Last updated: 2022-12-06

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Introduction

I take the pbmc data from fastTopics package, and run splitting PMF on the dataset.

library(fastTopics)
library(Matrix)
library(stm)

Attaching package: 'stm'
The following object is masked from 'package:fastTopics':

    poisson2multinom
data(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
cells = pbmc_facs$samples$subpop%in%c('B cell', 'NK cell')
Y = counts[cells,]
dim(Y)
[1]  1440 16791
# filter out genes that has few expressions(3% cells)
genes = (colSums(Y>0) > 0.03*dim(Y)[1])
Y = Y[,genes]
# make sure there is no zero col and row
sum(rowSums(Y)==0)
[1] 0
sum(colSums(Y)==0)
[1] 0
dim(Y)
[1] 1440 4015
S = tcrossprod(c(rowSums(Y)),c(colSums(Y)))/sum(Y)
Y = as.matrix(Y)

There are 5 main cell types and 16791 genes.

To start with, I considered two cell types, B cell, and NK cell. Then I filtered out genes that have no expression in more than \(3\%\) cells. The gene filtering is mainly for reducing the data size and the running time.

The final dataset is of dimension 1440 cells by 4015 genes. I set the scaling factors as \(s_{ij} = \frac{y_{i+}y_{+j}}{y_{++}}\). For comparison, I also fit flash 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 \(\tilde{y}_{ij} = \log(\frac{y_{ij}}{s_{ij}}+\frac{0.5}{a_j})\). However flash was not able to terminate at \(Kmax = 50\). The splitting PMF estiamted \(K=3\). In addition, the svd seems to also support \(K=3\), as the scree plot show 3 points clearly separated from the rest.

fit = readRDS('output/poisson_MF_simulation/fit_pbmc_2cells.rds')
fit_flashier = readRDS('output/poisson_MF_simulation/fit_flashier_pbmc_2cells.rds')
fit_svd = readRDS('output/poisson_MF_simulation/fit_svd_pbmc_2cells.rds')
plot(fit_svd$d)

fit$run_time
Time difference of 1.768594 hours
plot(fit$eblo_trace,type='l')

The PMF algorithm converges after \(~3000\) iterations and \(106\)mins.

fit$fit_flash$n.factors
[1] 3
plot(fit$sigma2,ylab = 'sigma2',xlab='gene',col='grey50')

plot(colSums(Y/c(rowSums(Y)))/dim(Y)[1],fit$sigma2,xlab='gene mean count(after library size adjustment)')

plot(colSums(Y==0)/dim(Y)[1],fit$sigma2,xlab='sparsity')

Plot of factors:

par(mfrow=c(3,1))
plot(fit$fit_flash$F.pm[,1],xlab='gene',ylab='first factor')
plot(fit$fit_flash$F.pm[,2],xlab='gene',ylab='second factor')
plot(fit$fit_flash$F.pm[,3],xlab='gene',ylab='third factor')

Plot of Loading:

cell_names = as.character(pbmc_facs$samples$subpop[cells])
color_cell = replace(cell_names,which(cell_names=='B cell'),'red')
color_cell = replace(color_cell,which(cell_names=='NK cell'),'blue')
par(mfrow=c(3,1))
plot(fit$fit_flash$L.pm[,1],xlab='cells',ylab='first loading',col=color_cell)
plot(fit$fit_flash$L.pm[,2],xlab='cells',ylab='second loading',col=color_cell)
plot(fit$fit_flash$L.pm[,3],xlab='cells',ylab='third factor',col=color_cell)

Plot of first two loadings:

par(mfrow=c(1,1))
plot(fit$fit_flash$L.pm[,1],fit$fit_flash$L.pm[,2],col=color_cell,xlab='first loading',ylab='second loading')
legend(c('topright'),c('B cell','NK cell'),col=c('red','blue'),pch=c(1,1))

Plot of second two loadings:

par(mfrow=c(1,1))
plot(fit$fit_flash$L.pm[,2],fit$fit_flash$L.pm[,3],col=color_cell,xlab='second loading',ylab='third loading')
legend(c('topleft'),c('B cell','NK cell'),col=c('red','blue'),pch=c(1,1))

