Simulation based on pbmc 3 cell types
DongyueXie
2022-12-09
Last updated: 2022-12-09
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Knit directory: gsmash/
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Setting
This is a simulation comparing splitting PMF and flash on factorizing Poisson matrix.
To make the simulated dataset close to a real single cell data, I
fitted a splitting PMF on a PBMC single cell data from
fastTopics package. I took cells from cell types in ‘B
cell’, ‘NK cell’,‘CD34+’ and then filtered out genes that has no
expression in more than \(3\%\) percent
of the cells. The two steps are mainly for reducing the dataset size.
The resulting dataset has 2127 cells and 5470 genes.
Then I fitted splitting PMF on the dataset, with the scaling factors
being \(s_{ij} =
\frac{y_{i+}y_{+j}}{y_{++}}\) and gene-specific variances. Then I
generated data from the fitted model, and repeated 5 times. When
simulating data, I took the first three topics(with PVE 0.24,0.20,0.17)
and discarded the rests. The flash was fit on transformed
count data, as \(\tilde{y}_{ij} =
\log(1+\frac{y_{ij}}{s_{ij}}\frac{a_j}{0.5})\) where \(a_j = median(s_{\cdot j})\). This
transformation is derived from \(\tilde{y}_{ij} =
\log(\frac{y_{ij}}{s_{ij}}+\frac{0.5}{a_j})\).
rmse = function(x,y){return(sqrt(mean((x-y)^2)))}
res = readRDS('output/poisson_MF_simulation/PMF5_K3simu_pbmc_3cells.rds')We first look at the number factors recovered from both methods. The true \(K\) is 3.
K_hat = c()
for(i in 1:length(res$output)){
K_hat = rbind(K_hat,c(res$output[[i]]$fitted_model$flash$n.factors,res$output[[i]]$fitted_model$splitting$fit_flash$n.factors))
}
colnames(K_hat) = c('flash','splittingPMF')
K_hat flash splittingPMF
[1,] 8 3
[2,] 12 3
[3,] 6 3
[4,] 7 3
[5,] 6 3Next we compare \(\hat L\hat F'\) and true \(LF'\).
fit = readRDS('output/poisson_MF_simulation/pbmc_3cells_Sij.rds')
kset = order(fit$fit$fit_flash$pve,decreasing = TRUE)[1:3]
Ltrue = fit$fit$fit_flash$L.pm[,kset]
Ftrue = fit$fit$fit_flash$F.pm[,kset]
Mu_true = tcrossprod(Ltrue,Ftrue)rmses= c()
for(i in 1:length(res$output)){
rmses = rbind(rmses,c(rmse(Mu_true,fitted(res$output[[i]]$fitted_model$flash)),rmse(Mu_true,fitted(res$output[[i]]$fitted_model$splitting$fit_flash))))
}
colnames(rmses) = c('flash','splittingPMF')
rmses flash splittingPMF
[1,] 0.5819739 0.1881947
[2,] 0.5819058 0.1854424
[3,] 0.5815135 0.1853517
[4,] 0.5817050 0.1877322
[5,] 0.5823862 0.1827952par(mfrow=c(2,1))
for(i in 1:length(res$output)){
plot(fitted(res$output[[i]]$fitted_model$flash),Mu_true,col='grey80',xlab='fitted',ylab='LF',main='flash')
abline(a=0,b=1)
plot(fitted(res$output[[i]]$fitted_model$splitting$fit_flash),Mu_true,col='grey80',xlab='fitted',ylab='LF',main='splitting')
abline(a=0,b=1)
}
par(mfrow=c(1,1))Next we look at how the structures of L and F are recovered by both methods.
We first plot loadings.
