Geometric and Topological Inference for Deep Representations of Complex Networks

Lin, Baihan

doi:10.1145/3487553.3524194

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…Existing TDA applications usually focus on the low-dimensional graph visualization and persistent homology of the data (e.g., computing the Betti numbers or barcodes up to the second dimension), because interpreting the biophysical meaning of the geometry and higher dimensional persistent modules is a conceptual challenge. Others have proposed hybrid approaches to combine the merits of data geometry and topology by adaptively selecting the proper thresholds in the pairwise distance matrix of the data points [17,18]. Another alternative to these low-dimensional TDA methods is simplicial analysis.…”

Section: Quest From Topological Data Analysismentioning

confidence: 99%

Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomics

Lin

2022

Algorithms

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The absence of a conventional association between the cell–cell cohabitation and its emergent dynamics into cliques during development has hindered our understanding of how cell populations proliferate, differentiate, and compete (i.e., the cell ecology). With the recent advancement of single-cell RNA sequencing (RNA-seq), we can potentially describe such a link by constructing network graphs that characterize the similarity of the gene expression profiles of the cell-specific transcriptional programs and analyze these graphs systematically using the summary statistics given by the algebraic topology. We propose single-cell topological simplicial analysis (scTSA). Applying this approach to the single-cell gene expression profiles from local networks of cells in different developmental stages with different outcomes reveals a previously unseen topology of cellular ecology. These networks contain an abundance of cliques of single-cell profiles bound into cavities that guide the emergence of more complicated habitation forms. We visualize these ecological patterns with topological simplicial architectures of these networks, compared with the null models. Benchmarked on the single-cell RNA-seq data of zebrafish embryogenesis spanning 38,731 cells, 25 cell types, and 12 time steps, our approach highlights gastrulation as the most critical stage, consistent with the consensus in developmental biology. As a nonlinear, model-independent, and unsupervised framework, our approach can also be applied to tracing multi-scale cell lineage, identifying critical stages, or creating pseudo-time series.

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Section: Quest From Topological Data Analysismentioning

confidence: 99%

Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomics

Lin

2022

Algorithms

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“…computing the Betti numbers or barcodes up to dimension 2), because interpreting the biophysical meaning of the geometry and higher dimensional persistent modules is a conceptual challenge. Others have proposed hybrid approaches to combine the merits of data geometry and topology by adaptively selecting the proper thresholds in the pairwise distance matrix of the data points [12,13]. Another alternative to these low-dimensional TDA methods is the simplicial analysis.…”

Section: Introductionmentioning

confidence: 99%

Single-Cell Topological Simplicial Analysis Reveals Higher-Order Cellular Complexity

Lin

2022

2022 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

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The absence of a conventional association between the cell-cell cohabitation and its emergent dynamics into cliques during development has hindered our understanding of how cell populations proliferate, differentiate, and compete, i.e. the cell ecology. With the recent advancement of the single-cell RNAsequencing (RNA-seq), we can potentially describe such a link by constructing network graphs that characterize the similarity of the gene expression profiles of the cell-specific transcriptional programs, and analyzing these graphs systematically using the summary statistics informed by the algebraic topology.We propose the single-cell topological simplicial analysis (scTSA). Applying this approach to the single-cell gene expression profiles from local networks of cells in different developmental stages with different outcomes reveals a previously unseen topology of cellular ecology. These networks contain an abundance of cliques of single-cell profiles bound into cavities that guide the emergence of more complicated habitation forms. We visualize these ecologi-1 cal patterns with topological simplicial architectures of these networks, compared with the null models. Benchmarked on the single-cell RNA-seq data of zebrafish embryogenesis spanning 38,731 cells, 25 cell types and 12 time steps, our approach highlights the gastrulation as the most critical stage, consistent with consensus in developmental biology. As a nonlinear, model-independent and unsupervised framework, our method can also be applied to tracing multiscale cell lineage, identifying critical stages, or creating pseudo-time series.

show abstract

Geometric and Topological Inference for Deep Representations of Complex Networks

Cited by 2 publications

References 15 publications

Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomics

Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomics

Single-Cell Topological Simplicial Analysis Reveals Higher-Order Cellular Complexity

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