Genome Biol. Measuring and mitigating PCR bias in microbiome data. In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. In any case, I would recommend using the preprocessCore package on Bioconductor, instead of my code, for performing quantile normalisation. Vieira Braga FA, Kar G, Berg M, Carpaij OA, Polanski K, Simon LM, Brouwer S, Gomes T, Hesse L, Jiang J, Fasouli ES, Efremova M, Vento-Tormo R, Talavera-López C, Jonker MR, Affleck K, Palit S, Strzelecka PM, Firth HV, Mahbubani KT, Cvejic A, Meyer KB, Saeb-Parsy K, Luinge M, Brandsma C-A, Timens W, Angelidis I, Strunz M, Koppelman GH, van Oosterhout AJ, Schiller HB, Theis FJ, van den Berge M, Nawijn MC, Teichmann SA. 2020. To quantile normalize two or more distributions to each other, without a reference distribution, sort as before, then set to the average (usually, arithmetical mean) of the distributions. Search Census counts were obtained using version 2.14.0 of the monocle Bioconductor R package.The probability mass function (PMF) of a compound Poisson distribution is obtained by placing a prior on the rate parameter of an ordinary Poisson distribution:
Droplet barcoding for single-cell transcriptomics applied to embryonic stem cells.
Patel AP, Tirosh I, Trombetta JJ, Shalek AK, Gillespie SM, Wakimoto H, Cahill DP, Nahed BV, Curry WT, Martuza RL, Louis DN, Rozenblatt-Rosen O, Suvà ML, Regev A, Bernstein BE. Quartile Formula (Table of Contents) Formula; Examples; Quartile Formula Definition . If the scale parameters were also held fixed, the QUMI target distribution would be identical for every cell and would predict a constant zero fraction across cells. The QUMI target distribution was set to Poisson-lognormal with shape 2.0. FWT wrote the draft manuscript, and revisions were suggested by RAI. Nat Immunol. Post was not sent - check your email addresses! To illustrate this, we applied quasi-UMI normalization, scran [We examined the effects of normalization on downstream dimension reduction using principal component analysis (PCA) [GLM-PCA dimension reduction applied to quasi-UMI counts reduces batch effects in the non-UMI Patel glioblastoma dataset. Picelli S, Björklund ÅK, Faridani OR, Sagasser S, Winberg G, Sandberg R. Smart-seq2 for sensitive full-length transcriptome profiling in single cells. Love MI, Hogenesch JB, Irizarry RA. 2015; 347(6226):1138–42. GLM-PCA was designed for UMI counts. We then identified the maximum expression value (count) for each simulated cell.
For each normalization method and gene, we computed the average expression and coefficient of variation on the Tung and Zheng test datasets. Phys Rev Lett. Unique molecular identifiers (UMIs) remove duplicates in read counts resulting from polymerase chain reaction, a major source of noise. We then converted the vector of read counts (or TPMs for Smart-seq2 data) from all genes in the cell to empirical quantiles (ranks).
2019; 176(4):928–94322. To determine reasonable shape parameter values, we computed MLEs for all cells in the training data.The shape parameters varied both within and between training datasets, with values ranging from 1.0 to 3.0 (Fig. Our method requires the shape parameter to be fixed. Typically, a single gene was placed into the highest QUMI bin due to the heavy tail of the target distribution.Since neither QUMI nor census normalization of TPM values removes cell-to-cell variation in total counts, we divided the normalized counts by the total counts of each cell, then multiplied all values by the median of the total count distribution across cells. The Poisson-lognormal model fits UMI count data well and can be used as a target distribution for QUMI normalization.