Last updated: 2021-04-12

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Knit directory: fastTopics-experiments/analysis/

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Here we compare the quality of the fits obtained from the different updates (EM and SCD, with and without extrapolation), and with different numbers of topics, \(K\).

Load the packages used in the analysis below, as well as some additional functions for creating the plots.

library(fastTopics)
library(ggplot2)
library(cowplot)
set.seed(1)

Load the 68k PBMC data, and the results of running fit_poisson_nmf on the 68k PBMC data, with different algorithms, and for various settings of \(K\).

load("../data/pbmc_68k.RData")
load("../output/pbmc68k/fits-pbmc68k.RData")
fits <- lapply(fits,poisson2multinom)

This plot shows the improvement in the log-likelihood as the rank, \(K\), is increased. The log-likelihoods are shown relative to the log-likelihood at \(K = 2\).

plot_loglik_vs_rank(fits) +
  theme_cowplot(font_size = 12)

Version Author Date
279ad71 Peter Carbonetto 2021-04-07

The next set of plots shows the improvement in the fit over time, for \(K\) from 2 to 12, using EM or SCD, with and without extrapolation. The quality of the fit is measured by the log-likelihood relative to the best log-likelihood that was identified among all methods compared.

prune_prefit_iters <- function (fit) {
  n <- nrow(fit$progress)
  fit$progress <- fit$progress[1000:n,]
  fit$progress <- transform(fit$progress,timing = timing/60^2)
  return(fit)
}
create_progress_plot <- function (fits, k, y = "loglik")
  plot_progress(fits,y = y,add.point.every = 100,shapes = 21,
                colors = c("dodgerblue","red","dodgerblue","red"),
                fills = c("dodgerblue","red","white","white")) +
  scale_y_continuous(trans = "log10",breaks = 10^seq(-8,8)) +
  guides(color = "none",fill = "none",size = "none",
         shape = "none",linetype = "none") +
  labs(x = "runtime (h)",title = paste("K =",k)) +
  theme_cowplot(font_size = 10) +
  theme(plot.title = element_text(size = 10,face = "plain"))
fits <- lapply(fits,prune_prefit_iters)
p <- vector("list",12)
for (i in 2:12)
  p[[i]] <- create_progress_plot(fits[dat$k == i],i)
plot_grid(p[[2]],p[[3]],p[[4]],p[[5]],
          p[[6]],p[[7]],p[[8]],p[[9]],
          p[[10]],p[[11]],p[[12]],
          nrow = 3,ncol = 4)

Version Author Date
279ad71 Peter Carbonetto 2021-04-07

These plots shows the evolution of the KKT residuals over time.

for (i in 2:12)
  p[[i]] <- create_progress_plot(fits[dat$k == i],i,y = "res")
plot_grid(p[[2]],p[[3]],p[[4]],p[[5]],
          p[[6]],p[[7]],p[[8]],p[[9]],
          p[[10]],p[[11]],p[[12]],
          nrow = 3,ncol = 4)

Version Author Date
279ad71 Peter Carbonetto 2021-04-07

An example in which the EM and (extrapolated) CD estimates greatly differ:

topic_colors <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c",
                  "#fb9a99","#e31a1c","#fdbf6f")
fit1 <- fits[["fit-pbmc68k-em-k=7"]]
fit2 <- fits[["fit-pbmc68k-scd-ex-k=7"]]
n    <- nrow(fit1$L)
pdat <- data.frame(x = as.vector(fit1$L),
                   y = as.vector(fit2$L),
                   k = factor(rep(1:7,each = n)))
pdat <- pdat[sample(7*n),]
p1 <- ggplot(pdat,aes(x = x,y = y,fill = k)) +
  geom_point(color = "white",shape = 21,size = 2) +
  scale_fill_manual(values = topic_colors) +
  labs(x = "EM estimate",y = "extrapolated CD estimate") +
  theme_cowplot(font_size = 12)
print(p1 + geom_abline(color = "black",linetype = "dotted"))