Use Jason’s method for visualizing loadings:

source('code/poisson_STM/plot_factors.R')
plot.factors(fit$fit_flash,cell_names,title='splitting PMF')

plot.factors(fit_flashier,cell_names,kset = c(1:10),title='flashier')


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] ggplot2_3.3.6      stm_1.0.9          Matrix_1.5-1       fastTopics_0.6-142
[5] workflowr_1.7.0   

loaded via a namespace (and not attached):
  [1] Rtsne_0.16         ebpm_0.0.1.3       colorspace_2.0-3  
  [4] smashr_1.3-6       ellipsis_0.3.2     rprojroot_2.0.3   
  [7] fs_1.5.2           rstudioapi_0.14    farver_2.1.1      
 [10] MatrixModels_0.5-1 ggrepel_0.9.2      fansi_1.0.3       
 [13] splines_4.2.1      cachem_1.0.6       rootSolve_1.8.2.3 
 [16] knitr_1.40         jsonlite_1.8.2     nloptr_2.0.3      
 [19] mcmc_0.9-7         ashr_2.2-54        uwot_0.1.14       
 [22] compiler_4.2.1     httr_1.4.4         assertthat_0.2.1  
 [25] fastmap_1.1.0      lazyeval_0.2.2     cli_3.4.1         
 [28] later_1.3.0        htmltools_0.5.3    quantreg_5.94     
 [31] prettyunits_1.1.1  tools_4.2.1        coda_0.19-4       
 [34] gtable_0.3.1       glue_1.6.2         reshape2_1.4.4    
 [37] dplyr_1.0.10       Rcpp_1.0.9         softImpute_1.4-1  
 [40] jquerylib_0.1.4    vctrs_0.4.2        wavethresh_4.7.2  
 [43] xfun_0.33          stringr_1.4.1      ps_1.7.1          
 [46] trust_0.1-8        lifecycle_1.0.3    irlba_2.3.5.1     
 [49] NNLM_0.4.4         nleqslv_3.3.3      getPass_0.2-2     
 [52] MASS_7.3-58        scales_1.2.1       hms_1.1.2         
 [55] promises_1.2.0.1   parallel_4.2.1     SparseM_1.81      
 [58] yaml_2.3.5         pbapply_1.6-0      sass_0.4.2        
 [61] stringi_1.7.8      SQUAREM_2021.1     highr_0.9         
 [64] deconvolveR_1.2-1  caTools_1.18.2     truncnorm_1.0-8   
 [67] horseshoe_0.2.0    rlang_1.0.6        pkgconfig_2.0.3   
 [70] matrixStats_0.62.0 bitops_1.0-7       ebnm_1.0-9        
 [73] evaluate_0.17      lattice_0.20-45    invgamma_1.1      
 [76] purrr_0.3.5        htmlwidgets_1.5.4  labeling_0.4.2    
 [79] cowplot_1.1.1      processx_3.7.0     tidyselect_1.2.0  
 [82] plyr_1.8.7         magrittr_2.0.3     R6_2.5.1          
 [85] generics_0.1.3     DBI_1.1.3          pillar_1.8.1      
 [88] whisker_0.4        withr_2.5.0        survival_3.4-0    
 [91] mixsqp_0.3-48      tibble_3.1.8       crayon_1.5.2      
 [94] utf8_1.2.2         plotly_4.10.1      rmarkdown_2.17    
 [97] progress_1.2.2     grid_4.2.1         data.table_1.14.6 
[100] callr_3.7.2        git2r_0.30.1       digest_0.6.29     
[103] vebpm_0.3.3        tidyr_1.2.1        httpuv_1.6.6      
[106] MCMCpack_1.6-3     RcppParallel_5.1.5 munsell_0.5.0     
[109] viridisLite_0.4.1  flashier_0.2.34    bslib_0.4.0       
[112] quadprog_1.5-8