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Adaptive Total-Variation Regularized Low-Rank Representation for Analyzing Single-Cell RNA-seq Data

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Abstract

High-throughput sequencing of single-cell gene expression reveals a complex mechanism of individual cell’s heterogeneity in a population. An important purpose for analyzing single-cell RNA sequencing (scRNA-seq) data is to identify cell subtypes and functions by cell clustering. To deal with high levels of noise and cellular heterogeneity, we introduced a new single cell data analysis model called Adaptive Total-Variation Regularized Low-Rank Representation (ATV-LRR). In scRNA-seq data, ATV-LRR can reconstruct the low-rank subspace structure to learn the similarity of cells. The low-rank representation can not only segment multiple linear subspaces, but also extract important information. Moreover, adaptive total variation also can remove cell noise and preserve cell feature details by learning the gradient information of the data. At the same time, to analyze scRNA-seq data with unknown prior information, we introduced the maximum eigenvalue method into the ATV-LRR model to automatically identify cell populations. The final clustering results show that the ATV-LRR model can detect cell types more effectively and stably.

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References

  1. Islam S, Zeisel A, Joost S, La Manno G, Zajac P, Kasper M, Lönnerberg P, Linnarsson S (2014) Quantitative single-cell RNA-seq with unique molecular identifiers. Nat Methods 11(2):163. https://doi.org/10.1038/nmeth.2772

    Article  CAS  PubMed  Google Scholar 

  2. Papalexi E, Satija R (2018) Single-cell RNA sequencing to explore immune cell heterogeneity. Nat Rev Immunol 18(1):35. https://doi.org/10.1038/nri.2017.76

    Article  CAS  PubMed  Google Scholar 

  3. Kiselev VY, Andrews TS, Hemberg M (2019) Challenges in unsupervised clustering of single-cell RNA-seq data. Nat Rev Genet 20(5):273–282. https://doi.org/10.1038/s41576-018-0088-9

    Article  CAS  PubMed  Google Scholar 

  4. Wang B, Zhu J, Pierson E, Ramazzotti D, Batzoglou S (2017) Visualization and analysis of single-cell RNA-seq data by kernel-based similarity learning. Nat Methods 14(4):414. https://doi.org/10.1038/nmeth.4207

    Article  CAS  PubMed  Google Scholar 

  5. Jiang H, Sohn LL, Huang H, Chen L (2018) Single cell clustering based on cell-pair differentiability correlation and variance analysis. Bioinformatics 34(21):3684–3694. https://doi.org/10.1093/bioinformatics/bty390

    Article  CAS  PubMed  Google Scholar 

  6. Park S, Zhao H (2018) Spectral clustering based on learning similarity matrix. Bioinformatics 34(12):2069–2076. https://doi.org/10.1093/bioinformatics/bty050

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Zheng R, Li M, Liang Z, Wu F-X, Pan Y, Wang J (2019) SinNLRR: a robust subspace clustering method for cell type detection by nonnegative and low rank representation. Bioinformatics 35(19):3642–3650. https://doi.org/10.1093/bioinformatics/btz139

    Article  CAS  PubMed  Google Scholar 

  8. Zhang W, Li Y, Zou X (2020) SCCLRR: a robust computational method for accurate clustering single cell RNA-seq data. IEEE J Biomed Health Inform 25(1):247–256

    Article  Google Scholar 

  9. Li X, Wang K, Lyu Y, Pan H, Zhang J, Stambolian D, Susztak K, Reilly MP, Hu G, Li M (2020) Deep learning enables accurate clustering with batch effect removal in single-cell RNA-seq analysis. Nat Commun 11(1):2338. https://doi.org/10.1038/s41467-020-15851-3

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D 60(1–4):259–268. https://doi.org/10.1016/0167-2789(92)90242-F

    Article  Google Scholar 

  11. Yao J, Xu Z, Huang X, Huang J (2018) An efficient algorithm for dynamic MRI using low-rank and total variation regularizations. Med Image Anal 44:14–27. https://doi.org/10.1016/j.media.2017.11.003

    Article  PubMed  Google Scholar 

  12. Leng C, Cai G, Yu D, Wang Z (2017) Adaptive total-variation for non-negative matrix factorization on manifold. Pattern Recogn Lett 98:68–74. https://doi.org/10.1016/j.patrec.2017.08.027

    Article  Google Scholar 

  13. Wang C, Gao Y-L, Liu J-X, Kong X-Z, Zheng C-H (2020) Single-cell RNA sequencing data clustering by low-rank subspace ensemble framework. IEEE/ACM Trans Comput Biol Bioinform. https://doi.org/10.1109/TCBB.2020.3029187

