. The relationship between MST and our persistent homological framework is also left out for a future study.…”

Section: Future Workmentioning

confidence: 99%

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Persistent Brain Network Homology From the Perspective of Dendrogram

Lee

Kang

Chung

et al. 2012

IEEE Trans. Med. Imaging

197

120

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The brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level. The problem with this standard method is that we do not have any generally accepted criteria for determining a proper threshold. Thus, we propose a novel multiscale framework that models all brain networks generated over every possible threshold. Our approach is based on persistent homology and its various representations such as the Rips filtration, barcodes and dendrograms. This new persistent homological framework enables us to quantify various persistent topological features at different scales in a coherent manner. The barcode is used to quantify and visualize the evolutionary changes of topological features such as the Betti numbers over different scales.By incorporating additional geometric information to the barcode, we obtain a single linkage dendrogram that shows the overall evolution of the network. The difference between the two networks is then measured by the Gromov-Hausdorff distance over the dendrograms.As an illustration, we modeled and differentiated the FDG-PET based functional brain networks of 24 attentiondeficit hyperactivity disorder children, 26 autism spectrum disorder children and 11 pediatric control subjects.

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“…Similarly, we also have graph filtration for the case of the sequence of nested binary networks [44] …”

Section: B Multiscale Network As Graph Filtrationmentioning

confidence: 99%

Section: Gromov-hausdorff Distancementioning

confidence: 99%

Section: Future Workmentioning

confidence: 99%

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Persistent Brain Network Homology From the Perspective of Dendrogram

Lee

Kang

Chung

et al. 2012

IEEE Trans. Med. Imaging

197

120

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show abstract

“…Then K d may be used as in Section 2.2 to embed the n images into a d-dimensional Euclidean space. [18]. Nonnegative definite similarity matrices have in recent years been frequently used in statistical model building for images; for a recent example see [31].…”

Section: Image Similarity and Dissimilaritymentioning

confidence: 99%

“…A different take on dissimilarities between functonal brain network images based on FDG-PET scans is found in [18].…”

Section: Image Similarity and Dissimilaritymentioning

confidence: 99%

Dissimilarity data in statistical model building and machine learning

Ji¹,

Poon²,

Yang³

et al. 2012

AMS/IP Studies in Advanced Mathematics

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Abstract. We explore three papers concerned with two methods for incorporating discrete, noisy, incomplete dissimilarity data into statistical/machine learning models for supervised, semisupervised or unsupervised machine learning. The two methods are RKE (Regularized Kernel Estimation), and RMU (Regularized Manifold Unfolding). Briefly put, the methods use dissimilarity information between objects in a training set to obtain a nonnegative definite matrix of (usually) relatively low rank, which is then used to embed the objects into a (usually) relatively low dimensional Euclidean space, where their coordinates can then be used as attributes in learning models of various types. Some suggestions for further work are noted.

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Degree‐based statistic and center persistency for brain connectivity analysis

Yoo

Lee

Chung³

et al. 2016

Human Brain Mapping

Self Cite

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Brain connectivity analyses have been widely performed to investigate the organization and functioning of the brain, or to observe changes in neurological or psychiatric conditions. However, connectivity analysis inevitably introduces the problem of mass-univariate hypothesis testing. Although, several cluster-wise correction methods have been suggested to address this problem and shown to provide high sensitivity, these approaches fundamentally have two drawbacks: the lack of spatial specificity (localization power) and the arbitrariness of an initial cluster-forming threshold. In this study, we propose a novel method, degree-based statistic (DBS), performing cluster-wise inference. DBS is designed to overcome the above-mentioned two shortcomings. From a network perspective, a few brain regions are of critical importance and considered to play pivotal roles in network integration. Regarding this notion, DBS defines a cluster as a set of edges of which one ending node is shared. This definition enables the efficient detection of clusters and their center nodes. Furthermore, a new measure of a cluster, center persistency (CP) was introduced. The efficiency of DBS with a known "ground truth" simulation was demonstrated. Then they applied DBS to two experimental datasets and showed that DBS successfully detects the persistent clusters. In conclusion, by adopting a graph theoretical concept of degrees and borrowing the concept of persistence from algebraic topology, DBS could sensitively identify clusters with centric nodes that would play pivotal roles in an effect of interest. DBS is potentially widely applicable to variable cognitive or clinical situations and allows us to obtain statistically reliable and easily interpretable results. Hum Brain Mapp 38:165-181, 2017. © 2016 Wiley Periodicals, Inc.

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Computing the Shape of Brain Networks Using Graph Filtration and Gromov-Hausdorff Metric

Cited by 80 publications

References 14 publications

Persistent Brain Network Homology From the Perspective of Dendrogram

Persistent Brain Network Homology From the Perspective of Dendrogram

Dissimilarity data in statistical model building and machine learning

Degree‐based statistic and center persistency for brain connectivity analysis

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