{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:16:32Z","timestamp":1772172992604,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009600","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:00:00Z","timestamp":1649030400000}}],"reference-count":57,"publisher":"Public Library of Science (PLoS)","issue":"3","license":[{"start":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T00:00:00Z","timestamp":1646870400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Annotation of cells in single-cell clustering requires a homogeneous grouping of cell populations. There are various issues in single cell sequencing that effect homogeneous grouping (clustering) of cells, such as small amount of starting RNA, limited per-cell sequenced reads, cell-to-cell variability due to cell-cycle, cellular morphology, and variable reagent concentrations. Moreover, single cell data is susceptible to technical noise, which affects the quality of genes (or features) selected\/extracted prior to clustering.<\/jats:p>\n                  <jats:p>\n                    Here we introduce sc-CGconv (\n                    <jats:bold>c<\/jats:bold>\n                    opula based\n                    <jats:bold>g<\/jats:bold>\n                    raph\n                    <jats:bold>conv<\/jats:bold>\n                    olution network for\n                    <jats:bold>s<\/jats:bold>\n                    ingle\n                    <jats:bold>c<\/jats:bold>\n                    lustering), a stepwise robust unsupervised feature extraction and clustering approach that formulates and aggregates cell\u2013cell relationships using copula correlation (Ccor), followed by a graph convolution network based clustering approach. sc-CGconv formulates a cell-cell graph using\n                    <jats:italic>Ccor<\/jats:italic>\n                    that is learned by a graph-based artificial intelligence model, graph convolution network. The learned representation (low dimensional embedding) is utilized for cell clustering. sc-CGconv features the following advantages. a. sc-CGconv works with substantially smaller sample sizes to identify homogeneous clusters. b. sc-CGconv can model the expression co-variability of a large number of genes, thereby outperforming state-of-the-art gene selection\/extraction methods for clustering. c. sc-CGconv preserves the cell-to-cell variability within the selected gene set by constructing a cell-cell graph through copula correlation measure. d. sc-CGconv provides a topology-preserving embedding of cells in low dimensional space.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1009600","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T13:58:57Z","timestamp":1646920737000},"page":"e1009600","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["A copula based topology preserving graph convolution network for clustering of single-cell RNA-seq data"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6694-5344","authenticated-orcid":true,"given":"Snehalika","family":"Lall","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3371-8516","authenticated-orcid":true,"given":"Sumanta","family":"Ray","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6370-2083","authenticated-orcid":true,"given":"Sanghamitra","family":"Bandyopadhyay","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,3,10]]},"reference":[{"key":"pcbi.1009600.ref001","doi-asserted-by":"crossref","DOI":"10.1038\/ncomms14049","article-title":"Massively parallel digital transcriptional profiling of single cells","volume":"8","author":"GX Zheng","year":"2017","journal-title":"Nature communications"},{"issue":"1","key":"pcbi.1009600.ref002","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13059-020-1926-6","article-title":"Eleven grand challenges in single-cell data science","volume":"21","author":"D L\u00e4hnemann","year":"2020","journal-title":"Genome biology"},{"key":"pcbi.1009600.ref003","article-title":"MarkerCapsule: Explainable Single Cell Typing using Capsule Networks","author":"S Ray","year":"2020","journal-title":"bioRxiv"},{"issue":"5","key":"pcbi.1009600.ref004","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1038\/nmeth.4236","article-title":"SC3: consensus clustering of single-cell RNA-seq data","volume":"14","author":"VY Kiselev","year":"2017","journal-title":"Nature methods"},{"issue":"1","key":"pcbi.1009600.ref005","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1186\/1755-8794-3-21","article-title":"SEURAT: visual analytics for the integrated analysis of microarray data","volume":"3","author":"A Gribov","year":"2010","journal-title":"BMC medical genomics"},{"issue":"6391","key":"pcbi.1009600.ref006","doi-asserted-by":"crossref","DOI":"10.1126\/science.aaq1723","article-title":"Cell type atlas