Version Author Date
50a3fca Peter Carbonetto 2021-04-10

An example in which the EM and (extrapolated) CD estimates largely agree:

topic_colors <- c("#8dd3c7","#ffffb3","#bebada","#fb8072","#80b1d3","#fdb462",
                  "#b3de69","#fccde5","#d9d9d9","#bc80bd","#ccebc5","#ffed6f")
fit1 <- fits[["fit-pbmc68k-em-k=12"]]
fit2 <- fits[["fit-pbmc68k-scd-ex-k=12"]]
n    <- nrow(fit1$L)
pdat <- data.frame(x = as.vector(fit1$L),
                   y = as.vector(fit2$L),
                   k = factor(rep(1:12,each = n)))
pdat <- pdat[sample(12*n),]
p2 <- ggplot(pdat,aes(x = x,y = y,fill = k)) +
  geom_point(color = "white",shape = 21,size = 2) +
  scale_fill_manual(values = topic_colors) +
  labs(x = "EM estimate",y = "extrapolated CD estimate") +
  theme_cowplot(font_size = 12)
print(p2 + geom_abline(color = "black",linetype = "dotted"))

Version Author Date
50a3fca Peter Carbonetto 2021-04-10

From the PCs of the mixture proportions, we define four clusters, roughly corresponding to (1) B cells, (2) dendritic and CD14+ monocytes, (3) CD34+ cells, and (4) T cells and natural killer cells:

fit  <- fits[["fit-pbmc68k-scd-ex-k=7"]]
pca  <- prcomp(fit$L)$x
n    <- nrow(pca)
x    <- rep("T+NK",n)
pc4  <- pca[,4]
pc6  <- pca[,6]
x[pc4 > 0.25] <- "B"
x[pc4 < -0.25] <- "CD14+dendritic"
x[pc6 > 0.8] <- "CD34+"
clusters <- factor(x)

The Structure plot summarizes the topic proportions in the cells. Here we subsample the larger clusters in order to better visualize the rarer cell types.

set.seed(1)
topics <- c(1:5,7,6)
topic_colors <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c",
                  "#fb9a99","#e31a1c","#fdbf6f")
rows <- sort(c(sample(which(clusters == "B"),746),
               sample(which(clusters == "CD14+dendritic"),806),
               which(clusters == "CD34+"),
               sample(which(clusters == "T+NK"),1213)))
p3 <- structure_plot(select_loadings(fit,loadings = rows),
                     grouping = clusters[rows],topics = topics,
                     colors = topic_colors[topics],n = Inf,perplexity = 70,
                     gap = 30,num_threads = 4,verbose = FALSE)
print(p3)                    


sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.7
# 
# Matrix products: default
# BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
# 
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] cowplot_1.0.0     ggplot2_3.3.0     fastTopics_0.5-24
# 
# loaded via a namespace (and not attached):
#  [1] ggrepel_0.9.0        Rcpp_1.0.5           invgamma_1.1        
#  [4] lattice_0.20-38      tidyr_1.0.0          prettyunits_1.1.1   
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# [13] backports_1.1.5      MatrixModels_0.4-1   evaluate_0.14       
# [16] coda_0.19-3          httr_1.4.2           pillar_1.4.3        
# [19] progress_1.2.2       rlang_0.4.5          lazyeval_0.2.2      
# [22] data.table_1.12.8    irlba_2.3.3          SparseM_1.78        
# [25] whisker_0.4          Matrix_1.2-18        rmarkdown_2.3       
# [28] labeling_0.3         Rtsne_0.15           stringr_1.4.0       
# [31] htmlwidgets_1.5.1    munsell_0.5.0        mixsqp_0.3-44       
# [34] compiler_3.6.2       httpuv_1.5.2         xfun_0.11           
# [37] pkgconfig_2.0.3      SQUAREM_2017.10-1    mcmc_0.9-6          
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# [43] workflowr_1.6.2.9000 quadprog_1.5-8       viridisLite_0.3.0   
# [46] withr_2.1.2          crayon_1.3.4         dplyr_0.8.3         
# [49] later_1.0.0          MASS_7.3-51.4        grid_3.6.2          
# [52] jsonlite_1.6         gtable_0.3.0         lifecycle_0.1.0     
# [55] git2r_0.26.1         magrittr_1.5         scales_1.1.0        
# [58] RcppParallel_4.4.2   stringi_1.4.3        farver_2.0.1        
# [61] fs_1.3.1             promises_1.1.0       vctrs_0.2.1         
# [64] tools_3.6.2          glue_1.3.1           purrr_0.3.3         
# [67] hms_0.5.2            yaml_2.2.0           colorspace_1.4-1    
# [70] ashr_2.2-51          plotly_4.9.2         knitr_1.26          
# [73] quantreg_5.54        MCMCpack_1.4-5