library(fastTopics)
library(Matrix)
library(stm)
Attaching package: 'stm'The following object is masked from 'package:fastTopics':
poisson2multinomrequire(gridExtra)Loading required package: gridExtradata(pbmc_facs)
counts <- pbmc_facs$counts
table(pbmc_facs$samples$subpop)
B cell CD14+ CD34+ NK cell T cell
767 163 687 673 1484 ## use only B cell and NK cell and CD34+
cells = pbmc_facs$samples$subpop%in%c('B cell', 'NK cell','CD34+')
counts = counts[cells,]
# filter out genes that has few expressions(3% cells)
genes = (colSums(counts>0) > 0.03*dim(counts)[1])
cell_names = pbmc_facs$samples$subpop[cells]
source('code/poisson_STM/plot_factors.R')plot0=plot.factors(fit$fit$fit_flash,cell.types=cell_names,kset=kset,title='True Loadings')
for(i in 1:length(res$output)){
plot1 = plot.factors(res$output[[i]]$fitted_model$flash,cell.types=cell_names,title='flash')
plot2 = plot.factors(res$output[[i]]$fitted_model$splitting$fit_flash,cell.types=cell_names,title='splittingPMF')
grid.arrange(plot1, plot0,plot2, ncol=3)
}
Plot of factors: the first simulation
library(flashier)Loading required package: magrittrpar(mfrow=c(1,3))
ldfed = ldf(fit$fit$fit_flash)
plot(ldfed$F[,1],main='factor 1')
plot(ldfed$F[,2],main='factor 2')
plot(ldfed$F[,3],main='factor 3')
par(mfrow=c(1,3))
ldfed1 = ldf(res$output[[1]]$fitted_model$splitting$fit_flash)
plot(ldfed1$F[,1],main='splittingPMF estimated factor 1')
plot(ldfed1$F[,2],main='splittingPMF estimated factor 2')
plot(ldfed1$F[,3],main='splittingPMF estimated factor 3')
par(mfrow=c(1,3))
ldfed2 = ldf(res$output[[1]]$fitted_model$flash)
plot(ldfed2$F[,1],main='flash estimated factor 1')
plot(ldfed2$F[,2],main='flash estimated factor 2')
plot(ldfed2$F[,3],main='flash estimated factor 3')
plot(ldfed2$F[,4],main='flash estimated factor 4')
plot(ldfed2$F[,5],main='flash estimated factor 5')
plot(ldfed2$F[,6],main='flash estimated factor 6')
sessionInfo()R version 4.2.1 (2022-06-23)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.5 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
locale:
[1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
[4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
[7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] flashier_0.2.34 magrittr_2.0.3 ggplot2_3.3.6 gridExtra_2.3
[5] stm_1.1.0 Matrix_1.5-1 fastTopics_0.6-142 workflowr_1.7.0
loaded via a namespace (and not attached):
[1] mcmc_0.9-7 bitops_1.0-7 matrixStats_0.62.0
[4] fs_1.5.2 progress_1.2.2 httr_1.4.4
[7] rprojroot_2.0.3 tools_4.2.1 bslib_0.4.0
[10] utf8_1.2.2 R6_2.5.1 irlba_2.3.5.1
[13] uwot_0.1.14 DBI_1.1.3 lazyeval_0.2.2
[16] colorspace_2.0-3 withr_2.5.0 wavethresh_4.7.2
[19] prettyunits_1.1.1 tidyselect_1.2.0 processx_3.7.0
[22] ebpm_0.0.1.3 compiler_4.2.1 git2r_0.30.1
[25] cli_3.4.1 quantreg_5.94 SparseM_1.81
[28] plotly_4.10.1 labeling_0.4.2 horseshoe_0.2.0
[31] sass_0.4.2 caTools_1.18.2 scales_1.2.1
[34] SQUAREM_2021.1 quadprog_1.5-8 callr_3.7.2
[37] pbapply_1.6-0 mixsqp_0.3-48 stringr_1.4.1
[40] digest_0.6.29 rmarkdown_2.17 MCMCpack_1.6-3
[43] deconvolveR_1.2-1 vebpm_0.3.3 pkgconfig_2.0.3
[46] htmltools_0.5.3 highr_0.9 fastmap_1.1.0
[49] invgamma_1.1 htmlwidgets_1.5.4 rlang_1.0.6
[52] rstudioapi_0.14 farver_2.1.1 jquerylib_0.1.4
[55] generics_0.1.3 jsonlite_1.8.2 dplyr_1.0.10
[58] smashr_1.3-6 Rcpp_1.0.9 munsell_0.5.0
[61] fansi_1.0.3 lifecycle_1.0.3 stringi_1.7.8
[64] whisker_0.4 yaml_2.3.5 nleqslv_3.3.3
[67] rootSolve_1.8.2.3 MASS_7.3-58 plyr_1.8.7
[70] Rtsne_0.16 grid_4.2.1 parallel_4.2.1
[73] promises_1.2.0.1 ggrepel_0.9.2 crayon_1.5.2
[76] lattice_0.20-45 cowplot_1.1.1 splines_4.2.1
[79] hms_1.1.2 knitr_1.40 ps_1.7.1
[82] pillar_1.8.1 softImpute_1.4-1 reshape2_1.4.4
[85] glue_1.6.2 evaluate_0.17 trust_0.1-8
[88] getPass_0.2-2 data.table_1.14.6 RcppParallel_5.1.5
[91] nloptr_2.0.3 vctrs_0.4.2 httpuv_1.6.6
[94] MatrixModels_0.5-1 gtable_0.3.1 purrr_0.3.5
[97] ebnm_1.0-9 tidyr_1.2.1 assertthat_0.2.1
[100] ashr_2.2-54 cachem_1.0.6 xfun_0.33
[103] NNLM_0.4.4 coda_0.19-4 later_1.3.0
[106] survival_3.4-0 viridisLite_0.4.1 truncnorm_1.0-8
[109] tibble_3.1.8 ellipsis_0.3.2