and lineage tree of a whole complex animal by single-cell transcriptomics","volume":"360","author":"M Plass","year":"2018","journal-title":"Science"},{"issue":"6391","key":"pcbi.1009600.ref007","doi-asserted-by":"crossref","DOI":"10.1126\/science.aaq1736","article-title":"Cell type transcriptome atlas for the planarian Schmidtea mediterranea","volume":"360","author":"CT Fincher","year":"2018","journal-title":"Science"},{"issue":"6","key":"pcbi.1009600.ref008","doi-asserted-by":"crossref","first-page":"e8746","DOI":"10.15252\/msb.20188746","article-title":"Current best practices in single-cell RNA-seq analysis: a tutorial","volume":"15","author":"MD Luecken","year":"2019","journal-title":"Molecular systems biology"},{"issue":"4","key":"pcbi.1009600.ref009","doi-asserted-by":"crossref","first-page":"314","DOI":"10.2174\/1574893614666181120095038","article-title":"Analysis of single-cell RNA-seq data by clustering approaches","volume":"14","author":"X Zhu","year":"2019","journal-title":"Current Bioinformatics"},{"key":"pcbi.1009600.ref010","article-title":"sc-REnF: An entropy guided robust feature selection for clustering of single-cell rna-seq data","author":"S Lall","year":"2020","journal-title":"bioRxiv"},{"issue":"8","key":"pcbi.1009600.ref011","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1093\/bioinformatics\/btw777","article-title":"Scater: pre-processing, quality control, normalization and visualization of single-cell RNA-seq data in R","volume":"33","author":"DJ McCarthy","year":"2017","journal-title":"Bioinformatics"},{"key":"pcbi.1009600.ref012","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.mam.2017.07.002","article-title":"Identifying cell populations with scRNASeq","volume":"59","author":"TS Andrews","year":"2018","journal-title":"Molecular aspects of medicine"},{"issue":"10","key":"pcbi.1009600.ref013","doi-asserted-by":"crossref","first-page":"e1009464","DOI":"10.1371\/journal.pcbi.1009464","article-title":"RgCop-A regularized copula based method for gene selection in single cell rna-seq data","volume":"17","author":"S Lall","year":"2021","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1009600.ref014","article-title":"Generating realistic cell samples for gene selection in scRNA-seq data: A novel generative framework","author":"S Lall","year":"2021","journal-title":"bioRxiv"},{"issue":"1","key":"pcbi.1009600.ref015","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13059-019-1861-6","article-title":"Feature selection and dimension reduction for single-cell RNA-Seq based on a multinomial model","volume":"20","author":"FW Townes","year":"2019","journal-title":"Genome biology"},{"issue":"4","key":"pcbi.1009600.ref016","doi-asserted-by":"crossref","first-page":"bbaa314","DOI":"10.1093\/bib\/bbaa314","article-title":"Goals and approaches for each processing step for single-cell RNA sequencing data","volume":"22","author":"Z Zhang","year":"2021","journal-title":"Briefings in Bioinformatics"},{"issue":"5","key":"pcbi.1009600.ref017","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1038\/nbt.4096","article-title":"Integrating single-cell transcriptomic data across different conditions, technologies, and species","volume":"36","author":"A Butler","year":"2018","journal-title":"Nature biotechnology"},{"issue":"5","key":"pcbi.1009600.ref018","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1038\/nbt.3192","article-title":"Spatial reconstruction of single-cell gene expression data","volume":"33","author":"R Satija","year":"2015","journal-title":"Nature biotechnology"},{"key":"pcbi.1009600.ref019","article-title":"Integrated analysis of multimodal single-cell data","author":"Y Hao","year":"2021","journal-title":"Cell"},{"issue":"1","key":"pcbi.1009600.ref020","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13059-019-1739-7","article-title":"CellSIUS provides sensitive and specific detection of rare cell populations from complex single-cell RNA-seq data","volume":"20","author":"R Wegmann","year":"2019","journal-title":"Genome biology"},{"key":"pcbi.1009600.ref021","article-title":"Structure-Aware Principal Component Analysis for Single-Cell RNA-seq Data","author":"S Lall","year":"2018","journal-title":"Journal of Computational Biology"},{"issue":"1","key":"pcbi.1009600.ref022","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1186\/s13059-016-1010-4","article-title":"GiniClust: detecting rare cell types from single-cell gene expression data with Gini index","volume":"17","author":"L Jiang","year":"2016","journal-title":"Genome biology"},{"issue":"7","key":"pcbi.1009600.ref023","doi-asserted-by":"crossref","first-page":"1888","DOI":"10.1016\/j.cell.2019.05.031","article-title":"Comprehensive integration of single-cell data","volume":"177","author":"T