    Article  PubMed  Google Scholar 

  14. Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2020) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609

    Article  Google Scholar 

  15. Abualigah L, Diabat A (2021) Advances in sine cosine algorithm: a comprehensive survey. Artif Intell Rev. https://doi.org/10.1007/s10462-020-09909-3

    Article  Google Scholar 

  16. Abualigah L, Diabat A (2020) A comprehensive survey of the Grasshopper optimization algorithm: results, variants, and applications. Neural Comput Appl 32:15533–15556

    Article  Google Scholar 

  17. Yin H, Liu H (2010) Nonnegative matrix factorization with bounded total variational regularization for face recognition. Pattern Recogn Lett 31(16):2468–2473. https://doi.org/10.1016/j.patrec.2010.08.001

    Article  Google Scholar 

  18. Cai J-F, Candès EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982. https://doi.org/10.1137/080738970

    Article  Google Scholar 

  19. Liu Z, Wang J, Liu G, Zhang L (2019) Discriminative low-rank preserving projection for dimensionality reduction. Appl Soft Comput 85:105768. https://doi.org/10.1016/j.asoc.2019.105768

    Article  Google Scholar 

  20. Pollen AA, Nowakowski TJ, Shuga J, Wang X, Leyrat AA, Lui JH, Li N, Szpankowski L, Fowler B, Chen P (2014) Low-coverage single-cell mRNA sequencing reveals cellular heterogeneity and activated signaling pathways in developing cerebral cortex. Nat Biotechnol 32(10):1053. https://doi.org/10.1038/nbt.2967

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Engel I, Seumois G, Chavez L, Samaniego-Castruita D, White B, Chawla A, Mock D, Vijayanand P, Kronenberg M (2016) Innate-like functions of natural killer T cell subsets result from highly divergent gene programs. Nat Immunol 17(6):728. https://doi.org/10.1038/ni.3437

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Ting DT, Wittner BS, Ligorio M, Jordan NV, Shah AM, Miyamoto DT, Aceto N, Bersani F, Brannigan BW, Xega K (2014) Single-cell RNA sequencing identifies extracellular matrix gene expression by pancreatic circulating tumor cells. Cell Rep 8(6):1905–1918. https://doi.org/10.1016/j.celrep.2014.08.029

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Yan Q, Ding Y, Xia Y, Chong Y, Zheng C (2017) Class probability propagation of supervised information based on sparse subspace clustering for hyperspectral images. Remote Sens 9(10):1017. https://doi.org/10.3390/rs9101017

    Article  Google Scholar 

  24. Treutlein B, Brownfield DG, Wu AR, Neff NF, Mantalas GL, Espinoza FH, Desai TJ, Krasnow MA, Quake SR (2014) Reconstructing lineage hierarchies of the distal lung epithelium using single-cell RNA-seq. Nature 509(7500):371. https://doi.org/10.1038/nature13173

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Goolam M, Scialdone A, Graham SJ, Macaulay IC, Jedrusik A, Hupalowska A, Voet T, Marioni JC, Zernicka-Goetz M (2016) Heterogeneity in Oct4 and Sox2 targets biases cell fate in 4-cell mouse embryos. Cell 165(1):61–74. https://doi.org/10.1016/j.cell.2016.01.047

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Deng Q, Ramsköld D, Reinius B, Sandberg R (2014) Single-cell RNA-seq reveals dynamic, random monoallelic gene expression in mammalian cells. Science 343(6167):193–196. https://doi.org/10.1126/science.1245316

    Article  CAS  PubMed  Google Scholar 

  27. Grover A, Sanjuan-Pla A, Thongjuea S, Carrelha J, Giustacchini A, Gambardella A, Macaulay I, Mancini E, Luis TC, Mead A (2016) Single-cell RNA sequencing reveals molecular and functional platelet bias of aged haematopoietic stem cells. Nat Commun 7:11075. https://doi.org/10.1038/ncomms11075

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Darmanis S, Sloan SA, Zhang Y, Enge M, Caneda C, Shuer LM, Gephart MGH, Barres BA, Quake SR (2015) A survey of human brain transcriptome diversity at the single cell level. Proc Natl Acad Sci 112(23):7285–7290. https://doi.org/10.1073/pnas.1507125112

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Usoskin D, Furlan A, Islam S, Abdo H, Lönnerberg P, Lou D, Hjerling-Leffler J, Haeggström J, Kharchenko O, Kharchenko PV (2015) Unbiased classification of sensory neuron types by large-scale single-cell RNA sequencing. Nat Neurosci 18(1):145. https://doi.org/10.1038/nn.3881

