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 and CD34+
cells = pbmc_facs$samples$subpop%in%c('B cell', 'NK cell','CD34+')
Y = counts[cells,]
dim(Y)
[1]  2127 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] 2127 5470
S = tcrossprod(c(rowSums(Y)),c(colSums(Y)))/sum(Y)
Y = as.matrix(Y)

There are 5 main cell types and 16791 genes.

I considered three cell types, B cell, and NK cell, CD34+ 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 2127 cells by 5470 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 \(Kmax = 50\).

fit = readRDS('output/poisson_MF_simulation/fit_pbmc_3cells.rds')
fit_flashier = readRDS('output/poisson_MF_simulation/fit_flashier_pbmc_3cells.rds')
fit_svd = readRDS('output/poisson_MF_simulation/fit_svd_pbmc_3cells.rds')
plot(fit_svd$d)

fit$run_time
Time difference of 5.526164 hours
plot(fit$eblo_trace,type='l')

The PMF algorithm converges after \(~4000\) iterations and \(5.5\)hours.

fit$fit_flash$n.factors
[1] 9
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')

fit$fit_flash$pve
[1] 0.2370928543 0.1533762217 0.2767542009 0.0056628916 0.0054895955
[6] 0.0028684677 0.0009619526 0.0249530695 0.0020927039

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')
color_cell = replace(color_cell,which(cell_names=='CD34+'),'green')
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('bottomright'),c('B cell','NK cell','CD34+'),col=c('red','blue','green'),pch=c(1,1,1))

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(1:15),title='flashier')

Run time analysis

The mean run time in seconds per iteration is

unlist(lapply(fit$run_time_break_down,mean))
         run_time_vga_init               run_time_vga 
                27.3456502                  1.4752794 
       run_time_flash_init run_time_flash_init_factor 
                 0.0914281                  0.3514608 
     run_time_flash_greedy run_time_flash_backfitting 
                 0.8914967                  1.5452666 
  run_time_flash_nullcheck 
                 0.2648255 
unlist(lapply(fit$run_time_break_down,sd))
         run_time_vga_init               run_time_vga 
                        NA                 0.27517911 
       run_time_flash_init run_time_flash_init_factor 
                0.02819979                 0.07791709 
     run_time_flash_greedy run_time_flash_backfitting 
                0.11357835                 0.13815415 
  run_time_flash_nullcheck 
                0.12643934

So each iteration takes about \(4.5\) seconds. The most time-consuming steps are backfitting(1 iteration), vga, and greedy. The main issue is it takes too long to converge, especially for larger dataset. Usually the larger the dataset, the more iterations are needed. Because the scale of objective function is much larger but the tolerance is still the same?

Need to find a criteria to stop the algorithm earlier?


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_1.1.0          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