Stuart","year":"2019","journal-title":"Cell"},{"issue":"1","key":"pcbi.1009600.ref024","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41467-021-21453-4","article-title":"Optimal marker gene selection for cell type discrimination in single cell analyses","volume":"12","author":"B Dumitrascu","year":"2021","journal-title":"Nature communications"},{"issue":"22","key":"pcbi.1009600.ref025","doi-asserted-by":"crossref","first-page":"e179","DOI":"10.1093\/nar\/gkx828","article-title":"Linnorm: improved statistical analysis for single cell RNA-seq expression data","volume":"45","author":"SH Yip","year":"2017","journal-title":"Nucleic acids research"},{"issue":"11","key":"pcbi.1009600.ref026","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1016\/j.patrec.2010.04.004","article-title":"Locality sensitive hashing: A comparison of hash function types and querying mechanisms","volume":"31","author":"L Pauleve","year":"2010","journal-title":"Pattern Recognition Letters"},{"key":"pcbi.1009600.ref027","doi-asserted-by":"crossref","unstructured":"Indyk P, Motwani R, Raghavan P, Vempala S. Locality-preserving hashing in multidimensional spaces. In: Proceedings of the twenty-ninth annual ACM symposium on Theory of computing. ACM; 1997. p. 618\u2013625.","DOI":"10.1145\/258533.258656"},{"key":"pcbi.1009600.ref028","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139924801","volume-title":"Mining of massive datasets","author":"J Leskovec","year":"2014"},{"key":"pcbi.1009600.ref029","doi-asserted-by":"crossref","unstructured":"Bawa M, Condie T, Ganesan P. LSH forest: self-tuning indexes for similarity search. In: Proceedings of the 14th international conference on World Wide Web. ACM; 2005. p. 651\u2013660.","DOI":"10.1145\/1060745.1060840"},{"key":"pcbi.1009600.ref030","unstructured":"Kipf TN, Welling M. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:160902907. 2016."},{"key":"pcbi.1009600.ref031","unstructured":"Kingma DP, Ba J. Adam: A method for stochastic optimization. arXiv preprint arXiv:14126980. 2014."},{"issue":"4","key":"pcbi.1009600.ref032","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.cels.2016.08.011","article-title":"A single-cell transcriptomic map of the human and mouse pancreas reveals inter-and intra-cell population structure","volume":"3","author":"M Baron","year":"2016","journal-title":"Cell systems"},{"issue":"5","key":"pcbi.1009600.ref033","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1016\/j.cell.2015.04.044","article-title":"Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells","volume":"161","author":"AM Klein","year":"2015","journal-title":"Cell"},{"issue":"6282","key":"pcbi.1009600.ref034","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1126\/science.aad0501","article-title":"Dissecting the multicellular ecosystem of metastatic melanoma by single-cell RNA-seq","volume":"352","author":"I Tirosh","year":"2016","journal-title":"Science"},{"issue":"1","key":"pcbi.1009600.ref035","first-page":"1","article-title":"PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells","volume":"20","author":"FA Wolf","year":"2019","journal-title":"Genome biology"},{"issue":"7","key":"pcbi.1009600.ref036","doi-asserted-by":"crossref","first-page":"3797","DOI":"10.1109\/TIT.2014.2320500","article-title":"R\u00e9nyi divergence and Kullback-Leibler divergence","volume":"60","author":"T Van Erven","year":"2014","journal-title":"IEEE Transactions on Information Theory"},{"issue":"11","key":"pcbi.1009600.ref037","article-title":"Visualizing data using t-SNE","volume":"9","author":"L Van der Maaten","year":"2008","journal-title":"Journal of machine learning research"},{"key":"pcbi.1009600.ref038","doi-asserted-by":"crossref","unstructured":"McInnes L, Healy J, Melville J. Umap: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:180203426. 2018.","DOI":"10.21105\/joss.00861"},{"issue":"6","key":"pcbi.1009600.ref039","doi-asserted-by":"crossref","first-page":"e98679","DOI":"10.1371\/journal.pone.0098679","article-title":"ForceAtlas2, a continuous graph layout algorithm for handy network visualization designed for the Gephi software","volume":"9","author":"M Jacomy","year":"2014","journal-title":"PloS one"},{"issue":"12","key":"pcbi.1009600.ref040","doi-asserted-by":"crossref","first-page":"1482","DOI":"10.1038\/s41587-019-0336-3","article-title":"Visualizing structure and transitions in high-dimensional biological data","volume":"37","author":"KR Moon","year":"2019","journal-title":"Nature biotechnology"},{"issue":"11","key":"pcbi.1009600.ref041","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1038\/s41592-019-0576-7","article-title":"Exploring single-cell data with deep multitasking neural networks","volume":"16","author":"M Amodio","year":"2019","journal-title":"Nature methods"},{"key":"pcbi.1009600.ref042","unstructured":"Ester M, Kriegel HP, Sander J, Xu X, et al. A density-based algorithm for discovering clusters in large spatial databases with noise. In: kdd. vol. 96; 1996. p. 226\u2013231."