    Article  CAS  PubMed  Google Scholar 

  30. Breton G, Zheng S, Valieris R, da Silva IT, Satija R, Nussenzweig MC (2016) Human dendritic cells (DCs) are derived from distinct circulating precursors that are precommitted to become CD1c+ or CD141+ DCs. J Exp Med 213(13):2861–2870. https://doi.org/10.1084/jem.20161135

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Vidal R, Favaro P (2014) Low rank subspace clustering (LRSC). Pattern Recogn Lett 43:47–61. https://doi.org/10.1016/j.patrec.2013.08.006

    Article  Google Scholar 

  32. Strehl A, Ghosh J (2002) Cluster ensembles—a knowledge reuse framework for combining multiple partitions. J Mach Learn Res 3:583–617. https://doi.org/10.1162/153244303321897735

    Article  Google Scholar 

  33. Robert V, Vasseur Y, Brault V (2020) Comparing high-dimensional partitions with the co-clustering adjusted Rand index. J Classif. https://doi.org/10.1007/s00357-020-09379-w

    Article  Google Scholar 

  34. Lvd M, Hinton G (2008) Visualizing data using t-SNE. J Mach Learn Res 9(11):2579–2605

    Google Scholar 

  35. Von Luxburg U (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416. https://doi.org/10.1007/s11222-007-9033-z

    Article  Google Scholar 

  36. Lu C, Yan S, Lin Z (2016) Convex sparse spectral clustering: single-view to multi-view. IEEE Trans Image Process 25(6):2833–2843. https://doi.org/10.1109/TIP.2016.2553459

    Article  Google Scholar 

  37. Hartigan JA, Wong MA (1979) Algorithm AS 136: a k-means clustering algorithm. J R Stat Soc Ser C 28(1):100–108. https://doi.org/10.2307/2346830

    Article  Google Scholar 

  38. Wold S, Esbensen K, Geladi P (1987) Principal component analysis. Chemom Intell Lab Syst 2(1–3):37–52. https://doi.org/10.1016/0169-7439(87)80084-9

    Article  CAS  Google Scholar 

  39. Tripathi V, Ellis JD, Shen Z, Song DY, Pan Q, Watt AT, Freier SM, Bennett CF, Sharma A, Bubulya PA (2010) The nuclear-retained noncoding RNA MALAT1 regulates alternative splicing by modulating SR splicing factor phosphorylation. Mol Cell 39(6):925–938. https://doi.org/10.1016/j.molcel.2010.08.011

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Lee SM, Na YK, Hong HS, Jang EJ, Yoon GS, Park JY, Kim DS (2011) Hypomethylation of the thymosin β 10 gene is not associated with its overexpression in non-small cell lung cancer. Mol Cells 32(4):343. https://doi.org/10.1007/s10059-011-0073-z

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Liu P-P, Xu Y-J, Dai S-K, Du H-Z, Wang Y-Y, Li X-G, Teng Z-Q, Liu C-M (2019) Polycomb protein EED regulates neuronal differentiation through targeting SOX11 in hippocampal dentate gyrus. Stem Cell Rep 13(1):115–131. https://doi.org/10.1016/j.stemcr.2019.05.010

    Article  CAS  Google Scholar 

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Acknowledgements

This work is supported in part by the National Natural Science Foundation of China under Grant No. 61872220, Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J18KA373, and the Jiangsu Key Construction Laboratory of IoT Application Technology No. 19WXWL05.

Funding

This work is supported in part by the National Natural Science Foundation of China under Grant No. 61872220, Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J18KA373, and the Jiangsu Key Construction Laboratory of IoT Application Technology No. 19WXWL05.

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Authors and Affiliations

  1. School of Computer Science, Qufu Normal University, Rizhao, China

    Jin-Xing Liu, Chuan-Yuan Wang, Juan Wang & Sheng-Jun Li

  2. Qufu Normal University Library, Qufu Normal University, Rizhao, China

    Ying-Lian Gao

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, China

    Yulin Zhang

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  1. Jin-Xing Liu
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  4. Yulin Zhang
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  5. Juan Wang
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Contributions

JXL and CYW contributed to the designment of the study. YLG proposed the ATV-LRR method, performed the experiments, and drafted the manuscript. JW and YLZ contributed to the data analysis. JXL and SJL contributed to improving the writing level of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Juan Wang.

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Liu, JX., Wang, CY., Gao, YL. et al. Adaptive Total-Variation Regularized Low-Rank Representation for Analyzing Single-Cell RNA-seq Data. Interdiscip Sci Comput Life Sci 13, 476–489 (2021). https://doi.org/10.1007/s12539-021-00444-5

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