Soneson C, Robinson MD. Also, Kelly Street and Jakob Theorell made valuable contributions to the software implementation.The review history is available as Additional file FWT was supported by NIH grant T32CA009337.
In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. Quantile normalization was originally developed for gene expression microarrays [1, 2] but today it is applied in a wide-range of data types including genotyping arrays [16, 17], RNA-Sequencing (RNA-Seq) [18-20], DNA methylation [21], ChIP-Sequencing [22, 23] and brain imaging [24-26]. It is helpful for me. Science.
Massively parallel digital transcriptional profiling of single cells.
klein_2015_d0d7 and klein_2015_d2d4 indicate different experimental conditions within the same datasetWhile it was necessary to fix the shape parameter before applying quantile normalization to the test data, each cell was allowed to have its own scale parameter. If multiple quantiles are given, first axis of the result corresponds to the quantiles. 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. Science. If the statistic was close to zero, that indicated the fitted model was well calibrated to the tail of the UMI count data. You can also search for this author in 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. But this is discordant with the fact that UMI count data exhibit variation in the zero fraction across cells [After estimating the scale parameter for each cell, we obtained empirical quantiles (ranks) from read counts and transformed the ranks to QUMI counts by matching to the target distribution’s theoretical quantiles (see the “In terms of computational speed, quasi-UMI normalization is comparable to census [Using the three test dataset UMI counts as ground truth, we compared the accuracy of Poisson-lognormal quasi-UMI (QUMI) counts with census counts and unnormalized read counts. We compared these to the same statistics computed using UMI counts as a ground truth using M-A plots. Specifically, let Once a target distribution for an individual cell was determined, we computed the log of the theoretical CDF by cumulatively applying the log-sum-exp transformation to the log-PMF function, which provided numerical stability. Poisson-lognormal shape parameter maximum likelihood estimates (MLEs) for the training datasets. f(\lambda)d\lambda $$ $$f(\lambda) = \frac{1}{\lambda\sigma\sqrt{2\pi}}\exp\left\{-\frac{(\log \lambda - \mu)^{2}}{2\sigma^{2}}\right\} $$ $$f(\lambda) = \frac{\alpha}{\theta}\left(1+\frac{\lambda}{\theta}\right)^{-(\alpha+1)} $$ We therefore computed histograms of the test statistic’s distribution across all cells in each training dataset and compared how close the distribution was to a target of zero.For each cell in the test data, we obtained a target quasi-UMI distribution by estimating the cell-specific scale parameter from the empirical zero fraction in read counts using the method of moments (MOM). bioRxiv. 2018; 15(4):255–61.
If the input contains integers or floats smaller than float64, the output data-type is float64. Pooling across cells to normalize single-cell RNA sequencing data with many zero counts. Science.
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