},{"issue":"6","key":"pcbi.1009600.ref043","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1038\/nmeth.2930","article-title":"Validation of noise models for single-cell transcriptomics","volume":"11","author":"D Gr\u00fcn","year":"2014","journal-title":"Nature methods"},{"issue":"16","key":"pcbi.1009600.ref044","doi-asserted-by":"crossref","first-page":"2865","DOI":"10.1093\/bioinformatics\/bty1044","article-title":"M3Drop: dropout-based feature selection for scRNASeq","volume":"35","author":"TS Andrews","year":"2019","journal-title":"Bioinformatics"},{"key":"pcbi.1009600.ref045","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0377-0427(87)90125-7","article-title":"Silhouettes: a graphical aid to the interpretation and validation of cluster analysis","volume":"20","author":"PJ Rousseeuw","year":"1987","journal-title":"Journal of computational and applied mathematics"},{"key":"pcbi.1009600.ref046","doi-asserted-by":"crossref","DOI":"10.1201\/b10451","volume-title":"Robust nonparametric statistical methods","author":"TP Hettmansperger","year":"2010"},{"issue":"D1","key":"pcbi.1009600.ref047","doi-asserted-by":"crossref","first-page":"D721","DOI":"10.1093\/nar\/gky900","article-title":"CellMarker: a manually curated resource of cell markers in human and mouse","volume":"47","author":"X Zhang","year":"2019","journal-title":"Nucleic acids research"},{"key":"pcbi.1009600.ref048","volume-title":"An introduction to copulas","author":"RB Nelsen","year":"2007"},{"key":"pcbi.1009600.ref049","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-12465-5","volume-title":"Copula theory and its applications","author":"P Jaworski","year":"2010"},{"issue":"1","key":"pcbi.1009600.ref050","first-page":"1","article-title":"CODC: a Copula-based model to identify differential coexpression","volume":"6","author":"S Ray","year":"2020","journal-title":"NPJ systems biology and applications"},{"key":"pcbi.1009600.ref051","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-642-12465-5_1","volume-title":"Copula theory and its applications","author":"F Durante","year":"2010"},{"issue":"5","key":"pcbi.1009600.ref052","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1007\/s11222-018-9846-y","article-title":"Computationally efficient Bayesian estimation of high-dimensional Archimedean copulas with discrete and mixed margins","volume":"29","author":"D Gunawan","year":"2019","journal-title":"Statistics and Computing"},{"issue":"284","key":"pcbi.1009600.ref053","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1080\/01621459.1958.10501481","article-title":"Ordinal measures of association","volume":"53","author":"WH Kruskal","year":"1958","journal-title":"Journal of the American Statistical Association"},{"key":"pcbi.1009600.ref054","unstructured":"Ding AA, Li Y. Copula correlation: An equitable dependence measure and extension of pearson\u2019s correlation. arXiv preprint arXiv:13127214. 2013."},{"key":"pcbi.1009600.ref055","doi-asserted-by":"crossref","first-page":"104708","DOI":"10.1016\/j.jmva.2020.104708","article-title":"On the copula correlation ratio and its generalization","volume":"182","author":"JH Shih","year":"2021","journal-title":"Journal of Multivariate Analysis"},{"key":"pcbi.1009600.ref056","doi-asserted-by":"crossref","unstructured":"Andoni A, Razenshteyn I, Nosatzki NS. Lsh forest: Practical algorithms made theoretical. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM; 2017. p. 67\u201378.","DOI":"10.1137\/1.9781611974782.5"},{"key":"pcbi.1009600.ref057","unstructured":"Duvenaud DK, Maclaurin D, Iparraguirre J, Bombarell R, Hirzel T, Aspuru-Guzik A, et al. Convolutional networks on graphs for learning molecular fingerprints. In: Advances in neural information processing systems; 2015. p. 2224\u20132232."}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1009600","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:00:00Z","timestamp":1649030400000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009600","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,18]],"date-time":"2023-11-18T12:57:08Z","timestamp":1700312228000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009600"}},"subtitle":[],"editor":[{"given":"Quan","family":"Zou","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,3,10]]},"references-count":57,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3,10]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1009600","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2021.11.15.468695","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,10]]}}}