Ripser: efficient computation of Vietoris–Rips persistence barcodes

Bauer, Ulrich

doi:10.1007/s41468-021-00071-5

Cited by 235 publications

(231 citation statements)

References 34 publications

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“…In order to identify signals of convergent evolution in SARS-CoV-2, we define a novel index of recurrence in reticulate phylogenies that is based on persistent homology and does not rely on a possibly sub-optimal tree reconstruction. We use a specifically designed algorithm, implemented in a recent version of Ripser [2], that associates to each bar in the persistence barcode an explicit topological cycle given by a series of isolates that approximates all potentially relevant evolutionary steps as faithfully as possible (see Methods). We further consider only SNV cycles, for which adjacent sequences only di↵er by single nucleotide variations (SNV) and that do not include more than one substition per site (Figure 2).…”

Section: Resultsmentioning

confidence: 99%

“…The alignment was compiled from all 303,651 high quality genomes in the complete GISAID EpiCoV dataset as of 28 February 2021. The computation involved the generation of a genetic distance matrix (Hamming distance) of the dataset with Hammingdist [20] and the subsequent computation of its persistence barcode with Ripser [2] (see Methods). The resulting barcode is shown in Figure 3 and features 2,899 bars across all genetic distance scales at the current level of diversification.…”

Section: Resultsmentioning

confidence: 99%

“…A limitation of most of the algorithms in the literature that compute the persistent homology of Vietoris-Rips filtrations, is that they do not provide the samples forming the cycles corresponding to the bars in the barcode. Fortunately, this feature became recently available for the software Ripser [2], so we used it to compute the persistent homology of the Vietoris-Rips filtration associated to the genetic distance matrix for each time bucket sub-alignment (whole genome and Spike gene). As we are only interested in SNV cycles, the computation of persistence barcodes for the time bucket sub-alignments was restricted to small genetic distance scales (Ripser scaling parameter threshold set to 2), which greatly increases the speed of the computation.…”

Section: Methodsmentioning

confidence: 99%

“…1 [38] and van Dorp et al2 [39]. For a complete list of mutations with statistically significant topological signal (tRI 2) see TableS2.…”

mentioning

confidence: 99%

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Topological data analysis identifies emerging adaptive mutations in SARS-CoV-2

Bleher

Hahn

Patiño-Galindo

et al. 2021

Preprint

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The COVID-19 pandemic has lead to a worldwide effort to characterize its evolution through the mapping of mutations in the genome of the coronavirus SARS-CoV-2. As the virus spreads and evolves it acquires new mutations that could have important public health consequences, including higher transmissibility, morbidity, mortality, and immune evasion, among others. Ideally, we would like to quickly identify new mutations that could confer adaptive advantages to the evolving virus by leveraging the large number of SARS-CoV-2 genomes. One way of identifying adaptive mutations is by looking at convergent mutations, mutations in the same genomic position that occur independently. The large number of currently available genomes, more than a million at this moment, however precludes the efficient use of phylogeny-based techniques. Here, we establish a fast and scalable Topological Data Analysis approach for the early warning and surveillance of emerging adaptive mutations of the coronavirus SARS-CoV-2 in the ongoing COVID-19 pandemic. Our method relies on a novel topological tool for the analysis of viral genome datasets based on persistent homology. It systematically identifies convergent events in viral evolution merely by their topological footprint and thus overcomes limitations of current phylogenetic inference techniques. This allows for an unbiased and rapid analysis of large viral datasets. We introduce a new topological measure for convergent evolution and apply it to the complete GISAID dataset as of February 2021, comprising 303,651 high-quality SARS-CoV-2 isolates taken from patients all over the world since the beginning of the pandemic. A complete list of mutations showing topological signals of convergence is compiled. We find that topologically salient mutations on the receptor-binding domain appear in several variants of concern and are linked with an increase in infectivity and immune escape. Moreover, for many adaptive mutations the topological signal precedes an increase in prevalence. We demonstrate the capability of our method to effectively identify emerging adaptive mutations at an early stage. By localizing topological signals in the dataset, we are able to extract geo-temporal information about the early occurrence of emerging adaptive mutations. The identification of these mutations can help to develop an alert system to monitor mutations of concern and guide experimentalists to focus the study of specific circulating variants.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…1 [38] and van Dorp et al2 [39]. For a complete list of mutations with statistically significant topological signal (tRI 2) see TableS2.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Topological data analysis identifies emerging adaptive mutations in SARS-CoV-2

Bleher

Hahn

Patiño-Galindo

et al. 2021

Preprint

Self Cite

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“…There are several software packages that implement a cohomology-based algorithm and report back the computed cocycles. JavaPlex [1] and Dionysus [32] are old players in the field, while much improved performance can be found using Ripser [5]. The Ripser software package has been reported to comfortably compute with 50 000 data points, generating over 2 000 000 simplices for degree 1 cohomology.…”

Section: Circular Coordinates Visualizationmentioning

confidence: 99%

Generalized penalty for circular coordinate representation

Luo¹,

Patania²,

Kim³

et al. 2021

FoDS

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<p style='text-indent:20px;'>Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. To do that, we use a generalized penalty function instead of an <inline-formula><tex-math id="M1">\begin{document}$ L_{2} $\end{document}</tex-math></inline-formula> penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analyses to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.</p>

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Persistent spectral graph

Wang

Nguyen

Wei

2020

Numer Methods Biomed Eng

106

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Persistent homology is constrained to purely topological persistence, while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low‐dimensional multiscale paradigm for revealing topological persistence and extracting geometric shapes from high‐dimensional datasets. For a point‐cloud dataset, a filtration procedure is used to generate a sequence of chain complexes and associated families of simplicial complexes and chains, from which we construct persistent combinatorial Laplacian matrices. We show that a full set of topological persistence can be completely recovered from the harmonic persistent spectra, that is, the spectra that have zero eigenvalues, of the persistent combinatorial Laplacian matrices. However, non‐harmonic spectra of the Laplacian matrices induced by the filtration offer another powerful tool for data analysis, modeling, and prediction. In this work, fullerene stability is predicted by using both harmonic spectra and non‐harmonic persistent spectra, while the latter spectra are successfully devised to analyze the structure of fullerenes and model protein flexibility, which cannot be straightforwardly extracted from the current persistent homology. The proposed method is found to provide excellent predictions of the protein B‐factors for which current popular biophysical models break down.

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Ripser: efficient computation of Vietoris–Rips persistence barcodes

Cited by 235 publications

References 34 publications

Topological data analysis identifies emerging adaptive mutations in SARS-CoV-2

Topological data analysis identifies emerging adaptive mutations in SARS-CoV-2

Generalized penalty for circular coordinate representation

Persistent spectral graph

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