Gene Coexpression Network Comparison via Persistent Homology

Duman, Ali Nabi; Pirim, Harun

doi:10.1155/2018/7329576

Cited by 8 publications

(8 citation statements)

References 32 publications

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“…This result is consistent with our initial observations based on co-expression networks, where we observed significant overlap in the modules detected in the ASD and control networks [6]. A recent paper took a related approach, using the bottleneck distance between persistence diagrams, to assess (dis)similarities between co-expression networks from Arabidopsis after exposure to multiple types of stressors [26].…”

Section: Discussionsupporting

confidence: 90%

Persistent homology analysis of brain transcriptome data in autism

Shnier

Voineagu

2019

J. R. Soc. Interface.

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Persistent homology methods have found applications in the analysis of multiple types of biological data, particularly imaging data or data with a spatial and/or temporal component. However, few studies have assessed the use of persistent homology for the analysis of gene expression data. Here we apply persistent homology methods to investigate the global properties of gene expression in post-mortem brain tissue (cerebral cortex) of individuals with autism spectrum disorders (ASD) and matched controls. We observe a significant difference in the geometry of inter-sample relationships between autism and healthy controls as measured by the sum of the death times of zero-dimensional components and the Euler characteristic. This observation is replicated across two distinct datasets, and we interpret it as evidence for an increased heterogeneity of gene expression in autism. We also assessed the topology of gene-level point clouds and did not observe significant differences between ASD and control transcriptomes, suggesting that the overall transcriptome organization is similar in ASD and healthy cerebral cortex. Overall, our study provides a novel framework for persistent homology analyses of gene expression data for genetically complex disorders.

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Section: Discussionsupporting

confidence: 90%

Persistent homology analysis of brain transcriptome data in autism

Shnier

Voineagu

2019

J. R. Soc. Interface.

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“…[7] and [25] computed persistence homology at dimension 0, 1, and 2 of the clique filtration to study weighted collaboration networks (size ∼36000) and weighted networks from different domains (size ∼54000) respectively. In biology domain, [12] clustered gene co-expression networks (size ∼400) based on distances be-tween Vietoris-Rips persistence diagram computed on each network. [21] studied Vietoris-Rips filtration of the functional brain networks computed on ∼100 region of interests (points) in human brains with different clinical disorders.…”

Section: Related Workmentioning

confidence: 99%

$ε$-net Induced Lazy Witness Complexes on Graphs

Arafat,

Basu,

Bressan

2020

Preprint

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Computation of persistent homology of simplicial representations such as the Rips and the Cěch complexes do not efficiently scale to large point clouds. It is, therefore, meaningful to devise approximate representations and evaluate the trade-off between their efficiency and effectiveness. The lazy witness complex economically defines such a representation using only a few selected points, called landmarks. Topological data analysis traditionally considers a point cloud in a Euclidean space. In many situations, however, data is available in the form of a weighted graph. A graph along with the geodesic distance defines a metric space. This metric space of a graph is amenable to topological data analysis. We discuss the computation of persistent homologies on a weighted graph. We present a lazy witness complex approach leveraging the notion of -net that we adapt to weighted graphs and their geodesic distance to select landmarks. We show that the value of the parameter of the -net provides control on the trade-off between choice and number of landmarks and the quality of the approximate simplicial representation. We present three algorithms for constructing an -net of a graph. We comparatively and empirically evaluate the efficiency and effectiveness of the choice of landmarks that they induce for the topological data analysis of different real-world graphs.

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“…[3] and [25] computed persistence homology at dimension 0,1 and 2 of the clique filtration to study weighted collaboration networks (size ∼36000) and weighted networks from different domains (size ∼54000) respectively. In biological networks, [11] clustered gene co-expression networks (size ∼ 400) based on distances between Vietoris-Rips persistence diagram computed on each net-…”

Section: Related Workmentioning

confidence: 99%

“…[3] and [25] computed persistence homology at dimension 0,1 and 2 of the clique filtration to study weighted collaboration networks (size ∼36000) and weighted networks from different domains (size ∼54000) respectively. In biological networks, [11] work. In molecular biology, persistent homology reveals different conformations of proteins [30,19] based on the strength of the bonds of the molecules.…”

Section: Related Workmentioning

confidence: 99%

Topological Data Analysis with $$\epsilon $$-net Induced Lazy Witness Complex

Basu

Bressan

2019

Lecture Notes in Computer Science

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Topological data analysis computes and analyses topological features of the point clouds by constructing and studying a simplicial representation of the underlying topological structure. The enthusiasm that followed the initial successes of topological data analysis was curbed by the computational cost of constructing such simplicial representations. The lazy witness complex is a computationally feasible approximation of the underlying topological structure of a point cloud. It is built in reference to a subset of points, called landmarks, rather than considering all the points as in theČech and Vietoris-Rips complexes. The choice and the number of landmarks dictate the effectiveness and efficiency of the approximation. We adopt the notion of -cover to define -net. We prove that -net, as a choice of landmarks, is an -approximate representation of the point cloud and the induced lazy witness complex is a 3-approximation of the induced Vietoris-Rips complex. Furthermore, we propose three algorithms to construct -net landmarks. We establish the relationship of these algorithms with the existing landmark selection algorithms. We empirically validate our theoretical claims. We empirically and comparatively evaluate the effectiveness, efficiency, and stability of the proposed algorithms on synthetic and real datasets.

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Gene Coexpression Network Comparison via Persistent Homology

Cited by 8 publications

References 32 publications

Persistent homology analysis of brain transcriptome data in autism

Persistent homology analysis of brain transcriptome data in autism

$ε$-net Induced Lazy Witness Complexes on Graphs

Topological Data Analysis with $$\epsilon $$-net Induced Lazy Witness Complex

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