A New Entropy for Hypergraphs

Bloch, Isabelle; Bretto, Alain

doi:10.1007/978-3-030-14085-4_12

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…every genomic locus is highly connected). There are different definitions of hypergraph entropy [8,24,25]. In our analysis, we exploit the eigenvalues of the hypergraph Laplacian matrix and fit them into the Shannon entropy formula [25].…”

Section: Methodsmentioning

confidence: 99%

“…There are different definitions of hypergraph entropy [8,24,25]. In our analysis, we exploit the eigenvalues of the hypergraph Laplacian matrix and fit them into the Shannon entropy formula [25]. In mathematics, eigenvalues can quantitatively represent different features of a matrix [26].…”

Section: Methodsmentioning

confidence: 99%

“…We used the hypergraph entropy proposed in [26] to quantify the organization of chromatin structure from Pore-C data.…”

Section: Methodsmentioning

confidence: 99%

“…Network entropy often is used to measure the connectivity and regularity of a network [13, 48, 49]. We used the hypergraph entropy proposed in [50] to quantify the organization of chromatin structure from Pore-C data. Denote the incidence matrix of the genomic hypergraph as H .…”

Section: Methodsmentioning

confidence: 99%

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Deciphering Multi-way Interactions in the Human Genome

Lindsly

Chen

Dilworth³

et al. 2021

Preprint

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Chromatin architecture, a key regulator of gene expression, is inferred through chromatin contacts. However, classical analyses of chromosome conformation data do not preserve multi-way relationships. Here we use long sequencing reads to map genome-wide multi-way contacts and investigate higher order chromatin organization of the human genome. We use the theory of hypergraphs for data representation and analysis, and quantify higher order structures in primary human fibroblasts and B lymphocytes. Through integration of multi-way contact data with chromatin accessibility, gene expression, and transcription factor binding data, we introduce a data-driven method to extract transcriptional clusters.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…We used the hypergraph entropy proposed in [26] to quantify the organization of chromatin structure from Pore-C data.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Deciphering Multi-way Interactions in the Human Genome

Lindsly

Chen

Dilworth³

et al. 2021

Preprint

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“…Hypergraph entropy has been recently explored by Hu et al [30], Wang et al [31] and Bloch et al [32]. In particular, the authors in [30] employ the probability distribution of the vertex degrees to fit into the Shannon entropy formula and establish its lower and upper bounds for special hypergraphs.…”

Section: Introductionmentioning

confidence: 99%

Tensor Entropy for Uniform Hypergraphs

Chen,

Rajapakse

2019

Preprint

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In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula. We show that this tensor entropy is an extension of von Neumann entropy for graphs. In addition, we establish results on the lower and upper bounds of the entropy and demonstrate that it is a measure of regularity for uniform hypergraphs in simulated and experimental data. We exploit the tensor train decomposition in computing the proposed tensor entropy efficiently. Finally, we introduce the notion of robustness for uniform hypergraphs.

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